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arXiv:quant-ph/0608108 · Physical Review E

Factorization of the dephasing process in a quantum open system

Y. B. Gao, C. P. Sun

Published Jan 10, 2007• 11 citations
arXivHTMLPDF

Abstract

The fluctuation-dissipation relation is well known for a quantum open system with energy dissipation. In this paper a similar underlying relation is found between the bath fluctuation and the dephasing of the quantum open system, for which energy is conserved, but the information is leaking into the bath. To obtain this relation we revisit the universal, but simple dephasing model with a quantum nondemolition interaction between the bath and the open system. Then we show that the decoherence factor describing the dephasing process is factorized into two parts, to indicate the two sources of dephasing, the vacuum quantum fluctuation, and the thermal excitations defined in the initial state of finite temperature.

DOI
10.1103/physreve.75.011105

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The fluctuation-dissipation relation is well known for a quantum open system with energy dissipation. In this paper a similar underlying relation is found between the bath fluctuation and the dephasing of the quantum open system, for which energy is conserved, but the information is leaking into the bath. To obtain this relation we revisit the universal, but simple dephasing model with a quantum nondemolition interaction between the bath and the open system. Then we show that the decoherence factor describing the dephasing process is factorized into two parts, to indicate the two sources of dephasing, the vacuum quantum fluctuation, and the thermal excitations defined in the initial state of finite temperature.
We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.
We study the entropy dynamics of a dephasing model, where a two-level system (TLS) is coupled with a squeezed thermal bath via a nondemolition interaction. This model is exactly solvable, and the time-dependent states of both the TLS and its bath can be obtained exactly. Based on these states, we calculate the entropy dynamics of both the TLS and the bath, and find that the dephasing rate of the system relies on the squeezing phase of the bath. In the zero-temperature and high-temperature limits, both the system and bath entropy increase monotonically in the coarse-grained time scale. Moreover, we find that the dephasing rate of the system relies on the squeezing phase of the bath, and this phase dependence cannot be precisely derived from the Born-Markovian approximation which is widely adopted in open quantum systems.
We study open quantum systems where the coupling between the system and its environment is of a quantum nondmolition (QND) type. Such a system undergoes decoherence without dissipation of energy. We obtain the master equation for the evolution of such a system under the influence of a squeezed thermal bath. From the master equation it can be seen explicitly that the process involves decoherence without any dissipation. We work out the decoherence causing term in the high and zero temperature limits and show that they match with known results in the different temperature regimes for the case of a thermal bath. We also make a comparison between the quantum statistical properties of QND and non-QND (i.e., involving decoherence as well as dissipation) types of evolution.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model interaction we use can generate nonnegligible couplings between the qubit states and the higher levels upto N∼10N\sim 10N∼10. In contrast to the pure two-level system, in a multilevel system the quantum information may leak out of the qubit subspace through nonresonant as well as resonant excitations induced by the environment. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, the environmental temperature, and the multilevel system parameters are varied. We observe the influence of all energy scales in the noise spectrum on the short time dynamics implying the dominance of nonresonant transitions at short times. The relaxation and dephasing times calculated, strongly depend on NNN for 4<N<104< N<104<N<10 and saturate for $10
In this letter, we introduce a novel method for investigating dissipation (gain) and thermalization in an open quantum system. In this method, the quantum system is coupled linearly with a copy of itself or with another system described by a finite number of bosonic operators. The time-dependent coupling functions play a fundamental role in this scheme. To demonstrate the efficiency and significance of the method, we apply it to some ubiquitous open quantum systems. Firstly, we investigate a quantum oscillator in the presence of a thermal bath at the inverse temperature βββ, obtaining the reduced density matrix, the Husimi distribution function, and the quantum heat distribution function accurately. The results are consistent with existing literature by appropriate choices for the time-dependent coupling function. To illustrate the generalizability of this method to systems interacting with multiple thermal baths, we study the interaction of a quantum oscillator with two thermal baths at different temperatures and obtain compatible results. Subsequently, we analyze a two-level atom with energy or phase dissipation and derive the spontaneous emission and the pure dephasing processes consistently using the new method. Finally, we investigate the Markovianity in a dissipative two-level system.
Abstract In this letter, we introduce a novel method for investigating dissipation (gain) and thermalization in an open quantum system. In this method, the quantum system is coupled linearly with a copy of itself or with another system described by a finite number of bosonic operators. The time-dependent coupling functions play a fundamental role in this scheme. To demonstrate the efficiency and significance of the method, we apply it to some ubiquitous open quantum systems. Firstly, we investigate a quantum oscillator in the presence of a thermal bath at the inverse temperature β, obtaining the reduced density matrix, the Husimi distribution function, and the quantum heat distribution function accurately. The results are consistent with existing literature by appropriate choices for the time-dependent coupling function. To illustrate the generalizability of this method to systems interacting with multiple thermal baths, we study the interaction of a quantum oscillator with two thermal baths at different temperatures and obtain compatible results. Subsequently, we analyze a two-level atom with energy or phase dissipation and derive the spontaneous emission and the pure dephasing processes consistently using the new method. Finally, we investigate the Markovianity in a dissipative two-level system.