Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Survival of coherence for open quantum systems in thermal baths

Filippo Giraldi, Francesco Petruccione

Published Oct 2, 2013• 14 citations
Publisher

Abstract

The loss of coherence in a general open quantum system interacting with a bosonic environment is analyzed. The reservoir is initially in a thermal state. The reduced dynamics is described by a non-Markovian time-local master equation. We consider spectral densities that are sub- or super-Ohmic at low frequencies and arbitrarily shaped at high frequencies. In the super-Ohmic regime, for noninteger frequency powers larger than 2, long time survival of coherence appears. In the latter regime, at vanishing temperature, the asymptotic amount of surviving coherence is stabilized to its initial value, up to a phase factor, by properly increasing the bandwidth and decreasing the low-frequency profile of the spectral density. For noninteger positive frequency powers less than 2, stretched exponential-like decoherence is found over long times. The relaxations to the asymptotic configurations become arbitrarily slow by approaching the frequency power 2 of the super-Ohmic regime. The same dependence on temperature, spectral density, and scale frequency appears for purity and concurrence of two qubits and coherence of a qubit.

DOI
10.1103/physreva.88.042102

Related papers

Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding

Anton Sergeevich Trushechkin

We consider a well-known, exactly solvable model of an open quantum system with pure decoherence. The aim of this paper is twofold. Firstly, decoherence is a property of open quantum systems important for both quantum technologies and the fundamental question of the quantum–classical transition. It is worth studying how the long-term rate of decoherence depends on the spectral density characterising the system–bath interaction in this exactly solvable model. Secondly, we address a more general problem of the Markovian embedding of non-Markovian open system dynamics. It is often assumed that a non-Markovian open quantum system can be embedded into a larger Markovian system. However, we show that such embedding is possible only for Ohmic spectral densities (for the case of a positive bath temperature) and is impossible for both sub- and super-Ohmic spectral densities. On the other hand, for Ohmic spectral densities, an asymptotic large-time Markovianity (in terms of the quantum regression formula) takes place.

arXiv:2311.16010•Mathematics•Dec 19, 2023•6 citations

Non-Markovian dynamics of a dephasing model in a squeezed thermal bath

Zhi He, Hao‐Sheng Zeng, Yu Chen +1 more

Abstract The non-Markovian dynamics of a qubit dephasing in a squeezed thermal environment with general Ohmic spectral density are investigated, and the analytical solution is presented for the models with sub-Ohmic, Ohmic, and super-Ohmic spectral densities in the zero-temperature limit. We study the non-Markovianity of the open qubit system, and find that it is very large in a certain regime of the squeezed parameters and almost vanishes outside this regime, given the parameters of the environmental spectrum. Furthermore, the non-Markovianity can be enhanced to surpass that of the unsqueezed case by adjusting the squeezing parameters. More interestingly, we find that given the other parameters, the non-Markovianity of a small coupling constant between the qubit and its environment may be larger than in the case of a large coupling constant; this is dependent on the competition between the coupling constant and the Ohmicity parameter of the environment. We also discuss the influence of squeezing operator on the quantum speed limit (QSL) time for the considered model, and find that the QSL time can be reduced via the adjustment of the squeezing operator.

Laser Physics Letters•May 13, 2019•6 citations

Trapping quantum coherence with a dissipative thermal bath

Jiaming Zhang, Bing Chen, Jing, Jun

In the long-time limit, an open quantum system coupled to a dissipative environment is believed to lose its coherence without driving or measurement. Counterintuitively, we provide a necessary condition on trapping the coherence of a two-level system entirely with a thermal bath. Based on a time-local master equation, it is found that the residue coherence survives even under a high-temperature bath as long as the long-time Lamb shift is exactly negative to the system transition frequency. This condition is generally met in the strong and even ultrastrong coupling regime that could be relaxed by increasing the environmental temperature. The counter-rotating interactions between system and bath is indispensable to the residue coherence, whose magnitude is affected by the system initial state and the bath structure.

arXiv:2209.01781•Sep 5, 2022•0 citations

Energy range for quantum coherence

Filippo Giraldi

Decoherence-free states have been found in Markovian open system dynamics and in the framework of non-Markovian fermionic environments. In the latter scenario we determine an energy range where quantum coherence is maintained over long times for every initial coherent configuration. In particular, for a two-state fermionic system interacting with a non-Markovian fermionic environment, undamped oscillating or stable coherence between the two energy eigenstates appears if the degenerate energy level is below a critical energy. If these energies coincide, the same behavior is observed in the superohmic regime and, under special conditions, the initial coherence is approached asymptotically. Equivalently, coherence persists if a defined dressed energy of the system is less than the band-gap energy of the reservoir. Same properties are found in the framework of bosonic environments.

Physical Review A•Jun 11, 2015•3 citations

Decoherence and the ultraviolet cutoff: non-Markovian dissipative dynamics of a charged particle in a magnetic field

Suraka Bhattacharjee, Koushik Mandal, Supurna Sinha

Abstract We derive a non-Markovian master equation for a charged particle in a magnetic field coupled to a bath and study decoherence by analyzing the temporal decay of the off-diagonal elements of the reduced density matrix in the position basis. The coherent oscillations characterized by the cyclotron frequency get suppressed as a result of decoherence due to coupling with the environment. We consider an Ohmic bath with three distinct models for the high-frequency cutoff for the spectral density of the bath and compare the three cases. As expected, the three cutoff models converge in the limit of the uppermost frequency of the bath tending to infinity. We notice a dramatic slowing down of loss of coherence in the low-temperature limit dominated by zero point quantum fluctuations compared to the high-temperature classical limit dominated by thermal fluctuations. We also go beyond the Ohmic model and study super-Ohmic and sub-Ohmic baths with the spectral densities deviating from a linear dependence on the frequency. Our results are testable in a state of the art cold atom laboratory.

arXiv:2301.06365•Journal of Physics A Mathematical and Theoretical•May 3, 2023•4 citations

Quantum speed limits of a qubit system interacting with a nonequilibrium environment

Zhi He, Chunmei Yao, Li Li +1 more

The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [ Phys. Rev. Lett . 103 210401 (2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s . We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit (QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubit-initial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states, where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.

