Spatial gaps correspond to the projection in position space of the gaps of a periodic structure whose envelope varies spatially. They can be easily generated in cold atomic physics using finite-size optical lattice, and provide a new kind of tunnel b
arriers which can be used as a versatile tool for quantum devices. We present in detail different theoretical methods to quantitatively describe these systems, and show how they can be used to realize in one dimension matter wave Fabry-Perot cavities. We also provide experimental and numerical results that demonstrate the interest of spatial gaps structures for phase space engineering. We then generalize the concept of spatial gaps in two dimensions and show that this enables to design multiply connected cavities which generate a quantum dot structure for atoms or allow to construct curved wave guides for matter waves. At last, we demonstrate that modulating in time the amplitude of the periodic structure offers a wide variety of possible atom manipulations including the control of the scattering of an incoming wave packet, the loading of cavities delimited by spatial gaps, their coupling by multiphonon processes or the realization of a tunable source of atoms. This large range of possibilities offered by space and time engineering of optical lattices demonstrates the flexibility of such band gap structures for matter wave control, quantum simulators and atomtronics.
We explore the manipulation in phase space of many-body wavefunctions that exhibit self-similar dynamics, under the application of sudden force and/or in the presence of a constant acceleration field. For this purpose, we work out a common theoretica
l framework based on the Wigner function. We discuss squeezing in position space, phase space rotation and its implications in cooling for both non-interacting and interacting gases, and time reversal operation. We discuss various optical analogies and calculate the role of spherical-like aberration in cooling protocols. We also present the equivalent of a spin-echo technique to improve the robustness of velocity dispersion reduction protocols.
We study the spreading of the wave function of a Bose-Einstein condensate accelerated by a constant force both in the absence and in the presence of atom-atom interactions. We show that, despite the initial velocity dispersion, the local velocity dis
persion defined at a given position downward can reach ultralow values and be used to probe very narrow energetic structures. We explain how one can define quantum mechanically and without ambiguities the different velocity moments at a given position by extension of their classical counterparts. We provide a common theoretical framework for interacting and non-interacting regimes based on the Wigner transform of the initial wave function that encapsulates the dynamics in a scaling parameter. In the absence of interaction, our approach is exact. Using a numerical simulation of the 1D Gross-Pitaevskii equation, we provide the range of validity of our scaling approach and find a very good agreement in the Thomas-Fermi regime. We apply this approach to the study of the scattering of a matter wave packet on a double barrier potential. We show that a Fabry-Perot resonance in such a cavity with an energy width below the pK range can be probed in this manner. We show that our approach can be readily transposed to a large class of many-body quantum systems that exhibit self-similar dynamics.
We have experimentally demonstrated a high level of control of the mode populations of guided atom lasers (GALs) by showing that the entropy per particle of an optically GAL, and the one of the trapped Bose Einstein condensate (BEC) from which it has
been produced are the same. The BEC is prepared in a crossed beam optical dipole trap. We have achieved isentropic outcoupling for both magnetic and optical schemes. We can prepare GAL in a nearly pure monomode regime (85 % in the ground state). Furthermore, optical outcoupling enables the production of spinor guided atom lasers and opens the possibility to tailor their polarization.
We report the transport of ultracold atoms with optical tweezers in the non-adiabatic regime, i.e. on a time scale on the order of the oscillation period. We have found a set of discrete transport durations for which the transport is not accompanied
by any excitation of the centre of mass of the cloud. We show that the residual amplitude of oscillation of the dipole mode is given by the Fourier transform of the velocity profile imposed to the trap for the transport. This formalism leads to a simple interpretation of our data and simple methods for optimizing trapped particles displacement in the non-adiabatic regime.
We report the achievement of an optically guided and quasi-monomode atom laser, in all spin projection states ($m_F =$ -1, 0 and $+1$) of F=1 in Rubidium 87. The atom laser source is a Bose-Einstein condensate (BEC) in a crossed dipole trap, purified
to any one spin projection state by a spin-distillation process applied during the evaporation to BEC. The atom laser is outcoupled by an inhomogenous magnetic field, applied along the waveguide axis. The mean excitation number in the transverse modes is $<n > = 0.65 pm 0.05$ for $m_F = 0 $ and $<n > = 0.8 pm 0.3$ for the low field seeker $m_F = -1$.
