Rational Femtosecond Control of Multiphoton Excitations:
from Weak-Field to Intermediate-Field Regime
Multiphoton absorption processes are among the processes over which femtosecond coherent control has been most effective. The present experimental and theoretical studies focus on rational pulse shaping based on identifying first the interference mechanism. The model system is atomic sodium. First will be presented a weak-field example of extended selective control among two-photon and three-photon absorption channels based on a symmetry property of the two-photon channel. Related to the three-photon control, results will be shown for controlling the generation of coherent broadband UV radiation (i.e., a shaped UV pulse) in a resonance-mediated three-photon NIR excitation. Then, results will be presented for two-photon absorption in the intermediate-field regime that involves both two- and four-photon transitions. The two-photon transitions are of non-resonant nature, while the four-photon transitions are (by definition) of resonance-mediated nature with either the initial or final state of the transition playing the role of the intermediate state. This leads to a different nature of the two-photon absorption in the intermediate-field regime as compared to the weak-field regime. Here, we have extended the powerful frequency-domain description beyond the lowest perturbative order (the 2nd one) to be of 4th order. This is a first step toward rational femtosecond control in a regime of considerable absorption yields. Time permitting, theoretical results will also be presented for multiphoton control with single-cycle pulses. Along the talk I'll also refer to aspects of photo-induced coherent information processing that we have implemented using the multiphoton control capabilities.
Yehuda Band,Ben Gurion University of the Negev, Beer Sheva, Israel
Interference with Bose-Einstein condensates
The investigation of interferences between particles is one of the most
basic tools to learn about the nature of quantum gases. Interferences
attracted much attention in particular for the case of Bose-Einstein
condensates (BECs) both theoretically and experimentally. The
interference of two parts of a single coherent condensate is well
understood, but the interference of two initially independent (i.e.,
fragmented) BECs, are not expected to show an interference pattern for
non-interacting particles. Fragmented BECs can be produced using a barrier
between the two traps which is so high and broad that tunneling between
them is negligible. We explore the effects of interaction for such
fragmented condensates when interaction is present, both from a mean-field
and from a full many-body point of view.
Tommaso Calarco, Universität Ulm, Germany
Fast and ultrafast quantum gates via optimal control of ultracold systems
Quantum optimal control applied to the implementation of quantum
information processing is a powerful tool to systematically enhance gate
fidelities. Examples from recent research are presented, ranging from
noise-resistant superconducting quantum gates to optimized transport of
atomic qubits in optical lattices and to ultrafast all-optical gates in
subwavelength optical potentials. Experimental imperfections are discussed
and their effect is analyzed quantitatively, showing fidelities compatible
with fault-tolerance thresholds for quantum computation even in the
presence of realistic disturbances.
Béatrice Chatel,
S. Weber, D. Bigourd, B. Girard,
IRSAMC Toulouse, France
Coherent control, quantum interferences and Gauss sums
In a first part I will introduce an all optical approach towards factoring numbers relying on modern pulse shaping technology . Indeed, the generation of arbitrarily shaped optical waveforms is of great interest in a number of fields ranging from coherent control to information processing. For example, pulse shapers have led to an elegant implementation of the Grover search algorithm using Rydberg atoms as quantum registers . Moreover, optical realizations of the Grover or the Bernstein-Vazirani algorithms have been used. Our work extends this line of research to factoring numbers using the Talbot effect . We report on the successful operation of an analogue computer designed to factor numbers. A sequence of shaped femtosecond pulses is used to implement a Gauss sum. N=1'340'333'404'807 is successfully factorized .
In a second part I will present another coherent control scheme based on quantum interferences to control the spin-precession of an atom . Further investigation on "non Franck-Condon excitation" will also be presented.
Daniel Comparat, Laboratoire Aimé Cotton Orsay, France
Femtosecond pulses and optical pumping of cesium cold molecules
Creating in an efficient way, a large and dense sample of ultracold molecules in their fundamental ground state, i.e. with neither vibration nor rotation, is an important step toward the realization of further experiments such as cold collisions, controlled chemistry, or accurate spectroscopic measurement. One further motivation is the possibility to go towards the realization of a Bose-Einstein molecular condensate.
We will report here on our progress to manipulate the internal degree of freedom of the cold molecules, formed via photoassociation, by using a femtosecond laser. The idea is to use the broadband character of the laser to excite the formed molecules and to modify by optical pumping the vibrational distribution of the molecules. The control of this distribution could then be obtained by shaping the laser. The first experimental attempts have revealed a reduction of the number of detected cold molecules. Simple rate-equation models of the dynamics have shown that optical pumping can be the predominant process: a sequence of femtoconde pulses modifying the distribution of the vibration levels. Using a REMPI molecular detection scheme we experimentally investigate the dynamics of the molecules after absorption of one femtoseconde laser photon: photoionization, (pre-)dissociation, or optical pumping with transfer of the molecules towards non detected molecules ? The next step would be to find and to optimize an interaction scheme in order to create molecules with a lower vibrational excitation, and ultimately with no vibration.
Nir Davidson, N. Bar-Gill, E. Rowen and R. Pugatch,
Weizmann Institute of Science, Rehovot, Israel
Many-Body Excitations and Decay in a BEC
Bulk excitations in dilute-gas Bose Einstein condensates has been extensively characterized using two-photon Bragg spectroscopy, revealing the well-known single-branch Bogoliubov spectrum [1]. For highly-elongated cylindrically-symmetric condensates with strong transverse confinement a multi-branch spectrum, corresponding to higher radial modes is obtained. These modes are well characterized by their (continuous) axial momentum, radial index and topological charge, which determines their angular momentum. We present the details of this multi-branch spectrum and its role as a reservior in the decay of excitations over the condensate ground state. We observed the manifestation of this complex structure of the BEC reservoir in a momentum-dependent resonance line shift. We also measure the effects of reservoir engineering on the decay of a the many-body excitations when the Bose Einstein condensate is loaded into an optical lattice. We show both enhancement and suppression of decoherence as a function of the lattice depth.
[1] "Bulk Bogoliubov excitations in a Bose-Einstein condensate",
R. Ozeri, N. Katz, J. Steinhauer, and N. Davidson,
Rev. of Mod. Phys. 77, 187 (2005).
Brett DePaola, Kansas State University, Manhattan (KS), USA
The Effects of Spectral Phase on Photoassociation with Excitation
Photoassociation is presently a research topic of great interest partly because of its potential applicability in the study of degenerate gas molecules. Both narrow line width, cw lasers and broad bandwidth, ultrafast lasers have been used to drive the photoassociation process; both laser types have their advantages and disadvantages. One of the advantages of the ultrafast laser is that one has available a spectrum of frequencies. Furthermore, both the spectral intensity and phase can be shaped using commercial instrumentation. In this talk we will present data showing the effects that various spectral phase patterns have on the efficiency with which cold Rb atoms are associated into translationally cold molecules, which are then further step-wise excited. In the work described here, the electronically
excited molecules are probed using a combination of a narrowband cw laser and time of flight spectroscopy. Used in concert, these tools provide a unique diagnostic into the excitation pathways. The spectral phase patterns that will be discussed include the sinusoidal, π/2 phase pulse, and a phase step function.
Alexander Dorn, Max-Planck-Institut für
Kernphysik, Heidelberg, Germany
Ionization of Laser Cooled and Trapped Lithium Atoms in Intense fs Laser Pulses
Reaction microscopes allow the coincident measurement of the momentum vectors of several electrons and ions released in ionization processes. We have combined such a multi-particle imaging spectrometer with a magneto-optical trap for lithium atoms. As result precise measurements of the ion and electron momentum distributions for reactions in a cold lithium gas are feasible.
Firstly, we will perform ionization studies of the fundamental three-electron system lithium by various projectiles ranging from intense laser pulses, synchrotron and free-electron-laser radiation to electrons and ions. Here results will be presented for ionization of lithium in intense laser pulses of 8 fs and 30 fs duration for the Li(2s) ground state and a mixture of Li(2s) and Li(2p) states. Pump-probe experiments with two 10 fs-laser pulses show momentum spectra which periodically change with the delay time between the pulses. This behaviour can be traced back to a coherent superposition of different states excited in the first laser pulse.
In future we plan to do photo-association studies producing lithium dimers using pump-dump schemes with short laser pulses. Furthermore, a cold atomic ensemble produced in a MOT is the first step on the way to the production of a ultra-cold quantum gas. Implementation of a dipole trap would allow to reach temperatures typical for a BECs or a cold Fermi gases.
Michael Drewsen, University of Aarhus, Denmark
Towards coherent control of single molecular ions
In recent years, the field of coherent control has reached an extremely high level of sophistication due to the amazing development of control in light sources. Without doubt, a complementary future control of the internal as well as external degrees of freedom of the target molecules will lead to new heights. A single trapped and cooled molecular ion, localized within a few cubic microns and initially prepared in a specific internal state, is such a target. Our near-future plans for investigating path-interference effects in the photodissociation of single MgH+ molecular ions when applying ns-second pulses will be discussed.
