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Journal of Statistical Mechanics Theory and Experiment

Zeno and anti-Zeno effects in a dissipative quantum Brownian oscillator model

Malay Bandyopadhyay

Published Apr 8, 2014• 4 citations
Publisher

Abstract

The purpose of this paper is to investigate the occurrence of the Zeno and anti-Zeno effects for the quantum Brownian motion of a harmonic oscillator. We show a controlled decay suppression and decay acceleration for a dissipative quantum harmonic oscillator. We demonstrate that the system–bath coupling parameter as well as the confining potential can critically control the Zeno and anti-Zeno dynamics. In this context, we discuss several heat bath models such as ohmic, Drude, and the black body radiation model.

DOI
10.1088/1742-5468/2014/04/p04001

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The purpose of this paper is to investigate the occurrence of the Zeno and anti-Zeno effects for the quantum Brownian motion of a harmonic oscillator. We show a controlled decay suppression and decay acceleration for a dissipative quantum harmonic oscillator. We demonstrate that the system–bath coupling parameter as well as the confining potential can critically control the Zeno and anti-Zeno dynamics. In this context, we discuss several heat bath models such as ohmic, Drude, and the black body radiation model.
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The quantum Zeno effect predicts that the decay of an unstable system can be slowed down by measuring the system frequently enough. In some systems, however, an enhancement of the decay due to frequent measurements, namely the anti-Zeno effect, may occur. In this paper we study the Zeno-anti-Zeno crossover for quantum Brownian motion. Moreover, we propose a way to manipulate the decay of the system and to observe a controlled continuous passage from decay suppression to decay acceleration by using reservoir engineering techniques.
In this paper we investigate the occurrence of the Zeno and anti-Zeno effects for quantum Brownian motion. We single out the parameters of both the system and the reservoir governing the crossover between Zeno and anti-Zeno dynamics. We demonstrate that, for high reservoir temperatures, the short time behaviour of environment induced decoherence is the ultimate responsible for the occurrence of either the Zeno or the anti-Zeno effect. Finally we suggest a way to manipulate the decay rate of the system and to observe a controlled continuous passage from decay suppression to decay acceleration using engineered reservoirs in the trapped ion context .
We investigate the quantum Zeno and anti-Zeno effects in quantum dissipative systems by employing a hierarchical equations of motion approach which is beyond the usual Markovian approximation, the rotating wave approximation, and the perturbative approximation. The quantum Zeno and anti-Zeno dynamics of a biased qubit-boson model and a biased qutrit-boson model are provided as illustrative examples. It is found that (i) there exists multiple Zeno--anti-Zeno crossover phenomena, (ii) the non-Markovian characteristic of the bath may be favorable for the accessibility of the Zeno dynamics, and (iii) high bath temperature may add the difficulty in observing the quantum Zeno effect in quantum dissipative systems.
We investigate the quantum Zeno and anti-Zeno effects in spin bath models: the spin-boson model and a spin-fermion model. We show that the Zeno--anti-Zeno transition is critically controlled by the system-bath coupling parameter, the same parameter that determines spin decoherence rate. We also discuss the crossover in a biased system, at high temperatures, and for a nonequilibrium spin-fermion system, manifesting the counteracting roles of electrical bias, temperature, and magnetic field on the spin decoherence rate.
Abstract We analyze the steady-state characteristics of a damped harmonic oscillator (system) in the presence of a non-Markovian bath characterized by Lorentzian spectral density. Although Markovian baths presume memoryless dynamics, the introduction of complex temporal connections by a non-Markovian environment radically modifies the dynamics of the system and its steady-state behaviour. We obtain the steady-state Green’s function and correlation functions of the system using the Schwinger–Keldysh formalism. In both rotating and non-rotating wave approximation, we analyzed various emergent properties like effective temperature and distribution function. We also explore the impact of dissipation and non-Markovian bath on the quantum Zeno and anti-Zeno effects. We show that a transition between Zeno to anti-Zeno effect can be tuned by bath spectral width and the strength of dissipation.