Signatures of quantum stability in a classically chaotic system

The relationship between the behaviour of classical and quantum systems, and how macroscopic classical phenomena originate in the quantum regime, remain subjects of dispute [1]. The issues involved are particularly marked for quantum versions of classically chaotic systems [2]. Experimental investigations of such systems began with studies of microwavedriven hydrogen [3]; subsequent work has also centred on microwave cavities [4], mesoscopic solid-state systems [5], and atom optics [6], the approach we adopt. In this Letter we consider the quantum δ-kicked accelerator [7, 8, 9], a δ-kicked rotor with an additional static linear potential. The δ-kicked rotor is one of the most extensively investigated systems in chaotic dynamics [10], and is equivalent to a free particle s ubjected periodically to instantaneous momentum kicks from a sinusoidal potential. Quantum mechanically, the effect of these kicks is to diffract the particles’ constituent de Bro glie waves into a series of discrete momentum states. In the δkicked accelerator, the linear potential modifies the chaot ic classical dynamics only slightly, yet can radically change the quantum behaviour. The phases accumulated between consecutive kicks by the momentum states are altered, leading to the creation of quantum accelerator modes [7, 8, 9]. We realize quantum δ-kicked accelerator dynamics in laser-cooled cesium atoms by the application of short pulses of a vertical standing wave of off-resonant laser light, which constitut es a sinusoidal potential; gravity provides the linear potent ial. Quantum accelerator modes, absent in the analogous classical dynamics, are observed and are characterized by a linear (with kick number) momentum transfer to a substantial fraction (∼ 20%) of the atoms. If coherent, this efficient momentum transfer promises applications in atom interferometry [11]. In this Letter we use a Ramsey-type interference experiment [12] to show that quantum accelerator modes do preserve coherence. We then relate the Ramsey fringe contrast to the fidelity f [13]; by a numerical analysis, we link the behaviour of f to the phase space structure of the δ-kicked accelerator in a pseudoclassical limit recently proposed by Fishman et al. [14]. Finally we explain differences in the observed fringe visibilities by examining the effect of the experime ntal range of kicking strengths.