Ron Folman, Ben Gurion University of the Negev, Beer Sheva,
Israel
Using cold atoms to probe surface phenomena
Ultra cold atoms, microns away from surfaces, are an extremely sensitive probe of static or fluctuating magnetic and electric fields. We will describe the potential of this new system to probe classical and quantum systems on the surface, and give details of recent experimental observations made with this new probe of long range order in electron scattering in completely disordered media.
Phillip L. Gould, University of Connecticut, Storrs (CT), USA
Control of Ultracold Collisional Processes with Frequency-Chirped Light*
We use frequency-chirped laser light
on the nanosecond time scale to control collisions between trapped ultracold
Rb atoms. Pulses of chirped light from a diode laser system excite atom
pairs to a long-range molecular potential. Their subsequent evolution
on this attractive potential can lead to loss from the trap. In general,
we observe a large transient collisional loss rate caused by efficient
adiabatic excitation of the atom pairs by the chirped light. With two
delayed chirped pulses in a pump-probe arrangement, we see both flux-enhancement
and pair-depletion effects. Comparing loss rates for positive and negative
linear chirps, we observe rather different behaviors. Depending on the
center detuning of the chirp, the loss rate for the negative chirp can
be either enhanced or suppressed relative to that for the positive chirp.
We attribute this to the multiple, in some cases coherent, interactions
between the colliding pair and the chirped light as the negative chirp
"follow" the resonance condition of the converging atom pair. We
also report on progress towards using shaped chirps to match the collisional
dynamics.
*work done in collaboration with M.J.
Wright, J.A. Pechkis, J.L. Carini, C.E. Rogers III, S. Kallush, and
R. Kosloff, and supported by DOE.
Joshua Jortner, Tel Aviv University, Israel
Shimshon Kallush, Hebrew University Jerusalem, Israel
Pre-Photoassociation: preparing the ground for an efficient photoassociation
Inspired by recent experimental works on long-range photoassociation (PA)
with ns pulses we
suggest methods to enhance the PA rate by promoting
amplitude from large internuclear distance to closer ones.
Two examples will be discussed:
1) Induction of momentum kick to the ground state population.
2) Direct population of bound molecular state by a signal-frequency laser,
using the quantum unitarity.
Local control method is invoked to give a better insight into the
mechanisms of the processes, and to improve their efficiency.
S. V. Alyabyshev, C. Hemming, Z. Li, T. V. Tscherbul, and
Roman V. Krems,
University of British Columbia, Vancouver, Canada
Prospects for controlling molecular collisions at low temperatures
The development of experimental techniques for the production of ultracold (nano-Kelvin temperature) atoms has generated a resurgence in atomic collision physics. New fields of research such as coherent control of atomic and molecular processes, quantum information and matter wave interferometry make extensive use of ultracold atoms. A major thrust of research is now to create ultracold molecules. The creation and trapping of ultracold molecules might revolutionize molecular physics and bring insight into fundamental questions of physical chemistry [1]. Spectroscopic measurements of unprecedented precision, external field control of chemical reactions, and molecular Bose-Einstein condensation may become possible, opening the door to new fundamental discoveries.
The main goal of this talk will be to outline the prospect for cold controlled chemistry. I will present our work on quantum dynamics of molecules at cold and ultracold temperatures in the presence of static and laser electromagnetic fields. The kinetic energy of molecules at subKelvin temperatures is smaller than perturbations due to interactions with external electric or magnetic fields available in the laboratory. External fields may therefore be used to induce dissociation of weakly bound molecules [2], stimulate forbidden electronic transitions and control dynamics of cold atoms and molecules in a variety of ways [3]. I will present our recent work on mechanisms of manipulating and controlling dynamics of cold molecules with external fields. In particular, I will discuss the possibility of using electric fields to induce Feshbach resonances [4, 5] in ultracold gases, to manipulate electron spin degrees of freedom of cold molecules [6] and to modify chemical reactions. I will describe interactions of molecules in a microwave laser cavity and show that microwave fields may alter the dynamics of molecular collisions at low temperatures. Finally, I will demonstrate that confining the motion of ultracold molecules to two dimensions, as can now routinely be done with ultracold atoms, may suppress inelastic collisions and chemical reactions at ultracold temperatures [7].
References:
[1] R. V. Krems, "Set for collision course", Nature Physics 3, 77 (2007).
[2] R. V. Krems, "Breaking van der Waals molecules with magnetic fields", Phys. Rev. Lett. 93, 013201 (2004).
[3] R. V. Krems, "Molecules near absolute zero and external field control of atomic and molecular dynamics", Int. Rev. Phys. Chem. 24, 99 (2005).
[4]. R. V. Krems, "Controlling collisions of ultracold atoms with dc electric fields", Phys. Rev. Lett. 96, 123202 (2006).
[5] Z. Li and R. V. Krems, Phys. Rev. A 75, 032709 (2007).
[6] T. V. Tscherbul and R. V. Krems, "Controlling electronic spin-relaxation of cold molecules with electric fields", Phys. Rev. Lett. 97, 083201 (2006).
[7] Z. Li, S. V. Alyabishev, R. V. Krems, "Ultracold Inelastic Collisions in Two Dimensions", to be published.
Albrecht Lindinger, Freie Universität Berlin, Germany
Coherent control on cold and ultracold alkali systems
Control of photo-induced molecular processes has attained considerable success in recent years. It became most exciting when self-learning feedback loop algorithms were employed where tailored laser pulses can be generated, which drive the induced processes at a maximum yield along desired paths. An important issue in this regard is the information coded in the optimized laser pulse shape which supplies insight about the underlying processes. Small alkali systems are suitable for this aim since they exhibit a number of bound states available for resonant transitions with weak fields which aids the theoretical description and hence the interpretation.
Closed loop optimizations on alkali dimers in a supersonic beam are first demonstrated for maximization of the ionization yield. Next, isotopomer selective optimizations are presented to examine the efficiency of the optimization procedure for the weak differences between the isotopic species. Surprisingly large enrichment factors are found and information about the dynamics on the involved vibrational states is extracted from the optimal pulse shapes, which provides a new spectroscopical approach of yielding distinct frequency pattern on fs-time scales. The experiments are compared with optimal control calculations in order to decipher the underlying processes in detail.
A main aspect of this contribution is the development of novel pulse shaping and optimal control methods. A major goal of this approach is to extract the most relevant information from the optimized laser field and hence to aid the interpretation. Moreover, novel pulse shaper schemes for combined phase, amplitude, and polarization pulse control were designed and applied on alkali dimers, even in a parametric encoding. The results demonstrate the perspectives of adding a new dimension by including also the polarization and hence all properties of the light field in the pulse modulation.
Currently, coherent control was applied to ultracold trapped ensembles motivated by the perspective to perform photoassociation and photostabilization of alkali systems. First results are received regarding optimized multi-photonic excitation to molecular ions and pump-probe experiments exposing signal oscillations. They provide indications for photoassociation and open the perspective for transitions to lower vibrational levels in the electronic ground state, which would be a first step to an internally cold molecular Bose Einstein condensate.
Eliane Luc-Koenig,
Françoise Masnou-Seeuws,
Laboratoire Aimé Cotton, Orsay, France
Prospects for the formation of stable ultracold molecules
via photoassociation with chirped laser pulses
Our group has
been working for a few years, in collaboration with the Jerusalem group,
at the theoretical description of photoassociation of ultracold atoms
with chirped laser pulses [1], considering mainly the examples of Cs
[1,2] and Rb [3]. Total adiabatic transfer within a photoassociation
window can be implemented. For pulses in the picosecond range, the chirp
parameter can be chosen to shape the vibrational wavepacket in the excited
state, in view of a focussing effect. The latter is shown to optimize
the stabilization into deeply bound levels of the ground state in a
pump-dump experiment [2].
In the ultracold
regime, the initial state has to be a s-wave stationary scattering
wavefunction describing a pair of colliding atoms. Two methods for performing
the Boltzmann average have been implemented [4]. Recently, we have investigated
[5] how the pulse is carving out a dynamical hole in the pair probability
density. Considering photoassociation into loosely bound levels of Cs2
0g-(6P3/2), we analyze the depletion
of the ground triplet state wavepacket and its evolution after the pulse.
We show that, due to a "momentum kick", a significant flux of population
is moving to short distances, at the timescale of the vibrational motion
in the excited state. This compression effect markedly increases the
pair density probability at short distances, so that photoassociation
with a conveniently delayed red-detuned second pulse will populate deeply
bound levels of Cs2 0g-(6P3/2).
Another signature of the hole is the formation of correlated pairs of
hot atoms.
In collaboration
with Jordi Mur-Petit and Pascal Naidon [6], we study how short pulse
photoassociation can probe the pair correlation function in an atomic
condensate. Calculations are performed for a metastable helium condensate,
where the correlated pairs of hot atoms are detected in the experiment
of the Westbrook's group [7].
References:
[1] E. Luc-Koenig, R. Kosloff, F. Masnou-Seeuws and M. Vatasescu, Phys. Rev. A 70, 034414 (2004), E. Luc-Koenig, M. Vatasescu and F. Masnou-Seeuws, Eur. Phys. J. D 31, 239-262 (2004).
[2] C. P. Koch, E. Luc-Koenig and F. Masnou-Seeuws, Phys. Rev. A 73, 033408 (2006).
