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arXiv:2503.02517 · Physical Review A

Coherent backscattering and coherent forward-scattering effects in variations of the random quantum kicked rotor

Hugo Thomas, Julien Hébraud, Bertrand Georgeot, Gabriel Lemarié, Christian Miniatura, Olivier Giraud

Published Jun 5, 2025• 1 citation
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Abstract

The authors investigate coherent interference effects in the quantum kicked rotor, a model of quantum chaos. They find that the signatures of these effects are unexpectedly sensitive to the initial time of observation, and reveal that this is due to a nontrivial, oscillatory background. By modeling and subtracting this background, they recover consistent contrast profiles, providing an insight into the accurate interpretation of cold atom experiments.

DOI
10.1103/physreva.111.063302

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•Jan 1, 2002•2 citations
The authors investigate coherent interference effects in the quantum kicked rotor, a model of quantum chaos. They find that the signatures of these effects are unexpectedly sensitive to the initial time of observation, and reveal that this is due to a nontrivial, oscillatory background. By modeling and subtracting this background, they recover consistent contrast profiles, providing an insight into the accurate interpretation of cold atom experiments.
Quantum-classical correspondence in many-dimensional quantum chaos is investigated by use of a coupled quantum kicked-rotors model. Even when the number of rotors is only two, results obtained are drastically different from those for a single-rotor system; that is, in the semiclassical limit the coupled system restores the essential features of classical chaos under appropriate conditions. In particular, the time-reversal experiment reveals that the classical chaotic mixing is recovered almost entirely; however, the recovered mixing is "conditional" in the sense that there exists a threshold for the recovery.
We investigate the parametric fluctuations in the quantum survival probability of an open version of the δ-kicked rotor model in the deep quantum regime. Spectral arguments (Guarneri I and Terraneo M 2001 Phys. Rev. E 65 015203(R)) predict the existence of parametric fractal fluctuations owing to the strong dynamical localization of the eigenstates of the kicked rotor. We discuss the possibility of observing such dynamically-induced fractality in the quantum survival probability as a function of the kicking period for the atom-optics realization of the kicked rotor. The influence of the atoms' initial momentum distribution is studied as well as the dependence of the expected fractal dimension on finite-size effects of the experiment, such as finite detection windows and short measurement times. Our results show that clear signatures of fractality could be observed in experiments with cold atoms subjected to periodically flashed optical lattices, which offer an excellent control on interaction times and the initial atomic ensemble.
We investigate the parametric fluctuations in the quantum survival probability of an open version of the δ-kicked rotor model in the deep quantum regime. Spectral arguments (Guarneri I and Terraneo M 2001 Phys. Rev. E 65 015203(R)) predict the existence of parametric fractal fluctuations owing to the strong dynamical localization of the eigenstates of the kicked rotor. We discuss the possibility of observing such dynamically-induced fractality in the quantum survival probability as a function of the kicking period for the atom-optics realization of the kicked rotor. The influence of the atoms' initial momentum distribution is studied as well as the dependence of the expected fractal dimension on finite-size effects of the experiment, such as finite detection windows and short measurement times. Our results show that clear signatures of fractality could be observed in experiments with cold atoms subjected to periodically flashed optical lattices, which offer an excellent control on interaction times and the initial atomic ensemble.
We study the effects of non-Hermiticity on quantum coherence via a noisy quantum kicked rotor (NQKR). The random noise comes from the fluctuations in kick amplitude at each time. The non-Hermitian driving indicates the imaginary kicking potential, representing the environment-induced atom gain and loss. In the absence of gain and loss, the random noise destroys quantum coherence manifesting dynamical localization, which leads to classical diffusion. Interestingly, in the presence of non-Hermitian kicking potential, the occurrence of dynamical localization is highly sensitive to the gain and loss, manifesting the restoration of quantum coherence. Using the inverse participation ratio arguments, we numerically obtain a phase diagram of the classical diffusion and dynamical localization on the parameter plane of noise amplitude and non-Hermitian driving strength. With the help of analysis on the corresponding quasieigenstates, we achieve insight into dynamical localization, and uncover that the origin of the localization is interference between multiple quasi-eigenstates of the quantum kicked rotor. We further propose an experimental scheme to realize the NQKR in a dissipative cold atomic gas, which paves the way for future experimental investigation of an NQKR and its anomalous non-Hermitian properties.
One major objective of controlling classical chaotic dynamical systems is exploiting the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. In a recent letter [Phys.~Rev.~Lett. 130, 020201 (2023)], a generalization of this targeting method to quantum systems was demonstrated using successive unitary transformations that counter the natural spreading of a quantum state. In this paper further details are given and an important quite general extension is established. In particular, an alternate approach to constructing the coherent control dynamics is given, which introduces a new time-dependent, locally stable control Hamiltonian that continues to use the chaotic heteroclinic orbits previously introduced, but without the need of countering quantum state spreading. Implementing that extension for the quantum kicked rotor generates a much simpler approximate control technique than discussed in the letter, which is a little less accurate, but far more easily realizable in experiments. The simpler method's error can still be made to vanish as ℏ→0\hbar \rightarrow 0ℏ→0.
This thesis presents an account of experimental and numerical investigations of two quantum systems whose respective classical analogues are chaotic. These are the delta-kicked rotor, a paradigm in classical chaos theory, and the novel delta-kicked accelerator, created by application of a constant external acceleration or torque to the rotor. The experimental realisation of these systems has been achieved by the exposure of laser-cooled caesium atoms to approximate delta-kicks from a pulsed, high-intensity, vertical standing wave of laser light. Gravity’s effect on the atoms can be controlled by appropriate shifting of the profile of the standing wave. Numerical simulations of the systems are based on a diffractive model of the potential’s effect. Each system’s dynamics are characterised by the final form of the momentum distribution and the dependence of the atoms’ mean kinetic energy on the number and time period of the delta-kicks. The phenomena of dynamical localisation and quantum resonances in the delta-kicked rotor, which have no counterparts in the system’s classical analogue, are observed and investigated. Similar experiments on the delta-kicked accelerator reveal the striking phenomenon of the quantum accelerator mode, in which a large momentum is transferred to a substantial fraction of the atomic ensemble. This feature, absent in the system’s classical analogue, is characterised and an analytic explanation is presented. The effect on each quantum system of decoherence, introduced through spontaneous emission in the atoms, is examined and comparison is made with the results of classical simulations. While having little effect on the classical systems, the level of decoherence used is found to degrade quantum signatures of behaviour. Classical-like behaviour is, to some extent, restored, although significant quantum features remain. Possible applications of the quantum accelerator mode are discussed. These include use as a tool in atom optics and interferometry, a technique for measuring gravity, and a method of preparing atoms in a particular region of phase space. This may allow measurement of quantum phase space stability, and hence investigation of quantum chaos and quantum-classical correspondence.