Nonlinear atom-opticalδ-kicked harmonic oscillator using a Bose-Einstein condensate

Abstract

We experimentally investigate the atom-optical delta-kicked harmonic oscillator for the case of nonlinearity due to collisional interactions present in a Bose-Einstein condensate. A Bose condensate of rubidium atoms tightly confined in a static harmonic magnetic trap is exposed to a one-dimensional optical standing-wave potential that is pulsed on periodically. We focus on the quantum anti-resonance case for which the classical periodic behavior is simple and well understood. We show that after a small number of kicks the dynamics is dominated by dephasing of matter wave interference due to the finite width of the condensate's initial momentum distribution.In addition, we demonstrate that the nonlinear mean-field interaction in a typical harmonically confined Bose condensate is not sufficient to give rise to chaotic behavior. The delta-kicked rotor is an extensively investigated system in the field of classical chaos theory. During the last decade great progress has been achieved in understanding quantum dynamics of a classically chaotic system using atom-optical techniques and cold atoms. From an experimental point of view, cold atoms in optical potentials [1,2,3,4,5] provide an ideal environment to explore quantum dynamics. To date, all experimental work has focused on linear atomic systems, (see, for example, [6,7,8,9] and references therein) where the quantum dynamics is stable due to the linearity of the Schrödinger equation. In stark contrast to the chaotic behavior of classical dynamics, the linear quantum systems exhibit anti-resonance (periodic motion), dynamical localization (quasi-periodic motion) or resonant dynamics [10,11].Recently, theoretical investigations have considered how the nonlinearity due to many-body (collisional) interactions in a Bose-Einstein condensate modifies the behavior of the atom-optical kicked rotor system, providing a route to chaotic dynamics. Gardiner et al. developed a theoretical formalism to treat the one-dimensional nonlinear kicked harmonic oscillator (a particular manifestation of the generic delta-kicked rotor) using GrossPitaevskii and Liouville-type equations to describe the dynamics of a Bose-Einstein condensate, and estimated the growth rate in the number of non-condensate particles [12]. Zhang et al. investigated the generalized quantum kicked rotor by considering a periodically kicked Bose condensate confined in a ring potential for the case of quantum anti-resonance [13]. As opposed to the familiar periodic behavior exhibited by a corresponding linear system, they predicted quasi-periodic variation in energy for a weak interaction strength and chaotic behavior for strong interactions.In this work we investigate the nonlinear delta-kicked harmonic oscillator by performing experiments on BoseEinstein condensates in a harmonic potential. A Bose condensate of rubidium atoms tightly confined in a static harmonic magnetic trap is exposed to a periodically pulsed one-dimensional optical standing-wave potential. Our focus is on the particular case of quantum antireso...

Number-conserving approach to a minimal self-consistent treatment of condensate and noncondensate dynamics in a degenerate Bose gas

“…We also note that such issues as potentially imperfectlybosonic quasiparticle operators are largely avoided if the initial system has a negligible non-condensate fraction, even if subsequent dynamics (for example investigations of chaotic dynamics [26,27,28,29,30,31,32,33,34,35,36,37]) can cause significant depletion [26,27,28], hence requiring the kind of self-consistent treatment presented here.…”

“…Two important situations where this may occur are: dynamics occurring at a (significant) finite temperature [25], of interest due to the unique possibility offered by dilute Bose-Einstein condensate experiments for quantitative tests of thermal field theories; and dynamics leading to dynamical instabilities in, and hence depletion of an initially low temperature condensate [26,27,28], such as may well occur in experiments [29,30,31] studying chaotic and quantum chaotic dynamics in Bose-Einstein condensates [32,33,34,35,36,37]. The desire to provide a relatively simple, consistent description of condensate and non-condensate dynamics motivates the work presented here, and a form of the approach we present was a key part in work carried out [38,39,40], to good agreement with experiment [25], in order to describe excitations at finite temperature of a dilute Bose-condensed gas.…”

Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?

“…In this work, however, we scan a different parameter than the one used in [12], which corresponded to quasimomentum. Here we use the kicking period τ as control parameter, which can be much better controlled in state-of-the-art experiments [10,14,17,18] than the initial value of momentum [11,18,27,28,29]. On the other hand, the use of τ confronts us with a new problem which is discussed in the following section.…”

“…Using atoms in the Bose-Einstein condensate phase as initial ensemble allows the experimentalist a much better control over the width of the quasimomentum distribution [35]. Values of ∆β 0.05 have been realised in this context [18,29,36]. Letting the condensate expand a little before the actual kicking evolution, allows one to reduce the atom-atom interactions to negligible values, with only slight changes in ∆β [36].…”

Generic superweak chaos induced by Hall effect

“…(3) with Eq. (4)], the quantized KHS should be experimentally realizable using atom-optics methods like the ordinary quantum kicked harmonic oscillator [26].…”