Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations

Fractional resonances in the atom-optical delta-kicked accelerator

We consider resonant dynamics in a dilute atomic gas falling under gravity through a periodically pulsed standing-wave laser field. Our numerical calculations are based on a Monte Carlo method for an incoherent mixture of noninteracting plane waves, and show that quantum resonances are highly sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. For particular values of the atomic acceleration, we observe fractional resonances. We investigate the effect of the initial atomic momentum width on the fractional resonances, and quantify the sensitivity …

Phase Noise in the Delta Kicked Rotor: From Quantum to Classical

We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, epsilon-classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamica…

Quantum resonances and decoherence for delta-kicked atoms

The quantum resonances occurring with delta-kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analyzed in detail. Exact results about the momentum distribution at exact resonance are established, both in the case of totally coherent dynamics and in the case when decoherence is induced by Spontaneous Emission. A description of the dynamics when the kicking period is close to, but not exactly at resonance, is derived by means of a quasi-classical approximation where the detuning from exact resonance plays the role of the Planck constant. In this way scaling …

Classical diffusion in double-delta-kicked particles

We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2δ$-KP). Recent experimental studies with cold atoms implied an underlying classical diffusion of type very different from the well-known paradigm of Hamiltonian chaos, the Standard Map. The kicks in each pair are separated by a small time interval $ε\ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2δ$-KP is partitioned into momentum `cells' partially separated by momentum-trapping regions where…

Quantum resonant effects in the delta-kicked rotor revisited

We review the theoretical model and experimental realization of the atom optics $δ-$kicked rotor (AOKR), a paradigm of classical and quantum chaos. We have performed a number of experiments with an all-optical Bose-Einstein condensate (BEC) in a periodic standing wave potential in an AOKR system. We discuss results of the investigation of the phenomena of quantum resonances in the AOKR. An interesting feature of the momentum distribution of the atoms obtained as a result of short pulses of light, is the variance of the momentum distribution or the kinetic energy $<p^{2}>/2m$ in units of the re…

在周期性踢动超冷气体中观测多体动力学退局域化

Observation of Many-body Dynamical Delocalization in a Kicked Ultracold Gas

本文通过实验研究周期性踢动的一维相互作用超冷气体，观测到相互作用驱动的动力学退局域化和多体量子混沌，并发现其能量呈亚扩散增长，为理论困难的领域提供了新认识。

An accelerator mode based technique for studying quantum chaos

We experimentally demonstrate a method for selecting small regions of phase space for kicked rotor quantum chaos experiments with cold atoms. Our technique uses quantum accelerator modes to selectively accelerate atomic wavepackets with localized spatial and momentum distributions. The potential used to create the accelerator mode and subsequently realize the kicked rotor system is formed by a set of off-resonant standing wave light pulses. We also propose a method for testing whether a selected region of phase space exhibits chaotic or regular behavior using a Ramsey type separated field expe…

Subdiffusion in wave packets with periodically kicked interactions

We study the quantum dynamics of a peculiar driven system, a Bose gas subjected to periodically kicked interactions. In the limit of infinitely short kicks, this system was recently shown to exhibit a fast exponential spreading of the wave function. Here we examine this problem for kicks or arbitrary duration and show that, in this case, the spreading is not exponential but rather subdiffusive at long time. This phenomenon stems from the competition between the kinetic and interaction energies within the kicks, which is absent in the limit of delta kicks. Our analysis further shows that the br…

Spectral form factor in a minimal bosonic model of many-body quantum chaos

We study spectral form factor in periodically-kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pair-wise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show that for intermediate-range interactions, random phase approximation can be used to rewrite the spectral form factor in terms of a bi-stochastic many-body process generated by an effective bosonic Hamiltonian. In the particle-number conserving case, i.e., when pa…

Theory of 2$δ$-kicked Quantum Rotors

We examine the quantum dynamics of cold atoms subjected to {\em pairs} of closely spaced $δ$-kicks from standing waves of light, and find behaviour quite unlike the well-studied quantum kicked rotor (QKR). Recent experiments [Jones et al, {\em Phys. Rev. Lett. {\bf 93}, 223002 (2004)}] identified a regime of chaotic, anomalous classical diffusion. We show that the corresponding quantum phase-space has a cellular structure, arising from a unitary matrix with oscillating band-width. The corresponding eigenstates are exponentially localized, but scale with a fractional power, $L \sim \hbar^{-0.75…

$2δ$-Kicked Quantum Rotors: Localization and `Critical' Statistics

The quantum dynamics of atoms subjected to pairs of closely-spaced $δ$-kicks from optical potentials are shown to be quite different from the well-known paradigm of quantum chaos, the singly-$δ$-kicked system. We find the unitary matrix has a new oscillating band structure corresponding to a cellular structure of phase-space and observe a spectral signature of a localization-delocalization transition from one cell to several. We find that the eigenstates have localization lengths which scale with a fractional power $L \sim \hbar^{-.75}$ and obtain a regime of near-linear spectral variances whi…