Entanglement and its dynamics in open, dissipative systems

Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gas-type systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states. We develop master equations to describe the system and its interaction with an environment, study toy models with two particles (qubits), where the master equation can often be solved analytically, and finally examine larger systems with possibly fluctuating particle numbers. We find that in gas-type systems, the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment, while this is not true in strongly coupled systems. But even then the temperature range where one can find entangled steady states is typically much higher with the reset mechanism.Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gas-type systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from the entanglement that one can find in thermal states. We develop master equations to describe the system and its interaction with an environment, study toy models with two particles (qubits), where the master equation can often be solved analytically, and finally examine larger systems with possibly fluctuating particle numbers. We find that in gas-type systems, the reset mechanism can produce an entangled steady state for an arbitrary temperature of the environment, while this is not true in strongly coupled systems. But even then the temperature range where one can find entangled steady states is typically much higher with the reset mechanism.

arXiv:quant-ph/0703138New Journal of PhysicsJul 13, 200729 citations

Steady-state entanglement in open and noisy quantum systems

Ludwig Hartmann, Wolfgang Dür, Hans J. Briegel

We show that quantum mechanical entanglement can prevail in noisy open quantum systems at high temperature and far from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number $N$ of interacting quantum particles, and can interact and exchange particles with some environments. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g., by replacing them with particles from the environment. We present a master equation that describes this process, which we can solve analytically for small $N$ . If we vary the interaction strength and the reset against decoherence rate, we find a threshold below which the equilibrium state is classically correlated and above which there is a parameter region with genuine entanglement.We show that quantum mechanical entanglement can prevail in noisy open quantum systems at high temperature and far from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number $N$ of interacting quantum particles, and can interact and exchange particles with some environments. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g., by replacing them with particles from the environment. We present a master equation that describes this process, which we can solve analytically for small $N$. If we vary the interaction strength and the reset against decoherence rate, we find a threshold below which the equilibrium state is classically correlated and above which there is a parameter region with genuine entanglement.

arXiv:quant-ph/0512219Physical Review ANov 3, 2006104 citations

Entanglement in quantum many-body systems far away from thermodynamic equilibrium

Hans J. Briegel

We show that quantum mechanical entanglement can prevail even in noisy open quantum many-body systems at high temperature and far away from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number N of interacting quantum particles, and it can interact and exchange particles with some environment. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g. by replacing them with particles from the environment.We show that quantum mechanical entanglement can prevail even in noisy open quantum many-body systems at high temperature and far away from thermodynamical equilibrium, despite the deteriorating effect of decoherence. The system consists of a number N of interacting quantum particles, and it can interact and exchange particles with some environment. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g. by replacing them with particles from the environment.

OSA Workshop on Entanglement and Quantum DecoherenceJan 1, 20080 citations

Non-Markovian dynamics of open quantum systems

Christen H. Fleming

An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..An open quantum system is a quantum system that interacts with some environment whose degrees of freedom have been coarse grained away. This model describes non-equilibrium processes more general than scattering-matrix formulations. Furthermore, the microscopically-derived environment provides a model of noise, dissipation and decoherence far more general than Markovian (white noise) models. The latter are fully characterized by Lindblad equations and can be motivated phenomenologically. Non-Markovian processes consistently account for backreaction with the environment and can incorporate effects such as finite temperature and spatial correlations. We consider linear systems with bilinear coupling to the environment, or quantum Brownian motion, and nonlinear systems with weak coupling to the environment. For linear systems we provide exact solutions with analytical results for a variety of spectral densities. Furthermore, we point out an important mathematical subtlety which led to incorrect master-equation coefficients in earlier derivations, given nonlocal dissipation. For nonlinear systems we provide perturbative solutions by translating the formalism of canonical perturbation theory into the context of master equations. It is shown that unavoidable degeneracy causes an unfortunate reduction in accuracy between perturbative master equations and their solutions. We also extend the famous theorem of Lindblad, Gorini, Kossakowski and Sudarshan on completely positivity to non-Markovian master equations. Our application is primarily to model atoms interacting via a common electromagnetic field. The electromagnetic field contains correlations in both space and time, which are related to its relativistic (photon-mediated) nature. As such, atoms residing in the same field experience different environmental effects depending upon their relative position and orientation. Our more accurate solutions were necessary to assess sudden death of entanglement at zero temperature. In contrast to previous claims, we found that all initial states of two-level atoms undergo finite-time disentanglement. We were also able to access regimes which cannot be described by Lindblad equations and other simpler methods, such as near resonance. Finally we revisit the infamous Abraham-Lorentz force, wherein a single particle in motion experiences backreaction from the electromagnetic field. This leads to a number of well-known problems including pre-acceleration and runaway solutions. We found a more a more-suitable open-system treatment of the nonrelativistic particle to be perfectly causal and dissipative without any extraneous requirements for finite size of the particle, weak coupling to the field, etc..