[3] C. P. Koch, F. Masnou-Seeuws and R. Kosloff, Phys. Rev. A 73, 043409 (2006),
J. Mur-Petit, E. Luc-Koenig and F. Masnou-Seeuws, Phys. Rev. A 75, 061404(R) (2007).
[4] C. P. Koch, R. Kosloff, E. Luc-Koenig, F. Masnou-Seeuws and A. Crubellier, J. Phys. B 39, S1017 (2006).
[5] E. Luc-Koenig, F. Masnou-Seeuws and R. Kosloff, Phys. Rev. A 75, 054711 (2007).
[6] P. Naidon and F. Masnou-Seeuws, Phys. Rev. A73, 043611 (2006).
[7] M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, A. Aspect, C. Westbrook, Science 310, 648 (2005),
J. Jeltes et al., Nature 445, 402 (2007).
Peter Maunz, University of Maryland and JQI, College Park, MD 20742,
USA
Ultrafast pulses for the entanglement of cold trapped atomic ions
Ultrafast laser pulses open up new possibilities for the quantum
manipulation of laser-cooled trapped ion systems. Appropriately
tailored pulses should allow the operation of fast multi-ion
entangling gates [1-3]. Ultrashort pulses can also be used to
efficiently excite an atom on a timescale much faster than the excited
state lifetime, and the resulting single emitted photon can be
entangled with the final quantum state of the atom for applications in
quantum networking [4].
In a recent experiment, we have exploited this atom-photon
entanglement in order to couple two single 171Yb atomic ions
separated by one meter. The ions are simultaneously excited with an
ultrafast pulse and the resulting two scattered photons are detected
in an antisymmetric Bell state [5,6]. This projects the quantum state
of the two ions in a likewise antisymmetric superposition state. We
demonstrate entanglement using a photonic frequency qubit [3] as well
as a polarization qubit [4] and fully characterize the produced
entangled state using quantum state tomography. Even though this
entanglement scheme is probabilistic, it allows for high fidelity
entanglement that can be used as a resource for entangling larger
numbers of qubits or for the propagation of quantum information over
very large distances. .
[1] J.J. Garcia-Ripoll, P. Zoller, and J. I. Cirac, Phys. Rev. Lett.
91, 157901 (2003)
[2] L.-M. Duan, Phys. Rev. Lett. 93, 100502 (2004).
[3] M. J. Madsen, et. al., Phys. Rev. Lett. 97, 040505 (2006).
[4] B. B. Blinov, et. al., Nature 428, 153 (2004).
[5] C. Simon and W.T.M. Irvine, Phys. Rev. Lett. 91, 110405 (2003)
[6] D.L. Moehring et al., Nature 449, 68 (2007)
Pascal Naidon, NIST, Gaithersburg MD, USA
Two-body transients in coupled atomic-molecular Bose-Einstein
condensates
Ultracold atoms can be associated into diatomic molecules by applying a
resonant
laser. This two-body process, known as photoassociation, may be limited at
high
laser intensities by the unitarity of the S-matrix. In the case of a Bose-
Einstein condensate of atoms, many-body models have predicted that the
conversion to molecules may be limited at even lower intensities, because
of
molecules breaking up into noncondensate atoms, a process called "rogue
dissociation".
In the talk, I will show that there are three regimes of photoassociation
in a
Bose-Einstein condensate, and that they all can be understood on the basis
of
time-dependent two-body theory. In particular, the rogue dissociation is
not a
many-body effect, but results from a "universal" transient response of
individual atom pairs. Finally, I will illustrate how the three regimes
could be
observed by photoassociating condensates of alkaline-earth atoms.
Silke Ospelkaus,
J. J. Zirbel, K.-K. Ni, A. Pe'er, B. Neyenhuis, C. E. Wieman,
D. S. Jin, J. Ye,
JILA, Boulder (CO), USA
Ultracold heteronuclear molecules of 40K and 87Rb
The production of dense ultracold polar molecular samples is a long standing
goal of AMO physics. Polar molecules have bright prospects as systems with
anisotropic interactions, as sensitive probes for precision measurements and
as qubits for the realization of quantum computation schemes.
One approach to this goal is to start with ultracold dual-species atomic
gases, and then associate atoms into weakly bound Feshbach molecules. These
molecules are then transferred into the absolute molecular ground state
using coherent optical deexcitation schemes.
As a starting point for the creation of ultracold polar molecules, we report
on the creation of heteronuclear Feshbach molecules from an ultracold gas
mixture of 40K-87Rb in an optical dipole trap. We create more than 30,000
molecules at about 200 nK. We have studied the inelastic loss of the
molecules as a function of the heteronuclear scattering length and find that
the quantum statistics of the particles involved in the collision has a
dramatic effect on the loss rate of the Feshbach molecules in the optical
dipole trap. In particular, we demonstrate that these weakly bound Feshbach
molecules can be long-lived. The ensemble is therefore an excellent starting
point for the application of transfer schemes into more deeply bound
vibrational levels.
Towards this end, we report on one-photon spectroscopy to probe excited
electronic states and and two-photon Raman spectroscopy to probe more deeply
bound ground state vibration levels. We discuss prospects of reaching the
ground state of the molecular system using coherent optical schemes.
Goran Pichler, Institute of Physics, Zagreb, Croatia
Influence of the frequency comb on atom velocity distribution
We observed that a femtosecond laser frequency comb changes the velocity distribution of rubidium or cesium
atoms due to the optical pumping effect. We believed that different parts of the frequency comb may serve various
purpose including cooling and eventually the formation of the ultracold molecules. However, the first results with atomic hyperfine filter and experiments with increased sensitivity by using lock-in detection show that the final goal is still elusive.
We hope to report the first results using Rb MOT and femtosecond laser frequency comb simultaneously.
Evgeny Shapiro, University of British Columbia, Canada
Piecewise Adiabatic Passage with a series of mutually coherent
femtosecond pulses
e study a new method of executing population transfers between
quantum states, aimed to combine the flexibility of quantum
control with broadband laser pulses with the robustness of adiabatic
passage. In the first part of the talk I will introduce
the method of Piecewise Adiabatic Passage [1], and review some of its
basic properties. In the second part, I will describe the
recent developments, including the experimental demonstration of
piecewise adiabatic following between two quantum states [2], and
the proposal of using Piecewise Adiabatic Passage for robust creation
and of ultracold ground-state molecules [3].
References
[1] E.A. Shapiro, V. Milner, C. Menzel-Jones, and M. Shapiro,
Phys. Rev. Lett. 99: 033002 (2007)
[2] S. Zhdanovich, E.A. Shapiro, M. Shapiro, J.W. Hepburn, V. Milner,
arXiv:0710.3145v1 [physics.atom-ph].
[3] E.A. Shapiro, A. Pe'er, J. Ye, M. Shapiro,
arXiv:0710.5502v1 [quant-ph].
Yaron Silberberg, Weizmann Institute of Science, Rehovot, Israel
On the Shape of the Photon
In many ultrafast optics laboratories we routinely synthesized femtosecond pulses with high precision to serve as the driving fields for coherent control experiments. Can we shape single photons? How short is a photon? I shall discuss how ideas borrowed from quantum control with classical pulses can be extended to nonclassical light sources, and in particular show how one can use pulse shaping tools on single photons.
Zsuzsa Sörlei, KFKI Budapest, Hungary
Mechanical
momentum transfer to magneto-optically trapped atoms by frequency modulated
laser pulses
Coherent manipulation
of cold atoms without heating them while changing their velocity or
position can be very useful in many experiments. To avoid temperature
increase during the manipulation, it is desirable to utilize stimulated
transitions between atomic states induced by pulses, or by frequency
modulated (chirped) pulses in the adiabatic passage regime.
We investigated
the behavior of Rb85 atoms trapped in a magneto optical trap
(MOT) in the field of a sequence of counter-propagating frequency chirped
short (in the range of ns) laser pulses for coherent manipulation in
the adiabatic passage regime. Measurements at various chirp rates were
carried out to find the region of the chirp and the intensity of the
frequency modulated light pulses, where the adiabatic excitation and
de-excitation gives the maximal force for the acceleration of the atoms
without temperature increase.
The light pulses
were generated by transmitting the frequency modulated light of a cw
diode laser with sinusoidally modulated pump current through a Fabry-Perot
(F-P) interferometer tuned to the resonance with the working transition.
The central frequency of the diode laser was regulated around the resonance
frequency of the spectral line by a dc bias current, resulting in variation
of the rate of the frequency chirp of the light pulse transmitted by
the F-P interferometer. The spatial displacement of the atomic cloud,
which depends on the mechanical momentum transferred to the atoms as
a result of interaction with a sequence of the frequency chirped laser
pulses, was detected by the fluorescence of the Rb atoms. The displacement
of the atoms in case of counter-propagating beams is measured to be
larger than in case of a single beam only in a restricted interval of
the chirp rate. Otherwise the ratio of the two beam/one beam displacement
is fluctuating around 1 or is smaller than one. This result is in qualitative
agreement with results of numerical simulations of the temporal behavior
of populations of the hyperfine levels manifold of the D2
line of the Rb85 atom using a computer code based on solution
of Bloch equations for density matrix elements taking into account spontaneous
decay of the excited states.