Chinese Physics B•Jul 26, 2016•5 citations
The loss of coherence in a general open quantum system interacting with a bosonic environment is analyzed. The reservoir is initially in a thermal state. The reduced dynamics is described by a non-Markovian time-local master equation. We consider spectral densities that are sub- or super-Ohmic at low frequencies and arbitrarily shaped at high frequencies. In the super-Ohmic regime, for noninteger frequency powers larger than 2, long time survival of coherence appears. In the latter regime, at vanishing temperature, the asymptotic amount of surviving coherence is stabilized to its initial value, up to a phase factor, by properly increasing the bandwidth and decreasing the low-frequency profile of the spectral density. For noninteger positive frequency powers less than 2, stretched exponential-like decoherence is found over long times. The relaxations to the asymptotic configurations become arbitrarily slow by approaching the frequency power 2 of the super-Ohmic regime. The same dependence on temperature, spectral density, and scale frequency appears for purity and concurrence of two qubits and coherence of a qubit.
We consider a well-known, exactly solvable model of an open quantum system with pure decoherence. The aim of this paper is twofold. Firstly, decoherence is a property of open quantum systems important for both quantum technologies and the fundamental question of the quantum–classical transition. It is worth studying how the long-term rate of decoherence depends on the spectral density characterising the system–bath interaction in this exactly solvable model. Secondly, we address a more general problem of the Markovian embedding of non-Markovian open system dynamics. It is often assumed that a non-Markovian open quantum system can be embedded into a larger Markovian system. However, we show that such embedding is possible only for Ohmic spectral densities (for the case of a positive bath temperature) and is impossible for both sub- and super-Ohmic spectral densities. On the other hand, for Ohmic spectral densities, an asymptotic large-time Markovianity (in terms of the quantum regression formula) takes place.
Abstract The non-Markovian dynamics of a qubit dephasing in a squeezed thermal environment with general Ohmic spectral density are investigated, and the analytical solution is presented for the models with sub-Ohmic, Ohmic, and super-Ohmic spectral densities in the zero-temperature limit. We study the non-Markovianity of the open qubit system, and find that it is very large in a certain regime of the squeezed parameters and almost vanishes outside this regime, given the parameters of the environmental spectrum. Furthermore, the non-Markovianity can be enhanced to surpass that of the unsqueezed case by adjusting the squeezing parameters. More interestingly, we find that given the other parameters, the non-Markovianity of a small coupling constant between the qubit and its environment may be larger than in the case of a large coupling constant; this is dependent on the competition between the coupling constant and the Ohmicity parameter of the environment. We also discuss the influence of squeezing operator on the quantum speed limit (QSL) time for the considered model, and find that the QSL time can be reduced via the adjustment of the squeezing operator.
In the long-time limit, an open quantum system coupled to a dissipative environment is believed to lose its coherence without driving or measurement. Counterintuitively, we provide a necessary condition on trapping the coherence of a two-level system entirely with a thermal bath. Based on a time-local master equation, it is found that the residue coherence survives even under a high-temperature bath as long as the long-time Lamb shift is exactly negative to the system transition frequency. This condition is generally met in the strong and even ultrastrong coupling regime that could be relaxed by increasing the environmental temperature. The counter-rotating interactions between system and bath is indispensable to the residue coherence, whose magnitude is affected by the system initial state and the bath structure.
Decoherence-free states have been found in Markovian open system dynamics and in the framework of non-Markovian fermionic environments. In the latter scenario we determine an energy range where quantum coherence is maintained over long times for every initial coherent configuration. In particular, for a two-state fermionic system interacting with a non-Markovian fermionic environment, undamped oscillating or stable coherence between the two energy eigenstates appears if the degenerate energy level is below a critical energy. If these energies coincide, the same behavior is observed in the superohmic regime and, under special conditions, the initial coherence is approached asymptotically. Equivalently, coherence persists if a defined dressed energy of the system is less than the band-gap energy of the reservoir. Same properties are found in the framework of bosonic environments.
Abstract We derive a non-Markovian master equation for a charged particle in a magnetic field coupled to a bath and study decoherence by analyzing the temporal decay of the off-diagonal elements of the reduced density matrix in the position basis. The coherent oscillations characterized by the cyclotron frequency get suppressed as a result of decoherence due to coupling with the environment. We consider an Ohmic bath with three distinct models for the high-frequency cutoff for the spectral density of the bath and compare the three cases. As expected, the three cutoff models converge in the limit of the uppermost frequency of the bath tending to infinity. We notice a dramatic slowing down of loss of coherence in the low-temperature limit dominated by zero point quantum fluctuations compared to the high-temperature classical limit dominated by thermal fluctuations. We also go beyond the Ohmic model and study super-Ohmic and sub-Ohmic baths with the spectral densities deviating from a linear dependence on the frequency. Our results are testable in a state of the art cold atom laboratory.
The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [ Phys. Rev. Lett . 103 210401 (2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s . We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit (QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubit-initial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states, where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.