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arXiv:2008.04359 · Physical Review A

Quantum-memory-enhanced dissipative entanglement creation in nonequilibrium steady states

Daniel Heineken, Konstantin Beyer, Kimmo Luoma, Walter T. Strunz

Published Nov 24, 2021• 19 citations
arXivHTMLPDF

Abstract

This article investigates dissipative preparation of entangled nonequilibrium steady states (NESS). We construct a collision model where the open system consists of two qubits which are coupled to heat reservoirs with different temperatures. The baths are modeled by sequences of qubits interacting with the open system. The model can be studied in different dynamical regimes: with and without environmental memory effects. We report that only a certain bath temperature range allows for entangled NESS. Furthermore, we obtain minimal and maximal critical values for the heat current through the system. Surprisingly, quantum memory effects play a crucial role in the long-time limit. First, memory effects broaden the parameter region where quantum correlated NESS may be dissipatively prepared and, second, they increase the attainable concurrence. Most remarkably, we find a heat current range that does not only allow, but even guarantees that the NESS is entangled. Thus, the heat current can witness entanglement of nonequilibrium steady states.

DOI
10.1103/physreva.104.052426

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This article investigates dissipative preparation of entangled nonequilibrium steady states (NESS). We construct a collision model where the open system consists of two qubits which are coupled to heat reservoirs with different temperatures. The baths are modeled by sequences of qubits interacting with the open system. The model can be studied in different dynamical regimes: with and without environmental memory effects. We report that only a certain bath temperature range allows for entangled NESS. Furthermore, we obtain minimal and maximal critical values for the heat current through the system. Surprisingly, quantum memory effects play a crucial role in the long-time limit. First, memory effects broaden the parameter region where quantum correlated NESS may be dissipatively prepared and, second, they increase the attainable concurrence. Most remarkably, we find a heat current range that does not only allow, but even guarantees that the NESS is entangled. Thus, the heat current can witness entanglement of nonequilibrium steady states.
Collision models provide a simple and versatile setting to capture the dynamics of open quantum systems. The standard approach to thermalization in this setting involves an environment of independent and identically prepared thermal qubits, interacting sequentially for a finite duration Δ t with the system. We compare this to a two-bath scenario in which collisional qubits are prepared in either their ground or excited states and the environment temperature is encoded in system-environment couplings. The system reaches the same thermal steady state for both settings, although even in this limit they describe fundamentally different physical processes, with the two-bath setup yielding a nonequilibrium state with finite heat currents. Non-Markovian dynamics arises when intraenvironment interactions in either setting are introduced. Here the system in the single-bath setup again reaches a steady state at the canonical temperature of the bath, but the nonequilibrium steady state of the two-bath setup tends to a different temperature due to the generation of strong system-environment and intraenvironment correlations. The two-bath setting is particularly suited to studying quantum trajectories, which are well defined also for the non-Markovian case. We showcase this with a trajectory analysis of the heat currents within a two-point measurement scheme. Finally, we consider how our results are impacted when the system-environment interaction leads to strict homogenization. Our results provide insights into the dynamics and thermodynamics of thermalization towards nonequilibrium steady states and the role of non-Markovian interactions.
We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths (IHBs) or two common heat baths (CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steady-state with stronger coupling regime between two qubits than qubit–baths. We do not make the rotating wave approximation (RWA) for the qubit–qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime, the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures. We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong (weak) coupling regime, the heat current increases (decreases) with coupling strength increasing when the temperature of one bath is lower (higher) than the other, and the energy detuning leads to a positive (negative) effect when the temperature is low (high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.
We show how entangled steady states can be prepared by purely dissipative dynamics in a system coupled to a thermal environment. While entanglement is hindered by thermalization when the system and environment exchange a conserved quantity, we demonstrate that breaking this conservation law through the system-environment interaction drives the system to a nonequilibrium steady state. Such an interaction will generate multiple competing equilibration channels, effectively mimicking baths at distinct chemical potentials. When the environment also supports long-range correlations, these channels mediate nonlocal dissipation capable of generating entanglement. We illustrate the scheme in a model of two nitrogen-vacancy (NV) centers weakly coupled to a spin-pumped magnet, where tuneable magnon excitations enable steady-state entanglement over finite distances. Our results identifies a general mechanism for dissipative entanglement generation, rooted in the conservation structure and environmental correlations rather than fine-tuned coherent control or active driving.
We analytically and numerically investigate the steady-state entanglement and coherence of two coupled qubits, each interacting with a local boson or fermion reservoir, based on the Bloch-Redfield master equation beyond the secular approximation. We find that there is nonvanishing steady-state coherence in the nonequilibrium scenario, which grows monotonically with the nonequilibrium condition quantified by the temperature difference or chemical potential difference of the two baths. The steady-state entanglement, in general, is a nonmonotonic function of the nonequilibrium condition as well as the bath parameters in the equilibrium setting. We also discover that weak interqubit coupling and high base temperature or chemical potential of the baths can strongly suppress the steady-state entanglement and coherence, regardless of the strength of the nonequilibrium condition. On the other hand, the energy detuning of the two qubits, when used in a compensatory way with the nonequilibrium condition, can lead to significant enhancement of the steady-state entanglement in some parameter regimes. In addition, the qubits typically have a stronger steady-state entanglement when coupled to fermion baths exchanging particles with the system than boson baths exchanging energy with the system, under similar conditions. We also identify a close connection between the energy current flowing through the system and the steady-state coherence. Preliminary investigations suggest that these results are insensitive to the form of the reservoir spectral densities in the Markovian regime. Feasible experimental realization of measuring the steady-state entanglement and coherence is discussed for the coupled qubit system in nonequilibrium environments. Our findings offer some general guidelines for optimizing the steady-state entanglement and coherence in the coupled qubit system and may find potential applications in quantum information technology.
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.
We study the effects of dissipation induced blockade on the dynamics of an open quantum system having two qubits in nonequilibrium independent baths. The qubits are driven by a classical field with a temporally modulated detuning. The introduction of blockade induced via two effective baths together with the effect of the driving field enable us to observe maximal entanglement oscillation of about unity that decays with a quasi-steady entanglement state oscillating about the 1/2 limit with adjustable decay rate. When the temperature difference between two baths is not large, maximal entanglement oscillation can still be observed in the model. In addition, the adjustment of the nonequilibrium thermal baths by modulating the dissipation and the application of time-dependent detuning give rise to rich entanglement dynamics. We further demonstrate numerically the practical implementation of the proposed scheme with a universal cavity QED setting.