Monte Carlo
simulations for a two-level atom have shown that the momentum transferred
to the atoms by a single counter-propagating partially overlapping pulse
pair can be several times the value of non-overlapping chirped pulses.
In certain parameter regions, the momentum transfer is accompanied by
negligible heating of the atoms and they are returned to the ground
state at the end of the interaction, avoiding the de-coherency effects
initiated by the spontaneous decay of the excited state.
We investigated
experimentally the mechanical effect of partially overlapping chirped
pulse pairs for trapped Rb85 atoms. The experimentally observed
displacement of the atomic packet agreed well with the theoretical prediction.
For further investigations of such kind with a wider range of experimental
parameters we are preparing chirped laser pulses in the ns range by
using electro-optical modulators.
L.C. Karssen, J.I Dijkhuis and
Peter van der Straten, Universiteit Utrecht, Netherlands
Laser cooling and trapping using pulsed lasers
Cooling of atoms using lasers is very efficient with the laser tuned slightly below resonance, where the velocity of the atoms is damped by scattering of photons. Trapping of atoms using lasers is very efficient far from resonance, where the atoms are trapped in potentials created by the light shift. We have studied cooling and trapping of atoms using lasers in the intermediate regime using a laser running both CW and mode-locked. The laser is tuned in two different ranges: below the D1 line and in between the D1 and D2 line. This has a profound effect on the number of atoms captured in the dipole trap and the temperature of the atoms. We observe a strong, so far unexplained, dependence of the parameters on the polarization of the laser light, both CW and mode-locked. We also observe different behavior of the parameters for the two isotopes of rubidium.
David J. Tannor, Weizmann Institute, Israel
Introduction to Coherent Control
This talk will be an overview of concepts and methods in quantum control. The control of chemical reactions using ultrashort lasers will be used to motivate and illustrate the concepts. First, intuitive control schemes will be presented, for example pump-dump, STIRAP, and interfering pathways.. Then concepts of pulse shaping will be introduced, including the methods of optimal control theory, local control theory and learning algorithms. Finally, the connection with the theory of controllability based on Lie algebras (also known as geometric control) will be presented. Applications will be presented from different areas of chemistry and physics.
Amichay Vardi, Ben Gurion University, Beer Sheva, Israel
Two-dimensional solitons in dipolar Bose-Einstein condensates
Starting with a Gaussian variational ansatz, we predict anisotropic bright
solitons in quasi-2D Bose-Einstein condensates (BECs) consisting of
particles
with dipole moments polarized perpendicular to the confinement direction.
The proposed structures could be realized in quantum Bose gases of
magnetically polarized Cr atoms or in BECs of electrically polarized
molecules.
Unlike isotropic solitons predicted for the moments aligned with the
confinement axis, no sign reversal of the dipole-dipole interaction is
necessary to support the solitons. Direct 3D numerical simulations confirm
the stability of the 2D solitons and suggest interesting dynamical effects
in their rotation and collisions.
Markus Kowalewski,Caroline Gollub, Giovanna Morigi, Pepijn W.H. Pinkse,
Regina de Vivie-Riedle,
Ludwig Maximilian University Munich, Germany
New applications of non-resonant Raman scattering in the context of molecular cavity cooling and vibrational quantum computing
Non-resonant Raman scattering is used as a flexible tool to control processes in the electronic groundstate. We discuss two applications on two different time scales. In the millisecond regime we aim for molecular cooling, in the femtosecond regime for vibrational quantum computing. In both scenarios coherence plays an important role, while the influence of the excited state is unwanted.
The preparation of ultracold ground state molecules is still challenging. One class of preparation strategies are optical methods, which have been enormously successful for atoms. Adapted versions of laser cooling, which try to optimize optical pumping into the molecular ground state, have been proposed [1], but their efficiency is limited by the absence of closed transitions in molecules. We present a theoretical approach [2,3] for the simulation of the cooling of internal and external molecular degrees of freedom in a cavity. The idea is to sequentially depopulate excited rovibrational levels by vacuum-stimulated Raman scattering into the mode of a high-finesse cavity. As model systems we choose the OH and the NO radicals. By using a combination of ab initio quantum chemical and experimental data we are able to determine the molecular properties needed for our cooling scheme. We discuss the details of the cooling process and predict the time scales needed to prepare a molecule in its ground state.
Molecules in their rotational and vibrational groundstate are suitable candidates for quantum computing [4]. Non-resonant stimulated Raman processes in the femtosecond regime are applied to implement quantum gates for vibrational qubits. One of the advantages of this idea, compared to our first approach in the IR regime [4], is the high flexibility in the choice of laser wavelengths in combination with well established shaping techniques in the visible frequency domain. The quantum gates can be optimized by a modified Krotov-OCT-scheme including restrictions on the laser fields in the frequency domain to assure simple pulse spectra. Stimulated Raman quantum gates are presented for a 2D-qubit system.
Combination of both ideas might open a way to realize molecular quantum computing in the gas phase.
References
1. J.T. Bahns, W.C. Stwalley, and P.L. Gould, J. Chem. Phys. 104, 9689 (1996).
2. G. Morigi, P. W. H. Pinkse, M. Kowalewski and R. de Vivie-Riedle, Phys. Rev. Lett. 99, 073001 (2007).
3. M. Kowalewski, G. Morigi, P. W. H. Pinkse and R. de Vivie-Riedle, Appl. Phys. B, accepted.
4 C. Tesch, R. de Vivie-Riedle, Phys. Rev. Lett. 343, 633 (2002).
Ian Walmsley,
Chris Foot, Thorsten Koehler, Matthew Anderson, Francoise Masnou-Seeuws,
Jovana Petrovic, Adam Wyatt, Jordi Mur-Petit, Alex Dicks, David McCabe, Duncan England, Melissa Friedman and Hugo Martay,
Oxford University & University College London, UK,
San Diego State University, USA,
Laboratoire Aimé Cotton, France
Progress in ultrafast photoassociation of ultracold atoms
We discuss experimental approaches
to the control of the photoassociation of ultracold atoms in a MOT using
shaped ultrashort optical pulses tuned to the lowest electronic molecular
resonance. Evidence for coherent effects in the formation of molecules
in their electronic ground state will be presented, and progress in
the detection of wavepacket formation and shaping in the A-b 0u+
manifolds will be reported. The problem of determining a unique signature
for vibrationally 'cool' molecules in the electronic ground state
will be raised, and some possible solutions mooted.
Matthias Weidemüller,
W. Salzmann, S. Götz, T. G. Mullins, M. Albert, J. Eng, R. Wester,
A. Merli, S. Weber, M. Plewicki, F. Sauer, F. Weise, L. Wöste, A. Lindinger, Universität Freiburg & Freie Universität Berlin, Germany
Coherent transients in the formation of ultracold molecules with shaped femtosecond pulses
We present
experiments on the formation of ultracold molecules by femtosecond laser
pulses in a pump-probe scheme [1]. Previous experiments [2,3] have only
demonstrated the dissociation of molecules by femtosecond pulses, whereas
now active photoassociation is observed. A shaped pump pulse excites
a collision pair of laser cooled rubidium atoms to a bound molecular
state below the 5s5p1/2 asymptote, from where the molecule
is transferred to the molecular ionic state by a probe pulse a few picoseconds
later. A femtosecond pulse shaper is used to apply a sharp low pass
filter to the pump pulse spectrum with a cutoff frequency a few wavenumbers
below the atomic D1 resonance. The photoassociation signal shows oscillatory
dynamics between the electronic molecular states coupled by the pump
pulse, resulting from the pump pulse's high electric field strength
and its specific spectral shape close to the molecular dissociation
limit. Simulations of the pump pulse excitation have been performed
by numerically solving the time dependent Schrödinger equation using
a mapped-fourier-grid-hamiltonian algorithm and are in excellent agreement
with the experimental results.
[1] W. Salzmann et al., submitted.
[2] W. Salzmann et al., Phys. Rev. A 73, (2006) 023414
[3] B. L. Brown et al., Phys. Rev. Lett. 96, (2006) 173002
[4] M. J. Wright et al., Phys. Rev. A, 75 (2007) 051401
J. Deiglmayr, J. Lange, C. Glück, K. Mörtlbauer, A. Grochola, Roland Wester*, M. Weidemüller,
Universität Freiburg, Germany
Perspectives for coherent formation and chemical reactions of ultracold molecules
Collisions of molecules at ultracold temperatures feature very different cross sections and dynamics as expected from classical room temperature dynamics [1]. Large inelastic vibrational relaxation rates have been measured for different vibrational states of cesium dimers in collisions with cesium atoms [2]. We study the formation of heteronuclear LiCs dimers [3] using active photoassociation with cw light. I will discuss these results and show how they can serve as a starting point for the coherent formation of internal ground state molecules and for investigations of chemical exchange reactions in the ultracold regime.
