We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nanometers excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chain of coherent micron-size Mach-Zehnder interferometers at the exit of which we get essentially a wave packet with a negative momentum, a result opposite to the prediction of classical physics.

The dynamical transition of an atomic Bose-Einstein condensate from a spatially periodic state to a staggered state with alternating sign in its wavefunction is experimentally studied using a onedimensional phase modulated optical lattice. We observe the crossover from quantum to thermal fluctuations as the triggering mechanism for the nucleation of staggered states. In good quantitative agreement with numerical simulations based on the truncated Wigner method, we experimentally investigate how the nucleation time varies with the renormalized tunneling rate, the atomic density, and the driving frequency. The effective inverted energy band in the driven lattice is identified as the key ingredient which explains the emergence of gap solitons as observed in numerics and the possibility to nucleate staggered states from interband excitations as reported experimentally.

We report on a new method to calibrate the depth of an optical lattice. It consists in triggering the intrasite dipole mode of the cloud by a sudden phase shift. The corresponding oscillatory motion is directly related to the intraband frequencies on a large range of lattice depths. Remarkably, for a moderate displacement, a single frequency dominates this oscillation for the zeroth and first order interference pattern observed after a sufficiently long time-of-flight. The method is robust against atom-atom interactions and the exact value of the extra external confinement of the initial trapping potential.

Using a blue-detuned laser, shaped into a nearly Laguerre-Gaussian (LG) donut mode, we channel atoms exiting a two-dimensional magneto-optical trap (2D-MOT) over a 30 cm distance. Compared to a freely propagating beam, the atomic flux (∼10(10) at/s) is conserved whereas the divergence is reduced from 40 to 3 mrad. So, 30 cm far the 2D-MOT exit, the atomic beam has a 1 mm diameter and the atomic density is increased by a factor of ∼200. The LG-channeled-2D-MOT has been studied versus the order of the LG mode (from 2 to 10) and versus the laser-atom frequency detuning (from 2 to 120 GHz).

We investigate experimentally a Bose Einstein condensate placed in a 1D optical lattice whose phase or amplitude is modulated in a frequency range resonant with the first bands of the band structure. We study the combined effect of the strength of interactions and external confinement on the 1 and 2-phonon transitions. We identify lines immune or sensitive to atom-atom interactions. Experimental results are in good agreement with numerical simulations. Using the band mapping technique, we get a direct access to the populations that have undergone n-phonon transitions for each modulation frequency.

We investigate a Bose Einstein condensate held in a 1D optical lattice whose phase undergoes a fast oscillation using a statistical analysis. The averaged potential experienced by the atoms boils down to a periodic potential having the same spatial period but with a renormalized depth. However, the atomic dynamics also contains a micromotion whose main features are revealed by a Kolmorogov-Smirnov analysis of the experimental momentum distributions. We furthermore discuss the impact of the micromotion on a quench process corresponding to a proper sudden change of the driving amplitude which reverses the curvature of the averaged potential.

We report on a generic cooling technique for atoms trapped in optical lattices. It consists in modulating the lattice depth with a proper frequency sweeping. This filtering technique removes the most energetic atoms, and provides with the onset of thermalization a cooling mechanism reminiscent of evaporative cooling. However, the selection is here performed in quasi-momentum space rather than in position space. Interband selection rules are used to protect the population with a zero quasi-momentum, namely the Bose Einstein condensate. Direct condensation of thermal atoms in an optical lattice is also achieved with this technique. It offers an interesting complementary cooling mechanism for quantum simulations performed with quantum gases trapped in optical lattices.Atomic and molecular physics have been strongly impacted by cooling techniques [1,2]. Laser cooling has triggered a boost of research activities to reach very low temperatures [3][4][5] and therefore to improve the control on the external degrees of freedom of atoms, with many applications in metrology [6,7]. Laser cooling down to degeneracy has been demonstrated only recently [8,9]. Those cooling techniques are tailor-made for a given species. Lasers shall indeed address specific atomic lines. Furthermore, the temperature achieved with laser cooling is strongly dependent on the width of the excited state of the considered cycling transition [10]. In contrast, evaporative cooling is a much more generic technique. The filtering technique of the most energetic atoms can be easily transposed from one species to another, and the cooling occurs through the re-thermalization of the atomic cloud. Only the cooling rate depends on the species. Evaporative cooling has originally been envisioned for hydrogen atoms for which laser cooling is not expected to be efficient [11], and successfully implemented on lasercooled alkali atoms to reach quantum degeneracy in nondissipative traps [12][13][14].In this article, we report on a generic cooling method inspired by evaporative cooling but adapted to atoms trapped in an optical lattice. It is indeed of upmost importance to find methods to decrease the temperature of atoms trapped in optical lattices since such systems are currently used to perform quantum simulations, and temperature may constitute an obstacle for some challenging experiments [19,20]. The advantage of optical lattices lies in their tunability: the geometry of the lattices can be easily modified, they can be made spin dependent and can be readily modulated in phase and amplitude. This latter possibility is at the origin of the so-called Floquet engineering which opens up interesting perspectives for generating effective hamiltonians and engineered artificial gauge fields [21,22].The method put forward in this article exploits interband transitions excited by amplitude modulation for non-zero quasi-momentum [23]. The modulation frequency is scanned through all the values of the considered interband transition. The chosen excited band obeys a selection ru...

We investigate experimentally a Bose Einstein condensate placed in a 1D optical lattice whose phase is modulated at a frequency large compared to all characteristic frequencies. As a result, the depth of the periodic potential is renormalized by a Bessel function which only depends on the amplitude of modulation, a prediction that we have checked quantitatively using a careful calibration scheme. This renormalization provides an interesting tool to engineer in time optical lattices. For instance, we have used it to perform simultaneously a sudden π-phase shift (without phase residual errors) combined with a change of lattice depth, and to study the subsequent out-of-equilibrium dynamics.