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arXiv:1605.07452 · Science China Physics Mechanics and Astronomy

Superballistic wavepacket spreading in double kicked rotors

Ping Fang, Jiao Wang

Published May 16, 2016• 4 citations
arXivHTMLPDF

Abstract

Abstract We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.

DOI
10.1007/s11433-016-0076-y

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We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with P T symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibit the staircase growth with time when the system parameter is in the neighborhood of the P T symmetry breaking point. If the system parameter is much larger than the P T symmetry breaking point, the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space. For the classical dynamics, the non-Hermitian kicking potential leads to the exponentially-fast increase of classical complex trajectories. As a consequence, the imaginary part of the trajectories exponentially diffuses with time, while the real part exhibits the normal diffusion. Our analytical prediction of the exponential diffusion of imaginary momentum and its breakdown time is in good agreement with numerical results. The quantum signature of the chaotic diffusion of the complex trajectories is reflected by the dynamics of the out-of-time-order correlators (OTOC). In the semiclassical regime, the rate of the exponential increase of the OTOC is equal to that of the exponential diffusion of the complex trajectories.

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Quantum -kicked rotor: the effect of amplitude noise on the quantum resonances

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We study analytically the effect of amplitude noise on the quantum resonances of an atom optics realization of the δ-kicked rotor. Noise is shown to add a time growth to the ‘deterministic’ energy and to induce a time increasing spreading in the momentum distribution; exact results are given for both effects. The ballistic peaks characteristic of the noiseless distribution for particular initial conditions broaden and eventually vanish, whereas the associated quadratic growth of energy persists; at large times, the survival probability decays as t −1 . Moreover, the nonexponential ‘localization’ linked to different initial conditions is gradually destroyed. Features specific to Gaussian noise, white and coloured, are analysed. The feasibility of experimental tests of these effects is discussed.

Journal of Physics A Mathematical and General•Mar 19, 2003•6 citations
Abstract We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.
We investigate a many-body interacting system of quantum kicked rotors, where each rotor resides in its respective quantum resonance. Rich many-body dynamics are found to emerge from the interplay between the principal and secondary resonances. In particular, for both the wavepacket and bipartite entanglement entropy, we analytically demonstrate three distinct dynamical regimes -- quadratic spreading (growth), period-2 oscillation, and their hybrid -- governed by the respective symmetries of the relevant potentials. Based on these symmetries, the connection between the wavepacket and the entanglement dynamics is illustrated. Other related issues are also discussed, including higher-order resonance effects, the robustness of the predicted dynamical behaviors, extension to many-body kicked tops, and relevance to experimental studies.
We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with P T symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibit the staircase growth with time when the system parameter is in the neighborhood of the P T symmetry breaking point. If the system parameter is much larger than the P T symmetry breaking point, the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space. For the classical dynamics, the non-Hermitian kicking potential leads to the exponentially-fast increase of classical complex trajectories. As a consequence, the imaginary part of the trajectories exponentially diffuses with time, while the real part exhibits the normal diffusion. Our analytical prediction of the exponential diffusion of imaginary momentum and its breakdown time is in good agreement with numerical results. The quantum signature of the chaotic diffusion of the complex trajectories is reflected by the dynamics of the out-of-time-order correlators (OTOC). In the semiclassical regime, the rate of the exponential increase of the OTOC is equal to that of the exponential diffusion of the complex trajectories.
Lindblad dynamics is one of the most popular approaches to study open quantum systems. This paper studies a kicked rotor; in particular, a two rotor system where one of the rotors is treated as the environment and the other is studied with the Lindblad master equation. The energy levels are solved explicitly in terms of Bessel functions and the results show that the energy levels exhibit dissipative behavior with variance in momentum increasing as ⟨p^2⟩=2Dt\langle\hat{p}^2\rangle=2Dt⟨p^​2⟩=2Dt similar to the classical kicked rotor. This result shows us how interaction between systems can break down quantum phenomena and result in more classical results, bridging the gap between the quantum and the classical world.
The quantum kicked rotor is a paradigmatic model system in quantum physics. As a driven quantum system, it features dynamical localization, specifically Anderson localization in momentum space. However, the interacting many-body kicked rotor is believed to break localization. Here, we present evidence for many-body dynamical localization for the Lieb-Liniger version of the many-body quantum kicked rotor. After some initial evolution, the momentum distribution of interacting quantum-degenerate bosonic atoms in one-dimensional geometry, kicked hundreds of times by means of a pulsed sinusoidal potential, stops spreading. Our results shed light on the boundary between the classical, chaotic world and the realm of quantum physics.
The kicked rotor provides a simple yet powerful model for introducing many of the central concepts of classical and quantum chaos. Despite its apparent simplicity, it exhibits rich dynamical behavior and has found applications across a wide range of fields, including atomic and optical physics, condensed matter physics, and emerging quantum technologies. This chapter begins by exploring foundational ideas using the kicked rotor as a unifying framework. We first discuss the transition from regular to chaotic motion in the classical system, and then introduce key quantum phenomena such as dynamical localization and quantum resonances. Special attention is devoted to the emergence of characteristic time scales and their role in the quantum-classical correspondence. To make these ideas more concrete, we also provide a brief overview of experimental realizations of the kicked rotor and its variants, illustrating how theoretical concepts are implemented in practice. In the second part of the chapter, we guide the reader toward more recent and advanced developments. Topics include near-resonant dynamics, topological features of kicked systems, the emergence of quantum dynamical phases inferred from classical transport properties, and extensions to non-Hermitian physics. We conclude with a discussion of open problems and future perspectives, outlining directions in which the kicked rotor continues to offer valuable insights.
We study analytically the effect of amplitude noise on the quantum resonances of an atom optics realization of the δ-kicked rotor. Noise is shown to add a time growth to the ‘deterministic’ energy and to induce a time increasing spreading in the momentum distribution; exact results are given for both effects. The ballistic peaks characteristic of the noiseless distribution for particular initial conditions broaden and eventually vanish, whereas the associated quadratic growth of energy persists; at large times, the survival probability decays as t −1 . Moreover, the nonexponential ‘localization’ linked to different initial conditions is gradually destroyed. Features specific to Gaussian noise, white and coloured, are analysed. The feasibility of experimental tests of these effects is discussed.