[1] R. V. Krems, Int. Rev. Phys. Chem. 24, 99 (2005); P. F. Weck and N. Balakrishnan, Int. Rev. Phys. Chem. 25, 283 (2006)
[2] P. Staanum, S. D. Kraft, J. Lange, R. Wester, M. Weidemüller, Phys. Rev. Lett. 96, 023201 (2006); N. Zahzam, T. Vogt, M. Mudrich, D. Comparat, P. Pillet, Phys. Rev. Lett. 96, 023202 (2006)
[3] S. D. Kraft, P. Staanum, J. Lange, L. Vogel, R. Wester, M. Weidemüller, J. Phys. B 39, S993 (2006)
Rosario González Férez, P. Sanchez-Moreno, M. Mayle, and P. Schmelcher,
Universidad Granada, Spain
Heteronuclear Dimers in Strong Electric Fields: Rovibrational
Spectra and Photoassociation
We investigate the effects of a strong static electric field on the
rovibrational spectra of diatomic heteronuclear molecules in their
electronic ground state. A full rovibrational approach was developed
including the coupling of the vibrational and rotational motions and
taking into account the dependence of the electric dipole moment on the
internuclear distance. For several alkali dimers, LiCs, KRb and RbCs
[1-3], a detailed analysis of the impact of the electric field is
performed: the hybridized and oriented rotational motion, the mixing of
angular momenta and the squeezing of the vibrational motion. In addition,
we will discuss the formation of ultracold molecules via stimulated
emission followed by a radiative deexcitation cascade in the presence of a
static electric field [4,5]. Taking as an example the LiCs, the dependence
of the corresponding cross section on the final rovibrational bound state,
on the energy of the continuum, and also on the static electric field
strength are analyzed in detail. We consider the cold and ultracold regime
where transitions from s-wave are the dominant, which means that in
absence of the static electric field only bound states with angular
momentum equal to one are populated. We will show that in the presence of
the static electric field transitions to bound states evolving from
field-free levels with zero angular momentums become possible. Hence, we
demonstrate the possibility to populate the lowest rotational excitations
via photoassociation. The modification of the radiative cascade due to the
electric field leads to narrow rotational state distributions in the
vibrational ground state. External fields might therefore represent an
additional valuable tool towards the ultimate goal of quantum state
preparation of molecules.
[1] R. Gonzalez-Ferez, M. Mayle, and P. Schmelcher, Chemical Physics 329
(2006) 203-215.
[2] M. Mayle, R. Gonzalez-Ferez, and P. Schmelcher, Physical Review A 75
(2007) 013421.
[3] P. Sanchez-Moreno, M. Mayle, R. Gonzalez-Ferez, and P. Schmelcher, in
preparation (2007).
[4] R. Gonzalez-Ferez, M. Mayle, and P. Schmelcher, Europhys. Lett. 78,
53001 (2007).
[5] R. Gonzalez-Ferez, M. Weidemueller, and P. Schmelcher, Physical Review
A
76, 023402 (2007).
I. Mourachko, S. L. Cornish, C. S. Adams and
Ifan G. Hughes, A. Homer and G. Roberts,
Durham University, UK
Coherent control of the formation of ultra-cold heteronuclear RbCs molecules
Macroscopic quantum states of ultracold molecules promise a broad range of exciting new physics, comparable to that resulting from Bose-Einstein condensation of atoms. We are building an experiment, and plan to explore the possibilities for generating such novel states of matter by building on the remarkable low temperatures achieved for atoms. Our approach makes use of closed-loop control of the synthesis of ultra-cold molecules from trapped ultra-cold atoms using shaped broadband optical pulses followed by laser ionisation of the atoms--molecules mixture and selective detection of molecular ions.
Details of the apparatus housing the Rb and Cs magneto optical trap will be given, along with the femtosecond and detection laser systems. A compact time of flight mass spectrometer has been designed to offer both high resolution and excellent optical access to the MOT in the entire horizontal and one vertical plane. This design uses six independent rod electrodes, in a Wiley-McLaren configuration, and allows both the time focusing of the ions and the deflection of the unwanted atomic ions out of the ion detector.
The long term goal of our work is to produce efficiently molecules in their lowest electronic, vibrational and rotational states that can subsequently be held in optical or magnetic traps for long periods without collisional dissociation.
Claus Peter Schulz,
Marcel Mudrich, Frank Stienkemeier,
Max Born Institut Berlin & Universität Freiburg, Germany
Quantum interference spectroscopy of alkali-helium exciplexes
formed on helium nanodroplets
Femtosecond
multiphoton pump-probe photoionization is applied to helium nanodroplets
doped with alkali atoms (K, Rb, Cs). The yield of, e.g., Rb+
ions features pronounced quantum interference fringes demonstrating
the coherence of a superposition of electronic states on a time scale
of tens of picoseconds. Furthermore, we observe quantum interference
fringes in the yield of formed alkali-helium exciplex molecules. The
quantum interferogram allows us to determine the vibrational structure
of these fragile molecules. From a sliced Fourier analysis one can not
only extract the population dynamics of vibrational states but also
follow their energetic evolution during the exciplex formation. Similarities
and differences in the formation of the exciplexes of the three alkali
metals will be discussed in the presentation.
Vladimir A. Yurovsky, Tel Aviv University, Israel
Effect of non-integrability on reactions and collisions in quasi-one-dimensional ultracold gases
Atom waveguides that tightly confine a motion of ultracold particles in two transverse directions [1] have been realized recently in elongated atomic traps, two-dimensional optical lattices, and atomic chips.
Quasi-one-dimensional Bose gases can be approximately described by the Lieb-Liniger-McGuire model with energy-independent zero-range atom-atom interactions.
This model is a rare example of integrable many-body systems. It has an exact Bethe-ansatz solution characterized by non-diffractive scattering, where the atoms can exchange their momenta, but the asymptotic momentum set remains unchanged. A consequence of integrability was observed in the quantum Newton's cradle experiment at Penn State [2], performed on an array of quasi-one-dimensional Bose gases out of equilibrium in a two-dimensional optical lattice. The momentum distributions are not observed to change with time as a result of thermalization.
Reflection and dissociation in atom-diatom collisions and three-atom association are forbidden within the Lieb-Liniger-McGuire model and can appear when the integrability is lifted [3]. Another possible observable effect of non-integrability is the stabilization of broad Feshbach dibosonic molecules in atom waveguides [4]. Non-integrability can also lead to thermalization due to a change of the asymptotic momentum set in three-atom elastic collisions, as well as due to general diffractive scattering. Thermalization was observed in recent Penn State experiments when the lattice depth is decreased, although the collision energy remains substantially below the transverse waveguide frequency.
1. V. A. Yurovsky, M. Olshanii, and D. S. Weiss, Adv. At. Mol. Opt. Phys., 55, 61, (2007).
2. T. Kinoshita, T. R. Wenger, and D. S. Weiss, Nature, 440, 900, (2006).
3. V. A. Yurovsky, A. Ben-Reuven, and M. Olshanii, Phys. Rev. Lett, 96, 163201, (2006).
4. V. A. Yurovsky, physics/0703168; Phys. Rev. A (in press).
Posters
Morag Amshalem, Hebrew University Jerusalem, Israel
Erez Boukoubza, Weizmann Institute, Rehovot, Israel
Three-level systems as amplifiers and attenuators: a thermodynamic analysis of the semiclassical evolution
Thermodynamics of a three-level maser was studied in the pioneering work
of Scovil-Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this Letter we consider the same three-level model, but we give a full thermodynamic analysis based on Hamiltonian and dissipative Lindblad superoperators. The first law of thermodynamics is obtained using a recently developed alternative [Phys. Rev. A 74, 063823 (2006)] to Alicki's definitions for heat flux and power [J. Phys. A 12, L103 (1979)]. Using a novel variation on Spohn's entropy production function [J. Math. Phys. (N.Y.) 19, 1227 (1978)], we obtain Carnot's efficiency inequality and the Scovil-Schulz-DuBois maser efficiency formula when the three-level system is operated as a heat engine (amplifier). Finally, we show that the three-level system has two other modes of operation -- a refrigerator mode and a squanderer mode -- both of which attenuate the electric field.
Erez Boukoubza, Weizmann Institute, Rehovot, Israel
Thermodynamic analysis of quantum light
amplification and light purification
Thermodynamics of a three-level maser was studied in the pioneering work of
Scovil and Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)]. In this work we
consider the same three-level model, but treat both the matter and the light
quantum mechanically. Specifically, we analyze an extended (three-level)
dissipative (ED) Jaynes-Cummings model (JCM) within the framework of a
quantum heat engine, using formulas for heat flux and power in bipartite
systems introduced in our previous work [E. Boukobza and D. J. Tannor Phys.
Rev. A 74, 063823 (2006)] Infinite amplification of the selected cavity mode
occurs even in this simple model, as seen by a positive steady state power.
However, initial field coherence is lost, as seen by the decaying
off-diagonal field density matrix elements, and by the Husimi-Kano Q
function. We show that after an initial transient time the field's entropy
rises linearly during the operation of the engine, which we attribute to the
dissipative nature of the evolution and not to matter-field entanglement. We
show that the second law of thermodynamics is satisfied in two formulations
(Clausius, Carnot) and that the efficiency of the ED JCM heat engine agrees
with that defined intuitively by Scovil and Schulz-DuBois. Finally, by
changing the relative excitation in the two photonic reservoirs we
demonstrate quantum light purification.
