Can a single-pulse standing wave induce chaos in atomic motion?

Abstract

Time-dependent Hamiltonian dynamics exhibit a wide range of novel effects in both classical and quantum domains [1,2]. Possibly the simplest time-dependent potential is the turning on and off of an interaction, though even here our intuition is clear only for the two extreme cases of fast passage and adiabatic interactions. Since the majority of cases fall between these two limits, it is important to develop a clear understanding and simple physical pictures at intermediate time scales. We show that when the interaction is nonlinear, the mere act of turning on and off a potential in this intermediate regime can lead to classical chaos. Further, we provide a clean experimental demonstration of the classical mechanism of resonance overlap [3 ‐ 5] which leads to classically diffusive growth. This general problem is posed in the context of atom optics with ultracold atoms. The nonlinear interaction is a single pulse of a one-dimensional standing wave of light. This type of time-dependent interaction is ubiquitous and occurs, for example, whenever an atomic beam passes through a standing wave of light. The starting point for this discussion is the model of a two level atom (transition frequency v0) interacting with a standing wave of near-resonant light (frequency vL) which is turned on and off with a time-dependent function fstd. For sufficiently large detuning dL › v0 2v L(relative to the natural linewidth), the excited state amplitude can be adiabatically eliminated [6], leading to a Hamiltonian for the ground state H › p 2 y2M 2 s ¯ hVeffy8df std cos2kLx.