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

arXiv:0906.0098 · Physical Review A

Effective quantum dynamics of two Brownian particles

O. S. Duarte, A. O. Caldeira

Published Sep 15, 2009• 22 citations
arXivHTMLPDF

Abstract

We use the system-plus-reservoir approach to study the quantum dynamics of a bipartite continuous variable system (two generic particles). We present an extension of the traditional model of a bath of oscillators which is capable of inducing an effective coupling between the two parts of the system depending on the choice made for the spectral density of the bath. The coupling is nonlinear in the system variables and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The reduced density operator is obtained by the functional integral method. The dynamical susceptibility of the reservoir is modeled in order to introduce, besides a characteristic frequency, a characteristic length that determines if the effective interaction potential is strong enough to induce entanglement between the particles. Our model provides a criterion of distance for identifying in which cases a common environment can induce entanglement. Three regimes are found: the short distance regime, equivalent to a bilinear system-reservoir coupling, the long distance regime in which the particles act like coupled to independent reservoirs, and the intermediate regime suitable for the competition between decoherence and induced entanglement.

DOI
10.1103/physreva.80.032110

Related papers

Thermal equilibrium of two quantum Brownian particles

D. Valente, A. O. Caldeira

The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the Brownian motion when the two particles are isolated and induces an effective interaction between them, depending on the choice of the spectral function of the bath. The coupling between the system and the environment guarantees the translational invariance of the system in the absence of an external potential. The entanglement between the particles is measured by the logarithmic negativity, which is shown to monotonically decrease with the increase of the temperature. A range of finite temperatures is found in which entanglement is still induced by the reservoir.

arXiv:0911.4894•Physical Review A•Jan 26, 2010•13 citations

Environment-induced two-mode entanglement in quantum Brownian motion

Christian Hörhammer, H. Büttner

The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.

arXiv:0708.2670•Physical Review A•Apr 4, 2008•57 citations

Non-Markovian entanglement dynamics of quantum continuous variable systems in thermal environments

Kuan-Liang Liu, Hsi‐Sheng Goan

We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of electromagnetic fields or two nanomechanical oscillators in the quantum domain. We use the quantum open system method to derive the non-Markovian master equations of the reduced density matrix for two different but related models of the continuous variable systems. The two models both consist of two interacting harmonic oscillators. In model A, each of the two oscillators is coupled to its own independent thermal reservoir, while in model B the two oscillators are coupled to a common reservoir. To quantify the degrees of entanglement for bipartite continuous variable systems in Gaussian states, logarithmic negativity is used. We find that the dynamics of the quantum entanglement is sensitive to the initial states, the oscillator-oscillator interaction, the oscillator-environment interaction and the coupling to a common bath or to different, independent baths.

arXiv:0706.0996•Physical Review A•Aug 14, 2007•130 citations

Rise and fall of entanglement between two qubits in a non-Markovian bath

Sayan Roy, Christian Otto, Raphaël Menu +1 more

We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.

arXiv:2303.13301•Physical Review A•Sep 7, 2023•7 citations

Non-Markovian dynamics, nonlocality, and entanglement in quantum Brownian motion

K. Shiokawa

The dynamical aspects of quantum Brownian motion at low temperatures are investigated. Exact calculations of quantum entanglement among two Brownian oscillators are given without invoking the Born-Markov or Born approximation widely used for the study of open systems. Nonlocality due to finite oscillator separation is studied. Our approach is applicable for arbitrary time scale, in particular suitable to probe the short-time regime at cold temperatures where many experiments on quantum information processing are performed. We study separability criteria based on the uncertainty relation, negativity, and entanglement of formation. We found a crossover behavior in a disentanglement process between quantum- and thermal-fluctuation-dominated regimes. The fluctuation-dissipation theorem is violated for two Brownian particles interacting with a common environment. The deviation from the relation originates in the interaction mediated by the environment, which drives two particles into a steady oscillatory state, preventing the system from thermalizing. Consequently there is a residual entanglement at low temperatures for arbitrary coupling strength. This entanglement is generated from the environment nonperturbatively even when two modes are not entangled initially. When the distance between two oscillators is varied, competition between entanglement induced from the environment and modified decoherence due to finite separation leads to the characteristic distance where entanglement is minimized.

arXiv:0809.1587•Physical Review A•Jan 9, 2009•16 citations

Statistical mechanics of entanglement mediated by a thermal reservoir

E. Kajari, Alexander Wolf, Eric Lutz +1 more

Two defect particles that couple to a harmonic chain, acting as common reservoir, can become entangled even when the two defects do not directly interact and the harmonic chain is effectively a thermal reservoir for each individual defect. This dynamics is encountered for sufficiently low temperatures of the chain and depends on the initial state of the two oscillators. In particular, when each defect is prepared in a squeezed state, entanglement can be found at time scales at which the steady state of a single defect is reached. We provide a microscopic description of the coupled quantum dynamics of chain and defects. By means of numerical simulations, we explore the parameter regimes for which entanglement is found under the specific assumption that both particles couple to the same ion of the chain. This model provides the microscopic setting where bath-induced entanglement can be observed.