Jennifer Carini, C.E. Rogers III, M.J. Wright, J.A. Pechkis,
and P.L. Gould,
University of Connecticut, USA
Generation of Nanosecond-Scale Frequency-Chirped Pulses
with Fiber-Based Phase and Amplitude Modulators
We report on producing nanosecond pulses of laser light whose frequency is arbitrarily chirped and whose amplitude is arbitrarily controlled. The chirp is achieved by sending the output from a 780 nm diode laser through a fiber-based electro-optical phase modulator within a fiber delay loop. Upon exiting the fiber, the light has accumulated the desired time-dependent phase. It then re-injection locks the diode laser, thus maintaining the high optical power. Larger phase modulations can be accumulated by using multiple passes through this loop, re-injection locking after each pass. We are able to produce arbitrary chirps by driving the phase modulator with an arbitrary waveform generator. Currently, we have been able to achieve chirp rates up to approximately 100 GHz/μs. To produce an arbitrary pulse amplitude, the light is sent through a fiber-based electro-optical amplitude modulator, driven with an arbitrary waveform generator. Using this technique, we have been able to achieve pulses as short as 4 ns FWHM. Such pulses will be useful in controlling collisions between ultracold Rb atoms.
Lev Chuntonov, Leonid Rybak, Andrey Gandman, Zohar Amitay,
Technion Haifa, Israel
Frequency-Domain Femtosecond Coherent Control of Two-Photon Absorption in the Intermediate-Field Regime
Coherent control
of femtosecond two-photon absorption in the intermediate-field regime
is analyzed in detail in the powerful frequency domain using an extended
4th-order perturbative description [1,2]. The corresponding
absorption is coherently induced by the weak-field non-resonant two-photon
transitions as well as by four-photon transitions involving three absorbed
photons and one emitted photon (see Figure 1). Even when the two-photon
transitions are of non-resonant nature, the four-photon transitions
are of resonant-mediated nature with either initial or final state of
the process playing the role of the intermediate state. The interferences
between these two groups of transitions lead to a difference between
the intermediate-field and weak-field absorption dynamics. The corresponding
interference nature (constructive or destructive) strongly depends (for
a given physical system) on the detuning direction of the pulse spectrum
from one-half of the two-photon transition frequency (fg/2).
Consequently, we rationally find that the absorption is enhanced over
the transform-limited pulse by any shaped pulse having a spectral phase
that is anti-symmetric around fg/2 and a spectrum that
is asymmetric around it (red- or blue-detuned according to the system).
The degree of enhancement increases as the field strength increases.
Depending on the pulse intensity, the anti-symmetric phase patterns
can also deviate to various extents from perfect anti-symmetry and still
exceed the performance of the transform-limited pulse. The model system
of the study is atomic sodium, for which both experimental and theoretical
results are obtained. The detailed understanding obtained here can serve
as a basis for coherent control with rationally-shaped femtosecond pulses
in a regime of sizable absorption yields.
[1] L.Chuntonov, L.Rybak, A.Gandman, and Z.Amitay,
arXiv:0709.0615
[2] L.Chuntonov, L.Rybak, A.Gandman, and Z.Amitay,
arXiv:0709.0486
Gagik Djotyan, J.S. Bakos, G. Demeter,
Zs. Sörlei, J. Szigeti, D. Dzsotjan, KFKI Budapest, Hungary
Robust coherent control of quantum states
by frequency-chirped ultrashort laser pulses
Population transfer to a target state or creation of a given coherent superposition of metastable states in multilevel quantum systems have numerous applications in the control of chemical reactions, improving efficiency of nonlinear processes in resonant media, quantum computing and processing of quantum and classical information, electromagnetically induced transparency, etc.
In this communication, we analyze possibilities of using ultrashort laser pulses with frequency chirp for effective and robust transfer of populations between the quantum states of multilevel systems (atoms or molecules) or creation of coherent superposition of these states.
The result of interaction of a short frequency chirped laser pulse with a two-level atom in the adiabatically following regime is well known: such pulse provides complete inversion of the atom at the end of the interaction. In more complex multilevel quantum systems, such pulses interact superposition of the working states and transfer the corresponding population to the target states leaving intact superposition of the states.
At the end of the interaction, one has population transferred to a target state along with a coherent superposition corresponding to superposition state left without change. An important peculiarity of such control of the states is that it depends on the relative phase of the interacting frequency-chirped laser pulses that provides a tool for governing the population transfer and induced coherence by varying the relative phase of the laser pulses.
Different schemes of the coherent control are considered including different structures of the working levels of the quantum systems: , V- and ladder- structured atoms and molecules. Among the considered schemes those ones are singled out that allow performing population transfer between metastable states or creation of coherent superposition of these states without appreciable excitation of the quantum system providing immunity of such schemes to decoherence due to the decay of the excited states. Such schemes are discussed in details in this communication.
The considered schemes are not sensitive to small-to-medium variations of the pulse area, speed of the frequency chirp or other parameters of the laser pulses and the quantum system. Because of no strict resonance conditions for the frequency chirped pulses, the proposed schemes are effective in media with homogeneously as well as inhomogeneously broadened transition lines.
Frauke Eimer, Andrea Merli, Fabian Weise, Sascha Birkner, Franziska Sauer, Stefan M. Weber, Ludger Wöste, Albrecht Lindinger, Wenzel Salzmann*, Terry Mullins*, Simone Götz, Judith Eng*, Magnus Albert*, Roland Wester* and Matthias Weidemüller*,
Freie Universität Berlin & *Universität Freiburg, Germany
Photoassociation of ultracold rubidium atoms by femtosecond-laserpulses
One promising mechanism for creating ultracold molecules is based on the photoassociation of ultracold atoms by ultrashort laser-pulses [1]. We investigate the photoassociation process with femtosecond-pulses in a magneto-optical 85Rb trap. For this purpose a two-colour pump-probe setup is used in which the amplitude of the pump-pulse spectrum is modulated. The observed molecular ion rate shows an oscillatory structure which is qualitatively reproduced by quantum-mechanical simulations. This oscillatory dynamic can be explained by coherent interactions of molecular electronic dipole with the spectrally modulated electric field. By varying the atomic density we were able to demonstrate, that photoassociation by femtosecond-laserpulses occurs. Also, the relevant frequency components could be determined by different modulations of the pump-pulse spectrum.
[1] C. P. Koch, R. Kosloff and F. Masnou-Seeuws, Phys. Rev. A 73, 043409 (2006)
Benjamin Fingerhut, Dorothee Geppert and Regina de Vivie-Riedle,
Ludwig Maximilian University Munich, Germany
Ultrafast Dissociation Pathways of Diphenylmethanes:
Challenges of a Reactive Multi-Level System
The primary processes in the formation of electrophilic precursor ions, key intermediates in organic synthesis, are studied on a microscopic scale by quantum chemical and quantum dynamical methods. We investigate ultrafast dissociation processes of diphenylmethanes in gas phase. For the competing reaction channels of the photochemically induced heterolysis and homolysis of diphenylmethyl chloride the interaction of different electronic states leads to the initial charge transfer from the phenyl π-system to the σ-bond of the leaving group. The formation of ionic and radicalic products is observed in polar solvents [1] and is attributed to the existence of conical intersections [2]. We were able to localize and characterize three conical intersections for the first time, which constitute the minima in the intersection space.
Based on our ab initio data we derived a system Hamiltonian which is suitable to describe the multidimensional dissociation process in a reduced reactive coordinate space [3]. Quantum dynamical calculations suggest that dissociation induced by a Fourier limited femtosecond laser pulse provides the ion pair as the main product in gas phase despite its higher potential energy. Selective addressability of the reaction channels by laser control will be discussed.
The light induced dissociation of the related diphenylmethane provides two different competing reaction channels, one of triplett formation and one of laser induced tunneling. Selective enhancement of the tunneling process offers the possibility to control the dissociation.
References
1. J. Bartl, S. Steenken, H. Mayr, and R.A. McClelland, J. Am. Chem. Soc. 112, 6918 (1990).
2. K. S. Peters, Chem. Rev. 107, 859 (2007).
3. B. Fingerhut, D. Geppert, and R. de Vivie-Riedle, Chem. Phys. in press (2007).
Andrei Gandman, Lev Chuntonov, Leonid Rybak, Zohar Amitay,
Technion Haifa, Israel
Multi-Channel Selective Femtosecond Coherent Control
Based on Symmetry Properties
The present experimental work implements a new scheme for extended multi-channel selective femtosecond coherent control based on symmetry properties of the excitation channels. Here, an atomic non-resonant two-photon absorption channel [1] is coherently incorporated in a resonance-mediated (2+1) three-photon absorption channel [2]. By proper pulse shaping, utilizing the invariance of the two-photon absorption to specific phase transformations of the pulse, the three-photon absorption is tuned independently over order-of-magnitude yield range for any possible two-photon absorption yield. Noticeable is a family of shaped pulses that are all dark with respect to the two-photon absorption (i.e., inducing zero two-photon absorption), while inducing widely tunable range of three-photon absorption. The work is conducted in the weak-field regime for which the two- and three-photon absorption are described, respectively, by second- and third-order perturbation theory. The model system is the Na atom. Figure 1 shows the two-channel excitation scheme of Na together with the phase patterns used for implementing the selective femtosecond coherent control. Each phase pattern results from the addition of two patterns: (i) a simple phase step that sets the two-photon absorption level, and (ii) a pattern that is anti-symmetric around one-half of the two photon transition frequency that tunes the three-photon absorption without affecting the two photon absorption.