Jan 1, 20116 citations

Quantum entanglement at high temperatures? Bosonic systems in nonequilibrium steady state

Jen-Tsung Hsiang, B. L. Hu

This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.This is the second of a series of three papers examining how viable it is for entanglement to be sustained at high temperatures for quantum systems in thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium steady state (NESS) conditions (Case C). The system we analyze here consists of two coupled quantum harmonic oscillators each interacting with its own bath described by a scalar field, set at temperatures T 1 > T 2. For constant bilinear inter-oscillator coupling studied here (Case C1) owing to the Gaussian nature, the problem can be solved exactly at arbitrary temperatures even for strong coupling. We find that the valid entanglement criterion in general is not a function of the bath temperature difference, in contrast to thermal transport in the same NESS setting [1]. Thus lowering the temperature of one of the thermal baths does not necessarily help to safeguard the entanglement between the oscillators. Indeed, quantum entanglement will disappear if any one of the thermal baths has a temperature higher than the critical temperature T c, defined as the temperature above which quantum entanglement vanishes. With the Langevin equations derived we give a full display of how entanglement dynamics in this system depends on T 1, T 2, the inter-oscillator coupling and the system-bath coupling strengths. For weak oscillator-bath coupling the critical temperature T c is about the order of the inverse oscillator frequency, but for strong oscillator-bath coupling it will depend on the bath cutoff frequency. We conclude that in most realistic circumstances, for bosonic systems in NESS with constant bilinear coupling, ‘hot entanglement’ is largely a fiction.

arXiv:1503.03587Journal of High Energy PhysicsNov 1, 201517 citations

Entanglement of two distant qubits driven by thermal environments

Víctor Montenegro, Vitalie Eremeev, Miguel Orszag

A model of entanglement generation of two initially disentangled qubits, each coupled to a separate cavity with the cavities connected by a fiber, is considered. The creation and evolution of the atomic entanglement are studied in the framework of the microscopic master equation capable of describing an open quantum system. The cavities and fiber are coupled to their own thermal environment. In these conditions, we compute the concurrence as a measure of the atomic entanglement and study the contribution of the environments at finite temperature to the dynamics of entanglement. As a result, one finds interesting effects where the thermal baths stimulate the generation of the entanglement in a given range of temperatures and the effect could be seen especially at some stage of the entanglement evolution. The range of temperatures at which entanglement increases is limited by some optimal values, depending on the physical characteristics of the system, such as operating cavity/fiber frequencies, atom–field detuning and couplings, and loss rates.A model of entanglement generation of two initially disentangled qubits, each coupled to a separate cavity with the cavities connected by a fiber, is considered. The creation and evolution of the atomic entanglement are studied in the framework of the microscopic master equation capable of describing an open quantum system. The cavities and fiber are coupled to their own thermal environment. In these conditions, we compute the concurrence as a measure of the atomic entanglement and study the contribution of the environments at finite temperature to the dynamics of entanglement. As a result, one finds interesting effects where the thermal baths stimulate the generation of the entanglement in a given range of temperatures and the effect could be seen especially at some stage of the entanglement evolution. The range of temperatures at which entanglement increases is limited by some optimal values, depending on the physical characteristics of the system, such as operating cavity/fiber frequencies, atom–field detuning and couplings, and loss rates.

Physica ScriptaFeb 1, 20126 citations

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of interacting quantum particles, and can interact and exchange particles with some environments. The effect of decoherence is counteracted by a simple mechanism, where system particles are randomly reset to some standard initial state, e.g., by replacing them with particles from the environment. We present a master equation that describes this process, which we can solve analytically for small

N

. If we vary the interaction strength and the reset against decoherence rate, we find a threshold below which the equilibrium state is classically correlated and above which there is a parameter region with genuine entanglement.