arXiv:1112.5300•Physical Review A•Apr 16, 2012•13 citations
We use the system-plus-reservoir approach to study the quantum dynamics of a bipartite continuous variable system (two generic particles). We present an extension of the traditional model of a bath of oscillators which is capable of inducing an effective coupling between the two parts of the system depending on the choice made for the spectral density of the bath. The coupling is nonlinear in the system variables and an exponential dependence on these variables is imposed in order to guarantee the translational invariance of the model if the two particles are not subject to any external potential. The reduced density operator is obtained by the functional integral method. The dynamical susceptibility of the reservoir is modeled in order to introduce, besides a characteristic frequency, a characteristic length that determines if the effective interaction potential is strong enough to induce entanglement between the particles. Our model provides a criterion of distance for identifying in which cases a common environment can induce entanglement. Three regimes are found: the short distance regime, equivalent to a bilinear system-reservoir coupling, the long distance regime in which the particles act like coupled to independent reservoirs, and the intermediate regime suitable for the competition between decoherence and induced entanglement.
The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the Brownian motion when the two particles are isolated and induces an effective interaction between them, depending on the choice of the spectral function of the bath. The coupling between the system and the environment guarantees the translational invariance of the system in the absence of an external potential. The entanglement between the particles is measured by the logarithmic negativity, which is shown to monotonically decrease with the increase of the temperature. A range of finite temperatures is found in which entanglement is still induced by the reservoir.
The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.
We study two continuous variable systems (or two harmonic oscillators) and investigate their entanglement evolution under the influence of non-Markovian thermal environments. The continuous variable systems could be two modes of electromagnetic fields or two nanomechanical oscillators in the quantum domain. We use the quantum open system method to derive the non-Markovian master equations of the reduced density matrix for two different but related models of the continuous variable systems. The two models both consist of two interacting harmonic oscillators. In model A, each of the two oscillators is coupled to its own independent thermal reservoir, while in model B the two oscillators are coupled to a common reservoir. To quantify the degrees of entanglement for bipartite continuous variable systems in Gaussian states, logarithmic negativity is used. We find that the dynamics of the quantum entanglement is sensitive to the initial states, the oscillator-oscillator interaction, the oscillator-environment interaction and the coupling to a common bath or to different, independent baths.
We analyze the dynamics of quantum correlations between two qubits coupled to a linear chain of oscillators. The chain mediates interactions between the qubits and acts as a non-Markovian reservoir. The model is amenable to an analytical solution when the initial state of the chain is Gaussian. We study the dynamics of the qubits' concurrence starting from a separable state and assuming that the chain spectrum is gapped and the chain is initially in a thermal state. We identify three relevant regimes that depend on the strength of the qubit-chain coupling in relation to the spectral gap. These are (i) the weak-coupling regime, where the qubits are entangled at the asymptotics, (ii) the strong-coupling regime, where the concurrence can exhibit collapses followed by revivals with exponentially attenuated amplitude, and (iii) the thermal damping regime, where the concurrence rapidly vanishes due to the chain's thermal excitations. In all cases, if entanglement is generated, this occurs after a finite time has elapsed. This time scale depends exponentially on the qubits' distance and is determined by the spectral properties of the chain. Entanglement irreversible decay, on the other hand, is due to the dissipative effect induced by the coupling with the chain and is controlled by the coupling strength between the chain and qubits. This study unravels the basic mechanisms leading to entanglement in a non-Markovian bath and allows one to identify the key resources for realizing quantum coherent dynamics of open systems.
The dynamical aspects of quantum Brownian motion at low temperatures are investigated. Exact calculations of quantum entanglement among two Brownian oscillators are given without invoking the Born-Markov or Born approximation widely used for the study of open systems. Nonlocality due to finite oscillator separation is studied. Our approach is applicable for arbitrary time scale, in particular suitable to probe the short-time regime at cold temperatures where many experiments on quantum information processing are performed. We study separability criteria based on the uncertainty relation, negativity, and entanglement of formation. We found a crossover behavior in a disentanglement process between quantum- and thermal-fluctuation-dominated regimes. The fluctuation-dissipation theorem is violated for two Brownian particles interacting with a common environment. The deviation from the relation originates in the interaction mediated by the environment, which drives two particles into a steady oscillatory state, preventing the system from thermalizing. Consequently there is a residual entanglement at low temperatures for arbitrary coupling strength. This entanglement is generated from the environment nonperturbatively even when two modes are not entangled initially. When the distance between two oscillators is varied, competition between entanglement induced from the environment and modified decoherence due to finite separation leads to the characteristic distance where entanglement is minimized.
Two defect particles that couple to a harmonic chain, acting as common reservoir, can become entangled even when the two defects do not directly interact and the harmonic chain is effectively a thermal reservoir for each individual defect. This dynamics is encountered for sufficiently low temperatures of the chain and depends on the initial state of the two oscillators. In particular, when each defect is prepared in a squeezed state, entanglement can be found at time scales at which the steady state of a single defect is reached. We provide a microscopic description of the coupled quantum dynamics of chain and defects. By means of numerical simulations, we explore the parameter regimes for which entanglement is found under the specific assumption that both particles couple to the same ion of the chain. This model provides the microscopic setting where bath-induced entanglement can be observed.