Quantum and classical dynamics of a Bose-Einstein condensate in a large-period optical lattice

Abstract

We experimentally investigate diffraction of a 87 Rb Bose-Einstein condensate from a 1D optical lattice. We use a range of lattice periods and timescales, including those beyond the Raman-Nath limit. We compare the results to quantum mechanical and classical simulations, with quantitative and qualitative agreement, respectively. The classical simulation predicts that the envelope of the time-evolving diffraction pattern is shaped by caustics: singularities in the phase space density of classical trajectories. This behavior becomes increasingly clear as the lattice period grows.

Analysis of Kapitza-Dirac diffraction patterns beyond the Raman-Nath regime

“…The presence of higher diffraction orders leads to population decays that are faster than those determined by the two-photon timescale in Eqs. (9) and (10). This is shown in inset (C) of Fig.…”

“…[10]). Note that in these equations, α is the pulse duration τ in units of the 2-photon recoil time τ…”

“…Originally predicted by Kapitza and Dirac [3] for electrons more than 75 years ago (and recently also observed for these [4]), it was first demonstrated in the 1980s with an atomic beam [5], and has since become a standard tool in atom interferometry for the coherent mixing of momentum modes [6,2]. The advent of Bose-Einstein condensates in the 1990s [7] has made it possible to directly observe the dynamics of matter-wave diffraction in time-of-flight images [8,9,10]. Moreover, the diffraction of condensate atoms from standing light waves finds applications in high-resolution spectroscopy [11] and metrology [12,13], and plays a fundamental role in superradiance [14,15].…”

“…the area of the applied pulse [5]. Outside the Raman-Nath regime, the diffraction dynamics exhibits collapses and revivals for constant interaction strength [8,9,10]. In this paper, we now specifically analyze the case of a pulsed interaction of variable duration but constant pulse area.…”

High Order Momentum States by Light Wave Scattering

“…7(d)), and the atomic number of each momentum state is possible to be read separately as N m (the momentum The lattice in our experiments is quite deep, so we concentrate on the short-pulse diffractions to avoid the de-coherence and heating effects of long pulses relevant for Bragg scattering. However, for more flexible momentum manipulation, our pulses are not so short as the Raman-Nath pulses (Huckans et al, 2009) used in previous works.…”