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We report on measurements of dynamical suppression of interwell tunneling of a Bose-Einstein condensate (BEC) in a strongly driven optical lattice. The strong driving is a sinusoidal shaking of the lattice corresponding to a time-varying linear potential, and the tunneling is measured by letting the BEC freely expand in the lattice. The measured tunneling rate is reduced and, for certain values of the shaking parameter, completely suppressed. Our results are in excellent agreement with theoretical predictions. Furthermore, we have verified that, in general, the strong shaking does not destroy the phase coherence of the BEC, opening up the possibility of realizing quantum phase transitions by using the shaking strength as the control parameter.

The measurements of the hyperfine structure of free, naturally occurring, alkali atoms are reviewed. The experimental methods are discussed, as are the relationships between hyperfine structure data and other atomic constants.

Accurately controlling a quantum system is a fundamental requirement in quantum information processing and the coherent manipulation of molecular systems. The ultimate goal in quantum control is to prepare a desired state with the highest fidelity allowed by the available resources and the experimental constraints. Here we experimentally implement two optimal high-fidelity control protocols using a two-level quantum system comprising Bose-Einstein condensates in optical lattices. The first is a short-cut protocol that reaches the maximum quantum-transformation speed compatible with the Heisenberg uncertainty principle. In the opposite limit, we realize the recently proposed transitionless superadiabatic protocols in which the system follows the instantaneous adiabatic ground state nearly perfectly. We demonstrate that superadiabatic protocols are extremely robust against control parameter variations, making them useful for practical applications

We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a trans-disciplinary perspective (astrophysics, nuclear physics, plasmas physics, metallic clusters, hydrodynamics,...) with a special emphasis on Bose-Einstein condensates.

We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well depth, Bloch oscillations were observed. Reducing the potential depth further, Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied and used as a probe for the effective potential resulting from mean-field interactions as predicted by Choi and Niu [Phys. Rev. Lett. 82, 2022 (1999)]. The effective potential was measured for various condensate densities and trap geometries, yielding good qualitative agreement with theoretical calculations.

We present a new laser-cooling scheme based on velocity-selective optical pumping of atoms into a nonabsorbing coherent superposition of states. This method has allo~ed us to achieve transverse cooling of metastable He atoms to a temperature of 2 pK, lower than both the usual Doppler cooling limit (23 pK) and the one-photon recoil energy (4 pK). The corresponding de Broglie wavelength (1.4 pm) is larger than the atomic-transition optical wavelength. PACS numbers: 32.80.Pj, 42.50.Vk The lowest temperature T which can be achieved by the usual laser-Doppler-cooling method is given, for a two-level atom, by kaT/2 = hI/4, where I is the spontaneous-emission rate from the excited atomic state (for Na, T=240 pK). ' In order to reach lower temperatures, proposals based on Raman two-photon processes in a three-level atom have been presented, ' but the efficiency of Raman cooling has not yet been demonstrated. Recently, surprisingly low temperatures (around 40 pK) have been measured for sodium and tentatively interpreted in terms of a new friction mechanism.The recoil energy (hk) /2M for an atom with mass M emitting a photon with momentum hk represents another landmark in the energy scale for laser cooling. It has been suggested that optical pumping in translation space might be used to cool the translational degrees of freedom below this so-called recoil limit, by velocity-selective recycling in a trap. In this Letter, we present a mechanism of laser cooling below the onephoton recoil energy, based on optical pumping of both internal and translational atomic degrees of freedom.This velocity-selective process is based on coherent trapping of atomic populations and has allowed us to achieve a one-dimensional cooling of He atoms in the triplet metastable state down to a temperature of about 2 pK. This temperature is lower than both the Doppler cooling limit (23 pK for 1D cooling) and the one-photon recoil energy (4 pK).Our scheme involves a closed three-level A configuration where two degenerate ground Zeeman sublevels g( m = + 1) are coupled to an excited level eo (m =0) by two counterpropagating a~and o -laser beams with the same frequency coL and the same intensity (solid lines of Fig. 1). For an atom at rest, two-photon Raman processes give rise to a nonabsorbing coherent superposition of g+ and g-. If the atom is moving along Oz, the Raman resonance condition is no longer fulfilled as a consequence of opposite Doppler shifts on the two counterpropagating laser beams. This simple argument explains how the phenomenon of coherent population trapping (a) 4He e, e=2 P, 3 (b) g=2 3s, FIG. l. (a) Two counterpropagating rx+ and cr-polarized laser beams interact with He atoms on the 2 Sl-2 Pl transition. (b) The Zeeman sublevels, and some useful ClebschGordan coefficients. Since the eo go transition is forbidden, all atoms are pumped into g~and g -after a few fluorescence cycles. These two levels are coupled only to eo, and a closed three-level A configuration is realized (solid lines).can be velocity selective for appropriate l...

By moving the pivot of a pendulum rapidly up and down one can create a stable position with the pendulum's bob above the pivot rather than below it [1]. This surprising and counterintuitive phenomenon is a widespread feature of driven systems and carries over into the quantum world. Even when the static properties of a quantum system are known, its response to an explicitly timedependent variation of its parameters may be highly nontrivial, and qualitatively new states can appear that were absent in the original system. In quantum mechanics the archetype for this kind of behaviour is an atom in a radiation field, which exhibits a number of fundamental phenomena such as the modification of its g-factor in a radiofrequency field [2] and the dipole force acting on an atom moving in a spatially varying light field [3]. These effects can be successfully described in the so-called dressed atom picture [4]. Here we show that the concept of dressing can also be applied to macroscopic matter waves [5], and that the quantum states of "dressed matter waves" can be coherently controlled. In our experiments we use BoseEinstein condensates in driven optical lattices and demonstrate that the many-body state of this system can be adiabatically and reversibly changed between a superfluid and a Mott insulating state [6, 7, 8] by varying the amplitude of the driving. Our setup represents a versatile testing ground for driven quantum systems, and our results indicate the direction towards new quantum control schemes for matter waves.An atom in a radiation field can be described in the dressed atom picture [4] (or in equivalent approaches using, e.g., Floquet quasienergy states) in which the modified properties of the driven system arise from "dressing" the atom's electronic states with the photons of the radiation field. This concept can also be applied to macroscopic matter waves in driven periodic potentials [5], where the "dressing" is provided by the oscillatory motion of the lattice potential. In analogy to the dressed atom picture, such "dressed matter waves" can exhibit new properties absent in the original system and thus allow enhanced control of its quantum states. Here we demonstrate that matter waves can be adiabatically transferred into a well-defined Floquet quasienergy state of a driven periodic potential while preserving their quantum coherence.Cold atoms in optical lattices [7] can be described in the Bose-Hubbard model by the parameter U/J, where J is the hopping term relating to tunneling between adjacent sites, and U is the on-site interaction energy (see Fig. 1a). When U/J is small, tunneling dominates and the atoms are delocalized over the lattice, whereas a large value means that the inter- action term is large compared to J and phase coherence is lost through the formation of number-squeezed states with increased quantum phase fluctuations. At a critical value of U/J the system undergoes a quantum phase transition to a Mott insulator state. Using optical lattices one can tune U/J by changing the lattice dept...