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Progress of Theoretical Physics

Averaged Semiquantum Method Is a Useful Tool to Predict the Decoherence of Kicked Harmonic Oscillator System

Z. Wang, Q.-l. Jie

Published Feb 1, 2010• 0 citations
Publisher

Abstract

We investigate the quantum-classical correspondence of kicked harmonic oscillator (KHO) model by the averaged semiquantum method. Furthermore, we investigate the decoherence of N dimensional kicked harmonic oscillator with different coupling strengths and the dimensionalities. The averaged semiquantum method origins from the time-dependent variational principle (TDVP) formulation and contains nondiagonal matrix elements, so it can be applied to study dissipation, measurement and decoherence problems. When applied to the harmonic oscillator model coupled to a heat bath with different coupling strengths and dimensionalities of the bath, we find that the loss of coherence between superposed wave packets can be also predicted by the averaged semiquantum method.

DOI
10.1143/ptp.123.199

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We investigate the quantum-classical correspondence of kicked harmonic oscillator (KHO) model by the averaged semiquantum method. Furthermore, we investigate the decoherence of N dimensional kicked harmonic oscillator with different coupling strengths and the dimensionalities. The averaged semiquantum method origins from the time-dependent variational principle (TDVP) formulation and contains nondiagonal matrix elements, so it can be applied to study dissipation, measurement and decoherence problems. When applied to the harmonic oscillator model coupled to a heat bath with different coupling strengths and dimensionalities of the bath, we find that the loss of coherence between superposed wave packets can be also predicted by the averaged semiquantum method.
We investigate the dynamics of a system coupled to an environment by averaged semiquantum method. The theory origins from the time-dependent variational principle (TDVP) formulation and contains nondiagonal matrix elements, thus it can be applied to study dissipation, measurement and decoherence problems in the model. In the calculation, the influence of the environment governed by differential dynamical equation is incorporated using a mean field. We have performed averaged semiquantum method for a spin-boson model, which reproduces the results from stochastic Schrodinger equation method and Hierarchical approach quite accurately. Moreover, we validate our results with noninteracting-blip approximation (NIBA) and generalized Smoluchowski equation (GSE). The problem dynamics in nonequilibrium environments has also been studied by our method. When applied to the harmonic oscillator model coupled to a heat bath with different coupling strengths and dimensionalities of the bath, we find that the loss of coherence predicted by semiquantum method is identical to the result of master equation with different initial state (Gaussian wave packet and superposed wave packets).
We investigate the dynamics of a system coupled to an environment by averaged semiquantum method. The theory origins from the time-dependent variational principle (TDVP) formulation and contains nondiagonal matrix elements. So it can be applied to study dissipation, measurement, and decoherence problems in the model (H = h S +h E +h I ). In the calculation, the influence of the environment govern by differential dynamical equation is incorporated through a mean field. We have performed averaged semiquantum method for a spin-boson model, which reproduce the results from stochastic Schrodinger equation method and Hierarchical approach quite accurately. The problems, dynamics in nonequilibrium environments, have also been studied by our method.
Abstract The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0 , the so-called Lamb–Dicke parameter η whose square is proportional to the effective Planck constant ℏ eff , and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting ℏ eff become negligible. In this paper we investigate how the ratio T , considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or ℏ eff parameters.
The decoherence of an anharmonic oscillator in a thermal harmonic bath is examined via a semiclassical approach. A computational strategy is presented and exploited to calculate the time dependence of the purity and the decay of individual matrix elements in the energy representation for a variety of initial states. The time dependence of the decoherence is found to depend on the temperature of the bath, the coupling strength, the initial state of the oscillator, and the choice of quantity measuring the decoherence. Recurrences in the purity and in the off-diagonal matrix elements are observed, as well as the collapse of these matrix elements to the diagonal, providing evidence for the retention of quantum coherence for time scales longer than that indicated by the purity. The results are used to analyze the utility of the Caldeira-Leggett and Redfield models of decoherence and to assess the dependence of dephasing rates on the degree of structure in phase space. In several cases we find that the dephasing dynamics can be described as an initial Zeno-effect regime, followed by a Caldeira-Leggett region, followed by recurrences.
We explore the properties of the quantum kicked harmonic oscillation governed by the Hamiltonian . The classical version of this model is known to exhibit certain type of stochastic behavior. We reduce the quantum equation of the model to quantum mapping equations. Numerical results of the mappings show that the behavior of the average energy as a function of time depends on the ration of the frequency of the external and that of the unperturbed system . The energy increases first very rapidly and then the energy growth saturates for irrational . The break time is independent of the strength of the external force, but is roughly proportional to . For a fixed rational the energy is damped oscillation for smaller T, and it is seemingly recurrent with time in the sense of Hogg and Huberman. In both cases, these behaviors of energy are independent of the strength of the external force and differ from the behavior of the quantum kicked rotator.
We consider the problem of a single quantum oscillator coupled linearly to a heat bath of independent harmonic modes. An exact solution is presented for the system-oscillator observables of interest. The exact results are then used to evaluate the utility of a variational approach to the problem that has proven useful recently in elucidating the dynamics of dissipatively coupled systems. We find that the variational approach does provide a good description for most, but not all, observables of interest. Both the exact and the variational treatment demonstrate the important role played by the low-frequency bath modes in determining qualitative features of the dynamical behavior.