[1] D. Meshulach and Y. Silberberg, Nature (London) 396, 239 (1998); Phys. Rev. A 60, 1287 (1999).
[2] A. Gandman, L. Chuntonov, L. Rybak, and Z. Amitay, Phys. Rev. A 75, 031401 (R) (2007); Phys. Rev. A 76, 053419 (2007).
Exact theoretical description of two ultracold atoms in a
single site of the 3D optical lattice using realistic potentials
A theoretical approach was developed that allows
for a full numerical description of a pair of ultracold atoms
trapped in a three-dimensional optical lattice. This approach
includes the possible coupling between center-of-mass and
relative motion coordinates in a configuration-interaction
type of calculations. The atoms are allowed to interact by
their full interaction potential that is, presently, only
limited to be central. With the aid of the newly developed
method deviations from the harmonic approximation are
discussed for the heteronuclear pairs. The developed method
is used to model experimental data.
Note: Implemented code uses REALISTIC potentials.
It is straitforward to study with implemented approach such
processes like phohoassociation
[for example we are authors of PRA76,022704].
Michael Khasin, Hebrew University Jerusalem, Israel
Yuri Khodorkovsky, Amichay Vardi & Gershon Kurizki,
Ben-Gurion University, Beer-Sheva & Weizmann Institute, Rehovot, Israel
Decoherence and entanglement in an open two-mode BEC: Bose enhancement of the quantum Zeno effect
We study the effect of decoherence on inter-particle entanglement and dynamical quantum depletion in the two-site Bose-Hubbard model of a Bose-Einstein condensate (BEC). Starting with the odd parity excited coherent state, the initial collisional loss of single particle coherence varies from small bound oscillations in the weak coupling regime, through hyperbolic depletion in the strong interaction regime, to a Gaussian decay under the pure collisional Hamiltonian.
The inclusion of pure phase noise, as in the continuous measurement of the relative number difference between the modes, is shown to enhance this quantum depletion. In comparison, the measurement of relative number between even and odd superpositions of the modes, slows down the loss of single-particle coherence. Decoherence can thus either restore or suppress quantum-field behavior, depending on the details of system-bath coupling and the overlap of decoherence pointer states with collisional-entanglement pointer states. The slowing down of collisional dephasing due to the coupling with the environment may be viewed as a many-body quantum-Zeno suppression of dynamical quantum depletion through continuous relative-number measurements. The extended effective decay times in the presence of projective measurement, are further enhanced with increasing number of particles N, by a bosonic factor of N/log(N).
Chii-Dong Lin, Kansas State University, Manhattan, KS, USA
Accurate retrieval of time-resolved atomic and molecular structure from laser induced photoelectron and high-harmonic spectra by few-cycle laser pulses
*
When atoms or molecules are placed in a short laser pulse, the electrons which are released by the laser' electric field earlier may return to recollide with the target ions. By analyzing accurate theoretical results from the solution of the time-dependent Schrödinger equation for rare gas atoms in few-cycle laser pulses, we established the general conclusion that the high-energy photoelectron momentum spectra and the high-order harmonics spectra can be used to extract differential elastic scattering and photo-recombination cross sections of the target ions by free electrons, respectively. [1] For high-harmonic generation, we have also shown that the phase of the electric dipole moment can be extracted from the phase of the high harmonics. [2] Using negative ions as targets, it is also possible to extract electron-atom scattering cross sections.[3] Since both electron scattering and photoionization (the reverse of photo-recombination) cross sections are the conventional means for determining the structure of atoms and molecules, these results imply that existing few-cycle infrared laser pulses can be implemented for ultrafast imaging of transient molecules with temporal resolution from a few down to sub-femtoseconds. [4] Recent experimental results for extracting structural information from laser-induced electron spectra will also be presented. [5]
*in collaboration with
with Toru Morishita, Anh-Thu Le, X. X. Zhou and Zhangjin Chen
[1] Toru Morishita, Anh-Thu Le, Zhangjin Chen and C. D.Lin,
Phys. Rev.Lett. (in press). Eprint:
arXiv:0707.3157
[2] A. T. Le et al, submitted. Eprint:
arXiv:0712.3577
[3] X. X. Zhou et al, submitted. Eprint:
arXiv:0712.0334
[4] Toru Morishita et al., New J.Phys. (in press). Eprint:
arXiv:0709.2391
[5] C. L. Cocke and K. Ueda, Private communications.
Michael Mundt, Weizmann Institute, Israel
Optimal control theory for interacting particles: a
multi-configuration time-dependent Hartree-Fock approach
Applying optimal control theory to interacting many-particle
systems
is a great challenge due to the immense efforts required to solve the
time-dependent Schroedinger equation for such systems. This is
especially true in situations in which perturbation theory breaks down
and solving the exact time-dependent Schroedinger equation is
especially true in situations in which perturbation theory breaks down
and solving the exact time-dependent Schroedinger equation is
required as, e.g., in strong-field physics.
In order to describe interacting many-particle systems different
approaches have been developed over the years. A promising method is
the multi-configuration time-dependent Hartree-Fock (MCTDHF) method
which allows to systematically improve the accuracy of the
wavefunction from the Hartree-Fock level to the fully correlated
result. On this poster we discuss the combination of MCTDHF and
optimal control theory. Since the MCTDHF equations are nonlinear
equations, common optimal control algorithms for the Schroedinger
equation cannot be applied and nonlinear optimal control theory has to
be used.
Hai Nguyen, University of Wisconsin Stevens Point, USA
Coherent Laser Matter Interactions: An experimental progress
Molecules formation at μK temperature range offer new opportunities and phenomena in chemistry, metrology, and even quantum physics. We will present an experimental progress of using an ultrafast laser system in conjunction with magneto optical trap recoil ion momentum spectroscopy (MOTRIMS) to investigate the products formed in the interaction of ultrafast laser pulses with cold trapped Rubidium atoms. We aim to produce cold molecular sample using femtosecond laser pulses for further investigations. The diagnostic system and the specific photo-association process will be described in detail. These investigations of molecular photo-association by femtosecond laser pulses contribute to the theoretical and experimental development which has impacts on new physics, chemistry and quantum computations.
José Palao, Christiane P. Koch, Ronnie Kosloff,
Universidad de La Laguna, Spain &
Freie Universität Berlin, Germany & Hebrew University Jerusalem,
Israel
Constrained Optimal Control Theory:
Avoiding population leakage to undesired states
A quantum system can be steered from an initial to a desired final state, or more generally, a given unitary transformation can be implemented by utilizing quantum interferences. Optimal control theory (OCT) is employed to design such laser pulses. The optimal pulses often imply high intensities and might thus drive unwanted multi-photon transitions, e.g. ionization, leading to loss of population. If population of the intermediate states in the multi-photon excitation pathways can be avoided at any time, the transition to the lossy channels is blocked. This can be formulated as an additional constraint in the formulation of OCT. The Krotov method is used to derive the algorithm for both optimization of a state-to-state transition and of a unitary transformation. The resulting algorithm turns out to be similar to formulating the control problem for a time-dependent target in previous work based on the variational approach to OCT [1-3]. The Krotov method offers the advantage that the conditions for monotonic convergence can be analyzed. The algorithm is illustrated with a simple molecular model containing three electronic states. Population transfer between levels in the electronic ground state is achieved by optical transitions through the first excited state, but avoiding population leakage to the second excited state.
References
[1] Y. Ohtsuki, G. Turinici and H. Rabitz, J. Chem Phys. 120, 5509 (2004).
[2] A. Kaiser and V. May, J. Chem. Phys. 121, 2528 (2004).
[3] I. Serban, J. Werschnik, and E. K. U. Gross, Phys. A 71, 053810 (2005).
Ulrich Poschinger, Kilian Singer and Ferdinand Schmidt-Kaler,
Universität Ulm, Germany
Application of optimal control techniques in scalable ion trap quantum logic
Strings of laser cooled ions in a Paul trap provide a yet unmatched degree of quantum control[1].
The drawback of this concept lies in the limited scalability, which can be overcome by operating a microstructured array of Paul traps and shuttling the ions between different trap sites. The shuttling operations are carried out by dynamically changing the confining voltages at the trap segments.
They have to be fast, robust and should not contribute excess energy to the ion qubit as this would spoil subsequent quantum logic operations. This setting suggests the application of optimal control (OCT) techniques. We present numerical results showing that OCT should indeed make such shuttling operations possible[2].
Furthermore, quantum logic logic gates can benefit from OCT as well since achieving high fidelities is crucial for attaining the quantum error correction threshold. We demonstrate numerically that shaped pulse sequences obtained by OCT allow for the implicit compensation of parameter offsets. Analogously to NMR experiments, the logic operations can therefore be robustified[3,4].
