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arXiv:1003.3737 · Physical Review A

Decoherence control in different environments

J. Paavola, Sabrina Maniscalco

Published Jul 27, 2010• 29 citations
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Abstract

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.

DOI
10.1103/physreva.82.012114

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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.
In this paper, we analyze two different techniques based on reservoir engineering method and quantum Zeno effect for controlling decoherence of a dissipative charged oscillator in the presence of an external magnetic field. Our main focus is to investigate the sensitiveness of these decoherence control techniques on the details of different environmental spectrum (J(ω)J(ω)J(ω)), and on the crucial role played by different system and reservoir parameters, e.g., external magnetic field (rcr_crc​), confinement length (r0r_0r0​), temperature (T), cut-off frequency of reservoir spectrum (ωcutω_{cut}ωcut​), and measurement interval (τττ). First, we consider the charged quantum oscillator in an initial nonclassical Schrodinger cat state and analyze the non-Markovian dynamics for the magneto-oscillator in contact with Ohmic, sub-Ohmic, and super-Ohmic environments. We show the procedure to control the quantumness of the Schrodinger cat state by tuning the parameters rcr_crc​, r0r_0r0​, and J(ω)J(ω)J(ω). On the other hand, we investigate the effect of nonselective energy measurement process on the mortification of quantumness of an initial Fock-Darwin state of the charged magneto-oscillator. We investigate in details the strategy to manipulate the continuous passage from decay suppression to decay acceleration by engineered reservoirs and by tuning the system or reservoir parameters, e.g., rcr_crc​, r0r_0r0​, T or τττ. As a result of that one can control environment induced decoherence (EID).
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 .
This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.