Band-gap structures for matter waves

Abstract

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 finitesize optical lattice, and provide a new kind of tunnel barriers 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.

Routes towards the experimental observation of the large fluctuations due to chaos-assisted tunneling effects with cold atoms

“…For instance, the Landau-Zener transition through the gap of two adjacent energy bands of a periodic lattice is nothing but a tunnel effect in the reciprocal space [2]. These effective barriers can be transposed in real space (spatial gaps) by shaping the envelope of the lattice [3][4][5][6]. Similarly, it is well known that two zones of a classical phase space separated by an invariant manifold of a dynamical system cannot be connected classically.…”

Engineering momentum profiles of cold-atom beams

“…Other studies related to the engineering of atomic beams have focused on the outcoupling of atoms from a Bose-Einstein condensate [15][16][17] or on controlling the transmission of atoms with careful manipulation of an optical lattice [18][19][20]. In contrast, the current article proposes a method for engineering atomic beams by coupling a trapped gas of atoms to a combination of individually tuned lasers.…”

Distributed quasi-Bragg beam splitter in crossed atomic waveguides

“…We thus study the local band gap structure produced by the potential , using the method described in ref. 15 . With the potential of Eq.…”

“…In order to get a more analytical insight on the shape of the spatial gaps, it is instructive to extend the perturbative approach of ref. 15 , and calculate the energy borders of the spatial gaps in the limit of low lattice depth. For a higher order band gap, the second order for example, by using a three-modes approximation we obtain: where .…”