[1] H.Häffner et al., Nature 438, 643 (2005)
[2] S. Schulz et al., Progress of Physics, Wiley 54, No. 8-10, 648 (2006)
[3] N. Khaneja et al., J. Magn. Reson. 172, 296-305 (2005)
[4] N. Timoney et al. quant-ph/0612106 (2006)
Yair Rezek, Hebrew University Jerusalem, Israel
Leonid Rybak, Lev Chuntonov, Andrey Gandman, Zohar Amitay,
Technion Haifa, Israel
NIR Femtosecond Control of Resonance-Mediated Generation of Coherent Broadband UV Emission
We use shaped near-infrared (NIR) excitation pulses to control the generation of coherent broadband ultraviolet (UV) radiation in an atomic resonance-mediated (2+1) three-photon excitation. The intensity and phase of each UV spectral component UV are determined by the interferences between all the multi-photon excitation pathways that lead to the final excitation energy corresponding to UV. There is a manifold of such pathways due to broad spectral bandwidth of the NIR femtosecond pulse. Thus, by shaping the driving NIR pulse, one can control the yield and shape of the emitted UV pulse. The resonance-mediated nature of the process allows for much higher degree of control over the UV emission, as compared to a non-resonant excitation. Experimental and theoretical results are presented for phase controlling the total yield of the UV emission in atomic sodium (Na) [1]. The corresponding excitation scheme is shown of Fig. 1. Based on our confirmed understanding, we also present a new simple scheme for producing shaped femtosecond pulses in the UV/VUV spectral range.
[1] L.Rybak, L. Chuntonov, A. Gandman, N. Shakour, and Z. Amitay, http://arxiv.org/abs/arXiv:0710.1226
Pablo Sanchez Moreno, Rosario González-Férez, Peter Schmelcher,
Universidad Granada
Molecular Rotational Dynamics in Nonadiabatically Switching
Homogeneous Electric Fields
We investigate the rotational dynamics of heteronuclear diatomic molecules
possessing a $^1\Sigma^+$ electronic ground state exposed to a strong
external time-dependent homogeneous electric field. The switching on and
off of the electric field is performed by exponential functions. Due to
the large absolute value of its permanent electric dipole moment as well
as the availability of the corresponding potential energy curve [1] and
electric dipole moment function [2], as well as its current interest we
focus on the LiCs molecule. We analyze the orientation and hybridization
of the angular motion, together with the population of pendular and
rotational states in the constant field and field-free regimes, as the
switching times are modified. We concentrate on the rovibrational ground
state as initial wave packet and on the regime of maximal field strengths
F=51.4-514 kV/cm. The switching times are taken in the interval from 800
fs to 800 ps, which covers the time regime between short laser pulse
duration and switching dc-fields. The exact results are compared with
those of an N-mode approach to the rotational dynamics derived within the
effective rotor approximation [3]. We demonstrate that it is possible to
predict in a robust way the amount of pendular states or partial waves
needed to properly describe the rotational dynamics in the constant field
and final field-free regimes, respectively. However, we show that once the
field is off the specific contribution of a certain rotational level is
rather sensible to the characteristic of the process, especially to the
switching on and off times. The final wave packet shows a wide variety of
localization and orientation phenomena arranged in characteristic
patterns, which alternate between two angular hemispheres and are periodic
in time.
[1] P. Staanum, A. Pashov, H. Knöckel, and E. Tiemann, Phys. Rev. A 75,
042513 (2007).
[2] M. Aymar and O. Dulieu, J. Chem. Phys. 122, 204302, (2005).
[3] R. Gonzalez Ferez and P. Schmelcher, Phys. Rev. A 69, 023402 (2004).
[4] P. Sanchez-Moreno, R. Gonzalez-Ferez, and P. Schmelcher, accepted PRA
(2007).
Kilian Singer, W. Schnitzler, N. M. Linke, J. Eble F. Schmidt-Kaler,
Universität Ulm, Germany
Experimental demonstration of a deterministic single ion source with an expected implantation resolution of a few nm
We have realized a universal deterministic single ion
source on the basis of an ion trap applicable to a wide range of
elements and molecules[1]. Initially, ultra cold Ca
ion crystals are trapped within a segmented linear trap. Those
ions are then deterministically extracted and shot into a detector
at a distance of 25 cm from the trap. With single ions, more than
90% of these extractions were successful. The kinetic energy
distribution of the ions amounts to less than 0.1%. We have also
demonstrated the extraction of mixed crystals containing other
dopant ions. For the implantation with nm precision, we plan to
utilize an electrostatic Einzel-lens to further improve the
spatial resolution of the extracted ions. These can then be used
to generate color centers in diamond for optical detection or to
implant P into Si. Both systems provide the foundation for the
realization of a solid state quantum computer [2,3]. In addition,
the electrical properties of semiconductor devices can be greatly
enhanced by the deterministic implantation of single ions [4].
[1] J. Meijer et. al., Appl. Phys. A 83, 321 (2006).
[2] F. Jelezko et. al., Phys. Rev. Lett. 93, 130501 (2004).
[3] B. E. Kane, Nature 393, 133 (1998).
[4] T. Shinada et. al., Nature 437, 1128 (2005)
Haim Suchowski, Thomas Polack, and David J. Tannor,
Weizmann Institute, Israel
Uncontrollable quantum systems: Connectivity, Irreducibility and Dynamical symmetries
It is well-known that a finite-dimensional quantum system is controllable if the Lie algebra of its generators has full rank. When the rank of the algebra is not full, there is a rich mathematical and physical structure that to date has been analyzed only in special cases.
We show that uncontrollable systems can be classified into reducible and irreducible ones. We argue that irreducibility is a more general criteria than connectivity, applying to degenerate as well as non-degenerate systems. We give an example from 3-level systems, and then extend this to general multi-level systems.
I.Tikhonenkov and A. Vardi,
Ben-Gurion University, Beer-Sheva, Israel
Confinement controlled dissociation of a molecular BEC
We study the effect of tight confinement on the collective, stimulated dissociation of molecular Bose-Einstein condensates (BECs) into boson constituents. In contrast to thermal reactions where outcomes are set solely by local variables, the long coherence length in this stimulated process implies that global length-scales can become crucially important. When the characteristic trap size is small with respect to the resonance healing length, confinement leads to the elimination of unstable dissociation modes and thereby to the stabilization of the condensate. This effect is analogous to the stabilization of attractively-interacting BECs against collapse due to the trap potential. The shape of the condensate affects the critical Feshbach coupling frequency. Both single-channel [1] and two-channel [2] dissociation processes were considered, suggesting the possibility to control coherent dissociation by manipulation of the size and shape of the trapping potentials.
References
[1]I. Tikhonenkov and A. Vardi, Phys. Rev. Lett. 98, 080403 (2007).
[2] I. Tikhonenkov and A. Vardi, J. Phys. B 40, S299 (2007).
Fabian Weise,
Andrea Merli, Frauke Eimer, Sascha Birkner, Franziska Sauer, Stefan M. Weber,
Ludger Wöste, Albrecht Lindinger, Wenzel Salzmann, Terry Mullins,
Simone Götz, Judith Eng, Magnus Albert, Roland Wester, Matthias
Weidemüller,
Freie Universität Berlin, & Universität Freiburg, Germany
Control of ultracold rubidium with shaped femtosecond laser pulses
By applying femtosecond laser pulse shaping techniques on ultracold gases, a next step in atomic and molecular physics is taken. So far, this emerging field is mainly treated in theory e.g. proposing photoassociation of ultracold atoms [1] or photostabilization [2] of ground state molecules.
We present experiments on ultracold rubidium in a magneto-optical trap:
In a closed loop experiment, the multi-photon ionization of Rb_2 is optimized using a parametric evolutionary algorithm. The result is approved by a systematic investigation of the relevant frequency components and allows to assign the transitions to certain electronic states [3].
In a pump probe scheme, the photoassociation process is investigated. Molecules are produced in their first electronically excited state by a pump, ionized by a probe pulse and mass selectively detected. The pump pulse is shaped with a frequency filter to avoid trap loss due to atomic resonances.
The ion signal shows oscillatory dynamics, caused by coherent interactions of molecular electronic dipole with the electric field. The observed characteristic structure is simulated by quantum dynamical calculations, which provide detailed insight in the underlying processes [4].
References
[1] C. P. Koch, R. Kosloff, and F Masnou-Seeuws, Phys. Rev. A 73, 043409 (2006)
[2] B. Schäfer-Bung, R. Mitric, and V. Bonacic-Koutecky, J. Phys. B: At. Mol. Opt. Phys. 39 S1043 (2006)
[3] F. Weise, S. Birkner, A. Merli, S. M. Weber, F. Sauer, L. Wöste, A. Lindinger, W. Salzmann, T. Mullins, J. Eng, M. Albert, R. Wester, and M. Weidemüller, Phys. Rev. A 76, 063404 (2007)
[4] W. Salzmann, T. Mullins, J. Eng, M. Albert, R. Wester, M. Weidemüller,
A. Merli, S. M. Weber, F. Sauer, M. Plewicki, F. Weise, L. Wöste, and A. Lindinger, Phys. Rev. Lett., submitted
)
or Christiane Koch.