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arXiv:1304.2864 · Europhysics Letters (EPL)

Steady entanglement out of thermal equilibrium

Bruno Bellomo, Mauro Antezza

Published Oct 1, 2013• 38 citations
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Abstract

We study two two-level atomic quantum systems (qubits) placed close to a body held at a temperature different from that of the surrounding walls. While at thermal equilibrium the two-qubit dynamics is characterized by non-entangled steady thermal states, we show that the absence of thermal equilibrium may bring to the generation of entangled steady states. Remarkably, this entanglement emerges from the two-qubit dissipative dynamic itself, without any further external action on the two qubits, suggesting a new protocol to create and protect entanglement which is intrinsically robust to environmental effects.

DOI
10.1209/0295-5075/104/10006

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We study two two-level atomic quantum systems (qubits) placed close to a body held at a temperature different from that of the surrounding walls. While at thermal equilibrium the two-qubit dynamics is characterized by non-entangled steady thermal states, we show that the absence of thermal equilibrium may bring to the generation of entangled steady states. Remarkably, this entanglement emerges from the two-qubit dissipative dynamic itself, without any further external action on the two qubits, suggesting a new protocol to create and protect entanglement which is intrinsically robust to environmental effects.
We study the internal dynamics, the quantum thermalization and the entanglementof elementary quantum systems (one or two atoms) placed close to a body held at atemperature different from that of the surrounding radiation.Concerning the single atom dynamics [1,2], we derive general expressions for lifetimeand density matrix valid for bodies of arbitrary geometry and dielectric permittivity.Out of equilibrium, the thermalization process and steady states become both qualitativelyand quantitatively significantly different from the case of radiation at thermalequilibrium. For the case of a three-level atom close to a slab of finite thickness, wepredict the occurrence of population inversion and an efficient cooling mechanism forthe quantum system, whose effective internal temperature can be driven to values muchlower than both involved temperatures. Our results show that non-equilibrium configurationsprovide new promising ways to control the state of an atomic system.We also consider two two-level atomic quantum systems (qubits) [3]. While at thermalequilibrium the two-qubit dynamics is characterized by not entangled steady thermalstates, we show that absence of thermal equilibrium may bring to the generationof entangled steady states. Remarkably, this entanglement emerges from the two-qubitdissipative dynamic itself, without any further external action on the two qubits, suggestinga new protocol to produce and protect entanglement which is intrinsically robustto environmental effects.======================[1] Bruno Bellomo, Riccardo Messina, and Mauro Antezza, Europhys. Lett. 100, 20006(2012).[2] Bruno Bellomo, Riccardo Messina, Didier Felbacq, and Mauro Antezza, Phys. Rev.A 87, 012101 (2013).[3] Bruno Bellomo, and Mauro Antezza, arXiv:1304.2864 (2013).
We investigate the creation of entanglement between two quantum emitters interacting with a realistic common stationary electromagnetic field out of thermal equilibrium. In the case of two qubits we show that the absence of equilibrium allows the generation of steady entangled states, which is inaccessible at thermal equilibrium and is realized without any further external action on the two qubits. We first give a simple physical interpretation of the phenomenon in a specific case and then we report a detailed investigation on the dependence of the entanglement dynamics on the various physical parameters involved. Sub- and super-radiant effects are discussed, and qualitative differences in the dynamics concerning both creation and protection of entanglement according to the initial two-qubit state are pointed out.
Abstract. We investigate the creation of entanglement between two quantum emitters interacting with a realistic common stationary electromagnetic field out of thermal equilibrium. In the case of two qubits we show that the absence of equilibrium allows the generation of steady entangled states, which is inaccessible at thermal equilibrium and is realized without any further external action on the two qubits. We first give a simple physical interpretation of the phenomenon in a specific case and then we report a detailed investigation on the dependence of the entanglement dynamics on the various physical parameters involved. Sub- and super-radiant effects are discussed, and qualitative differences in the dynamics concerning both creation and protection of entanglement according to the initial two-qubit state are pointed out.
We study an ensemble of two-level quantum systems (qubits) interacting with a common electromagnetic field in the proximity of a dielectric slab whose temperature is held different from that of some far surrounding walls. We show that the dissipative dynamics of the qubits driven by this stationary and out of thermal equilibrium field allows the production of steady many-body entangled states, different from the case at thermal equilibrium where steady states are always nonentangled. By studying up to ten qubits, we point out the role of symmetry in the entanglement production, which is exalted in the case of permutationally invariant configurations. In the case of three qubits, we find a strong dependence of tripartite entanglement on the spatial disposition of the qubits, and in the case of six qubits we find several highly entangled bipartitions where entanglement can, remarkably, survive for large qubit-qubit distances up to $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$.
The challenge of harnessing entanglement during the non-equilibrium dynamics of open quantum systems, especially at high temperatures, is highly prominent within recent scientific researches. Due to the ongoing trend of miniaturization of quantum devices that exploit quantum correlations, proposing novel schemes to overcome this challenge is itself a crucial task within current quantum technological research. We contribute to this research by proposing a new scheme to control entanglement dynamics of a non-equilibrium two-qubit Heisenberg XXZ spin chain model in an external magnetic field. The design of the scheme is based on a coupling asymmetry in the model induced by the asymmetrical connection of qubits to two independent thermal reservoirs. While in the absence of the coupling asymmetry, non-equilibrium effects generally suppress the dynamical generation of thermal entanglement, making entanglement production impossible at high mean temperatures of reservoirs, it is shown that this asymmetry in the coupling potentially enables us to generate a maximal non-equilibrium entanglement even in the high mean temperature regime. We show that the coupling asymmetry can also lead to a complete protection of the maximum initial entanglement between the qubits at high mean temperatures of the reservoirs thanks to the non-equilibrium conditions. Depending on the initial state of the two qubits, this can be achieved either by accessing a coherence-free subspace or by fully reviving the initial qubit-qubit entanglement. Furthermore, we investigate the quantum heat transport of the chain, and find that by turning on the asymmetry in the qubit-reservoir coupling, although the chain loses its initial thermal rectification property over time, it regains this property and maintain it until the non-equilibrium steady state is reached. Our results show that, at higher temperature gradients, the chain leverages the steady-state entanglement to completely block the heat released from the hot reservoir. Our findings can be significant for heat management in quantum computing devices such as solid-state thermal circuits.
We discuss a simple quantum thermal machine for the generation of steady-state entanglement between two interacting qubits. The machine is autonomous in the sense that it uses only incoherent interactions with thermal baths, but no source of coherence or external control. By weakly coupling the qubits to thermal baths at different temperatures, inducing a heat current through the system, steady-state entanglement is generated far from thermal equilibrium. Finally, we discuss two possible implementations, using superconducting flux qubits or a semiconductor double quantum dot. Experimental prospects for steady-state entanglement are promising in both systems.