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arXiv:quant-ph/0506090 · Europhysics Letters (EPL)

Chaotic quantum decay in driven biased optical lattices

S Mossmann, C Schumann, H. J Korsch

Published Oct 18, 2005• 0 citations
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Abstract

Quantum decay in an ac driven biased periodic potential modeling cold atoms in optical lattices is studied for a symmetry broken driving. For the case of fully chaotic classical dynamics the classical exponential decay is quantum mechanically suppressed for a driving frequency ωin resonance with the Bloch frequency ω_B, qω=rω_B with integers q and r. Asymptotically an algebraic decay ~t^{-γ} is observed. For r=1 the exponent γagrees with $q$ as predicted by non-Hermitian random matrix theory for q decay channels. The time dependence of the survival probability can be well described by random matrix theory. The frequency dependence of the survival probability shows pronounced resonance peaks with sub-Fourier character.

DOI
10.1209/epl/i2005-10289-5

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Quantum decay in an ac driven biased periodic potential modeling cold atoms in optical lattices is studied for a symmetry broken driving. For the case of fully chaotic classical dynamics the classical exponential decay is quantum mechanically suppressed for a driving frequency ωin resonance with the Bloch frequency ω_B, qω=rω_B with integers q and r. Asymptotically an algebraic decay ~t^{-γ} is observed. For r=1 the exponent γagrees with qqq as predicted by non-Hermitian random matrix theory for q decay channels. The time dependence of the survival probability can be well described by random matrix theory. The frequency dependence of the survival probability shows pronounced resonance peaks with sub-Fourier character.
Quantum decay in an ac driven biased periodic potential modeling cold atoms in optical lattices is studied for a symmetry broken driving. For the case of fully chaotic classical dynamics the classical exponential decay is quantum mechanically suppressed for a driving frequency omega in resonance with the Bloch frequency omega_B, q omega = r omega_B with integers q and r. Asymptotically an algebraic decay ~ t^{-gamma} is observed. For r=1 the exponent gamma agrees with q as predicted by non-Hermitian random matrix theory for q decay channels. The time dependence of the survival probability can be well described by random matrix theory. The frequency-dependence of the survival probability shows pronounced resonance peaks with sub-Fourier character.
We predict and numerically observe strong periodic orbit effects in the properties of weakly open quantum systems with a chaotic classical limit. Antiscars lead to a large number of exponentially narrow isolated resonances when the single-channel (or tunneling) opening is located on a short unstable orbit of the closed system; the probability to remain in the system at long times is thus exponentially enhanced over the random matrix theory prediction. The distribution of resonance widths and the probability to remain are quantitatively given in terms of only the stability matrix of the orbit on which the opening is placed. The long-time remaining probability density is nontrivially distributed over the available phase space; it can be enhanced or suppressed near orbits other than the one on which the lead is located, depending on the periods and classical actions of these other orbits. These effects of the short periodic orbits on quantum decay rates have no classical counterpart, and first appear on times scales much larger than the Heisenberg time of the system. All the predictions are quantitatively compared with numerical data.
The dynamics of cold Bose atoms in driven tilted optical lattices is analyzed focusing on destruction of Wannier-Stark localization and the phenomenon of band collapse. It is argued that an understanding of the experimental results requires thorough account for interaction effects. These are suppression of the ballistic spreading of atoms for resonant driving (a multiple of the driving frequency coincides with the Bloch frequency) and unbounded sub-diffusive spreading of atoms for off-resonant driving.
We perform echo spectroscopy on ultracold atoms in atom-optics billiards to study their quantum dynamics. The detuning of the trapping laser is used to change the "perturbation", which causes a decay in the echo coherence. Two different regimes are observed: first, a perturbative regime in which the decay of echo coherence is nonmonotonic and partial revivals of coherence are observed in contrast with the predictions of random matrix theory. These revivals are more pronounced in traps with mixed dynamics as compared to traps where the dynamics is fully chaotic. Next, for stronger perturbations, the decay becomes monotonic and independent of the strength of the perturbation. In this regime no clear distinction can be made between chaotic traps and traps with mixed dynamics.
Quantum systems upon interaction with the environment undergo decoherence or decay towards classical states. The dynamics of the quantum coherence at the borderline between quantum and classical world is not fully understood yet. The quantum coherence is generally known to exponentially decay in time so that macroscopic quantum superpositions are not sustained for a long time. In many practical applications, it is necessary to maintain quantum coherences for as long as possible. In this work, we use the experimental test-bed of cold atoms in a pulsed one-dimensional optical lattice to realise an atom-optics kicked rotator. We manipulate the waiting time between consequent kicks in this system by taking it as a random variable from a L\'{e}vy distribution. In this noisy scenario, we show that coherence can be made to decay slower than an exponential form. This manifests in the form of quantum subdiffusion that can be controlled through the L\'{e}vy exponent. The experimental results are in good agreement with the analytical expressions and numerical simulations for the mean energy growth of atom-optics kicked rotor.