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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Classical and quantum periodically driven scattering in one dimension

Michael Henseler, Thomas Dittrich, Klaus Richter

Published Sep 25, 2001• 39 citations
Publisher

Abstract

Irregular scattering at harmonically driven one-dimensional potential wells is studied both on the classical and the quantum level. We show that an ac-driven single square well, and a smooth well with oscillating bottom, are sufficient to generate chaotic scattering. For a square well with oscillating bottom, we introduce the concept of pseudointegrable scattering. The quantum dynamics of these models is treated using Floquet scattering theory, which is exact for arbitrary amplitude and frequency of the driving. In the deep quantum regime, scattering is dominated by multiphoton exchanges with the driving field, leading to complex resonance structures in transmission and reflection. For strong and fast driving, the ac-driven square well develops an effective double-well potential that introduces coherent tunneling in the scattering. We identify signatures of classical chaotic scattering in a phase-space representation of the quantum dynamics.

DOI
10.1103/physreve.64.046218

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Irregular scattering at harmonically driven one-dimensional potential wells is studied both on the classical and the quantum level. We show that an ac-driven single square well, and a smooth well with oscillating bottom, are sufficient to generate chaotic scattering. For a square well with oscillating bottom, we introduce the concept of pseudointegrable scattering. The quantum dynamics of these models is treated using Floquet scattering theory, which is exact for arbitrary amplitude and frequency of the driving. In the deep quantum regime, scattering is dominated by multiphoton exchanges with the driving field, leading to complex resonance structures in transmission and reflection. For strong and fast driving, the ac-driven square well develops an effective double-well potential that introduces coherent tunneling in the scattering. We identify signatures of classical chaotic scattering in a phase-space representation of the quantum dynamics.
The quantum dynamics of a quartic double well, subjected to a harmonically oscillating field, is studied in the framework of the Floquet formalism. The modifications of the familiar tunneling process due to driving and dissipation are investigated numerically and explained in terms of the quasienergy spectrum. In absence of dissipation, there is a onedimensional manifold in the parameter space spanned by amplitude and frequency of the driving force, where tunneling is almost completely suppressed by the coherent driving. The influence of dissipation is described on basis of the reduced density matrix in the Floquet representation. In particular, we consider the effect of weak Ohmic damping. In the classical limit, this system corresponds to a damped bistable Duffing oscillator
We investigate the coherent control of quantum tunneling for a single particle held in a driven double-well potential. For a moderate-frequency region, we demonstrate that the irregular quantum tunneling is associated with classically chaotic dynamics. A set of lower resonance-like frequencies is found, for which the coherent destruction of tunneling in the sense of the time average is illustrated numerically. For a high-frequency region, it is shown that the particle is located at the bottom of each well alternately for a long time and the time located in one well can be modulated by adjusting the driving field. The results could be useful for the experiments of controlling single-particle tunneling [see, e.g., E. Kierig, U. Schnorrberger, A. Schietinger, J. Tomkovic, and M. K. Oberthaler, Phys. Rev. Lett. 100, 190405 (2008).].
The quantum dynamics of a particle in a double-well potential under a monochromatic external driving force is computed by using a minimum-uncertainty Gaussian wave packet as an initial state. Irregular or regular time development of dynamical variables is obtained, depending on whether the initial wave packet is located in the classical chaotic sea or the regular region in phase space, respectively. Tunnelings between nonresonant islands and between resonant islands are obtained. Tunneling times between nonresonant islands decrease smoothly, in general, with the increase of the amplitude of the driving force, but tunneling times between resonant islands are more erratic.
We study a wavepacket tunneling in one-dimensional periodically driven double-well system using entangled trajectory molecular dynamics method. The tunneling dynamics dependents on the amplitude and frequency of the driven force are present. Both resonant and nonresonant tunneling process are enhanced by the driven force when the system is chaotic under classical dynamics. We give entangled trajectory in phase space compared to corresponding classical trajectory with same initial state to visually show quantum tunneling process. The average values of quantum tunneling probability after long time evolution have been shown in the parameter spaces, the effect of resonance and chaos on the tunneling dynamics are present. The relation between chaos and the uncertainly product is discussed in the end. © 2016 Wiley Periodicals, Inc.
We present effects of an external driving on the tunneling dynamics of interacting bosons confined in a double-well potential. At large values of a periodic driving potential, the dynamics become chaotic, with a distinct difference between tuning of the amplitude or the phase of the driving term with regard to the route leading to chaos. For example, we find that a controlled increase in the amplitude of the driving term with a fixed phase leads to quasiperiodic route to chaos. While tuning of the frequency with a fixed (large) amplitude leads to a crisis-induced intermittency route to a chaotic dynamics, where the system intermittently visits different attractors in the phase space. Surprisingly, a chirp frequency superposed on a harmonic signal suppresses the chaotic motion, thereby yielding an orderly dynamics, pretty similar to a (damped) Rabi oscillation.
We use periodically modulated magnetic fields to drive spin-1 Bose-Einstein condensates (BECs) and study the corresponding spin-mixing dynamics. Due to the time-dependent driving, this system permits chaotic dynamics depending on the drive parameters, which could not occur in previous studies. From the investigation of the Poincar\'e sections, we find there exist complex trajectories in the phase space, leading to very complicated structures of the phase space with mixed regular and chaotic regions. By calculating the quasienergy levels of the corresponding Floquet operators, the signatures of quantum chaos are also found in this system. The level spacing distribution is very close to the Poisson distribution or Wigner distribution when the corresponding classical dynamics is regular or chaotic.