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arXiv:2010.05885 · Physical Review A

Entanglement generation in quantum thermal machines

Milton Aguilar, Nahuel Freitas, Juan Pablo Paz

Published Dec 23, 2020• 10 citations
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Abstract

We show that in a linear quantum machine, a driven quantum system that evolves while coupled with thermal reservoirs, entanglement between the reservoir modes is unavoidably generated. This phenomenon, which occurs at sufficiently low temperatures and is at the heart of the third law of thermodynamics, is a consequence of a simple process: the transformation of the energy of the driving field into pairs of excitations in the reservoirs. For a driving with frequency ${\ensuremath{\omega}}_{d}$ we show entanglement exists between environmental modes whose frequencies satisfy the condition ${\ensuremath{\omega}}_{i}+{\ensuremath{\omega}}_{j}={\ensuremath{\omega}}_{d}$. We show that this entanglement can persist for temperatures that can be significantly higher than the lowest achievable ones with sideband resolved cooling methods.

DOI
10.1103/physreva.102.062422

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We show that in a linear quantum machine, a driven quantum system that evolves while coupled with thermal reservoirs, entanglement between the reservoir modes is unavoidably generated. This phenomenon, which occurs at sufficiently low temperatures and is at the heart of the third law of thermodynamics, is a consequence of a simple process: the transformation of the energy of the driving field into pairs of excitations in the reservoirs. For a driving with frequency \ensuremathωd{\ensuremath{\omega}}_{d}\ensuremathωd​ we show entanglement exists between environmental modes whose frequencies satisfy the condition \ensuremathωi+\ensuremathωj=\ensuremathωd{\ensuremath{\omega}}_{i}+{\ensuremath{\omega}}_{j}={\ensuremath{\omega}}_{d}\ensuremathωi​+\ensuremathωj​=\ensuremathωd​. We show that this entanglement can persist for temperatures that can be significantly higher than the lowest achievable ones with sideband resolved cooling methods.
We study intraenvironmental classical and quantum correlations in a thermal machine, which is modeled as a driven quantum system coupled with thermal reservoirs. We compute the mutual information, the quantum discord, and the entanglement between two parts of the environment formed by oscillators centered around two different frequencies. We show that there are only two processes that generate time-extensive correlations in the long-time limit. First, there is a resonant process which is responsible for the transport of excitations between different environmental modes due to the absorption (or emission) of energy from (or into) the driving field. Second, there is a nonresonant process that transforms the energy from the external driving into pairs of excitations in two environmental modes. We show that there is a regime when the mutual information and the quantum discord between the parts of the environment correlated by these two processes grow quadratically in time, while entanglement production is time extensive.
We present a theoretical investigation of entanglement generation in an external quantum system during its interaction with a quantum autonomous thermal machine (QATM) under non-Markovian dynamics. The QATM, composed of two qubits each coupled to independent thermal reservoirs, interacts with an external system of two additional qubits. By analyzing the Hilbert space structure, energy level configurations, and temperature gradients, we define a common interaction between the QATM qubits and the external system qubits, which allows the definition of two thermodynamic cycles (A and B) governed by virtual temperatures and energy-conserving transitions. We demonstrate that the QATM can act as a structured reservoir able to induce non-Markovian memory effects highlighted by negative entropy production rates. Using mutual information and concurrence, we show that entanglement is generated only using cycle A, which is associated with stronger non-Markovian behavior and higher coherence correlations. Our results demonstrate that temperature differences, Hilbert space structure, and coherence serve as quantum resources for controlling and enhancing entanglement in quantum thermodynamic settings, with parameters consistent with experimental superconducting qubit platforms.
Classical engines turn thermal resources into work, which is maximized for reversible operations. The quantum realm has expanded the range of useful operations beyond energy conversion, and incoherent resources beyond thermal reservoirs. This is the case of entanglement generation in a driven-dissipative protocol, which we hereby analyze as a continuous quantum machine. We show that for such machines the more irreversible the process, the larger the concurrence. Maximal concurrence and entropy production are reached for the hot reservoir being at negative effective temperature, beating the limits set by classic thermal operations on an equivalent system.
In a bipartite system subject to decoherence from two separate reservoirs, entanglement is typically destroyed faster than where there is a single reservoir. Surprisingly, however, the existence of separate reservoirs can also have a beneficial entangling effect: if the qubits are coupled and driven externally by a classical field, the system ends in a stationary state characterized by a finite degree of entanglement. This phenomenon occurs only in a certain region of the parameter space and the structure of the stationary state has a universal form which does not depend on the initial state or on the specific physical realization of the qubits. We show that the entanglement thus generated can be propagated within a quantum network using simple local unitary operations. We suggest the use of such systems as 'batteries of entanglement' in quantum circuits.
The study of quantum thermodynamics is key to the development of quantum thermal machines. In contrast to most of the previous proposals based on discrete strokes, here we consider a working substance that is permanently coupled to two or more baths at different temperatures and continuously driven. To this end, we investigate parametrically driven quantum harmonic oscillators coupled to heat baths via a collision model. Using a thermodynamically consistent local master equation, we derive the heat flows and power of the working device, which can operate as an engine, refrigerator, or accelerator, and analyze the instantaneous and average efficiencies and coefficients of performance. Studying the regimes of both slow and fast driving of the system, we find that an increased driving frequency can lead to a change of functioning to a dissipator. Finally, we investigate the effect of squeezing one of the thermal baths: it leads to an apparent higher efficiency compared to the corresponding Carnot value of an equilibrium bath with the same temperature and to sustained entanglement between the working substance oscillators in the limit cycle.
In a bipartite system subject to decoherence from two separate reservoirs, entanglement is typically destroyed faster than where there is a single reservoir. Surprisingly, however, the existence of separate reservoirs can also have a beneficial entangling effect: if the qubits are coupled and driven externally by a classical field, the system ends in a stationary state characterized by a finite degree of entanglement. This phenomenon occurs only in a certain region of the parameter space and the structure of the stationary state has a universal form which does not depend on the initial state or on the specific physical realization of the qubits. We show that the entanglement thus generated can be propagated within a quantum network using simple local unitary operations. We suggest the use of such systems as 'batteries of entanglement' in quantum circuits.