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arXiv:quant-ph/0602133 · Physical Review Letters

Zeno and Anti-Zeno Effects for Quantum Brownian Motion

Sabrina Maniscalco, Jyrki Piilo, Kalle‐Antti Suominen

Published Sep 27, 2006• 81 citations
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Abstract

In this Letter, 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 behavior of environment induced decoherence is ultimately 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.

DOI
10.1103/physrevlett.97.130402

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In this Letter, 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 behavior of environment induced decoherence is ultimately 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.
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 .
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.
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.
The occurrence of either the quantum Zeno effect (QZE) or anti-Zeno effect (AZE) resulting from the short-time behavior of the environment-induced decoherence for quantum Brownian motion (QBM) model has been discussed [S. Maniscalco, J. Piilo, and K. A. Suominen, Phys. Rev. Lett. 97, 130402 (2006)]. We discuss here while the shuttering time period (length) of the frequent observations is changed, the system of interest, i.e., a nanomechanical oscillator, will undergo a QZE to AZE crossover. Instead of interacting with an equilibrium bosonic bath in a QBM model, we investigate the occurrence of either QZE or AZE of a nanomechanical oscillator coupled to a nonequilibrium fermionic reservoir [quantum point contact (QPC) detector as a measuring device]. We find that Zeno and anti-Zeno behaviors depend on the values of the system and reservoir parameters such as the oscillator frequency, energy cutoff, bias voltage, and reservoir temperature.
We investigate two techniques for controlling decoherence, focusing on the crucial role played by the environmental spectrum. We show how environments with different spectra lead to very different dynamical behaviors. Our study clearly proves that such differences must be taken into account when designing decoherence control schemes. The two techniques we consider are reservoir engineering and quantum Zeno control. We focus on a quantum harmonic oscillator initially prepared in a nonclassical state and derive analytically its non-Markovian dynamics in the presence of different bosonic thermal environments. On the one hand, we show how, by modifying the spectrum of the environment, it is possible to prolong or reduce the life of a Schr\"odinger cat state. On the other hand, we study the effect of nonselective energy measurements on the degradation of quantumness of initial Fock states. In this latter case, we see that the crossover between quantum Zeno and anti-Zeno effects, discussed by Maniscalco et al. [Phys. Rev. Lett. 97, 130402 (2006)], is highly sensitive to the details of the spectrum. In particular, for certain types of spectra, even very small variations of the system frequency may cause a measurement-induced acceleration of decoherence rather than its inhibition.
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.