We report on the efficient design of quantum optimal control protocols to manipulate the motional states of an atomic Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Our protocols operate on the momentum comb associated with the lattice. In contrast to previous works also dealing with control in discrete and large Hilbert spaces, our control schemes allow us to reach a wide variety of targets by varying a single parameter, the lattice position. With this technique, we experimentally demonstrate a precise, robust and versatile control: we optimize the transfer of the BEC to a single or multiple quantized momentum states with full control on the relative phase between the different momentum components. This also allows us to prepare the BEC in a given eigenstate of the lattice band structure, or superposition thereof.

The field of quantum simulation, which aims at using a tunable quantum system to simulate another, has been developing fast in the past years as an alternative to the all-purpose quantum computer. So far, most efforts in this domain have been directed to either fully regular or fully chaotic systems. Here, we focus on the intermediate regime, where regular orbits are surrounded by a large sea of chaotic trajectories. We observe a quantum chaos transport mechanism, called chaos-assisted tunneling, that translates in sharp resonances of the tunneling rate and provides previously unexplored possibilities for quantum simulation. More specifically, using Bose-Einstein condensates in a driven optical lattice, we experimentally demonstrate and characterize these resonances. Our work paves the way for quantum simulations with long-range transport and quantum control through complexity.

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 the production of s-wave scattering halos from collisions between the momentum components of a Bose–Einstein condensate released from an optical lattice. The lattice periodicity translates in a momentum comb responsible for the quantization of the halos’ radii. We report on the engineering of those halos through the precise control of the atom dynamics in the lattice: we are able to specifically enhance collision processes with given center-of-mass and relative momenta. In particular, we observe quantized collision halos between opposite momenta components of increasing magnitude, up to 6 times the characteristic momentum scale of the lattice.

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...

In quantum gases, two-body interactions are responsible for a variety of instabilities that depend on the characteristics of both trapping and interactions. These instabilities can lead to the appearance of new structures or patterns. We report on the Floquet engineering of such a parametric instability, on a Bose–Einstein condensate held in a time-modulated optical lattice. The modulation triggers a destabilization of the condensate into a state exhibiting a density modulation with a new spatial periodicity. This new crystal-like order, which shares characteristic correlation properties with a supersolid, directly depends on the modulation parameters: The interplay between the Floquet spectrum and interactions generates narrow and adjustable instability regions, leading to the growth, from quantum or thermal fluctuations, of modes with a density modulation noncommensurate with the lattice spacing. This study demonstrates the production of metastable exotic states of matter through Floquet engineering and paves the way for further studies of dissipation in the resulting phase and of similar phenomena in other geometries.

We investigate the production of s−wave scattering halos from collisions between the momentum components of a Bose-Einstein condensate released from an optical lattice. The lattice periodicity translates in a momentum comb responsible for the quantization of the halos' radii. We report on the engineering of those halos through the precise control of the atom dynamics in the lattice: we are able to specifically enhance collision processes with given center-of-mass and relative momenta. In particular, we observe quantized collision halos between opposite momenta components of increasing magnitude, up to 6 times the characteristic momentum scale of the lattice.