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arXiv:2406.09580

Steady-state work extraction from two coupled qubits embedded within equilibrium and non-equilibrium reservoirs

Maryam Hadipour, Soroush Haseli

Published Jun 13, 2024• 0 citations
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Abstract

Work extraction is a fundamental aspect in thermodynamics. In the context of quantum physics, ergotropy quantifies the maximum amount of work that can be obtained from quantum system through cyclic unitary process. In this work, the steady-state ergotropy of two coupled qubit, each interacting locally with its individual boson or fermion reservoir, will be examined. In this work, both equilibrium and non-equilibrium scenarios for bosonic and fermionic environments interacting with the qubits will be considered. In scenarios where two coupled qubits embedded within equilibrium boson reservoirs, it has been observed that the temperature of the reservoirs and the inter-qubits interaction strangth act as detrimental factors in work extraction. In the case of fermionic equilibrium reservoirs, it will be observed that ergotropy grows monotonically with the reservoirs chemical potential. In the non-equilibrium boson reservoirs, the temperature difference between the two reservoirs is a destructive factor for ergotropy. In non-equilibrium fermion reservoirs, the situation is somewhat more complicated. For r base chemical potential values that are smaller than the qubit transition frequency, the behavior of ergotropy is non-monotonic. However, for base chemical potential values that are larger than the transition frequency, ergotropy grows monotonically with the reservoirs chemical potential difference. Also, we study the situation in which the coupled qubits are asymmetric. It is observed that the maximum work will be extracted in the situation where the coupled qubits within both boson and fermion reservoirs be symmetric .

DOI
10.48550/arxiv.2406.09580

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Work extraction is a fundamental aspect in thermodynamics. In the context of quantum physics, ergotropy quantifies the maximum amount of work that can be obtained from quantum system through cyclic unitary process. In this work, the steady-state ergotropy of two coupled qubit, each interacting locally with its individual boson or fermion reservoir, will be examined. In this work, both equilibrium and non-equilibrium scenarios for bosonic and fermionic environments interacting with the qubits will be considered. In scenarios where two coupled qubits embedded within equilibrium boson reservoirs, it has been observed that the temperature of the reservoirs and the inter-qubits interaction strangth act as detrimental factors in work extraction. In the case of fermionic equilibrium reservoirs, it will be observed that ergotropy grows monotonically with the reservoirs chemical potential. In the non-equilibrium boson reservoirs, the temperature difference between the two reservoirs is a destructive factor for ergotropy. In non-equilibrium fermion reservoirs, the situation is somewhat more complicated. For r base chemical potential values that are smaller than the qubit transition frequency, the behavior of ergotropy is non-monotonic. However, for base chemical potential values that are larger than the transition frequency, ergotropy grows monotonically with the reservoirs chemical potential difference. Also, we study the situation in which the coupled qubits are asymmetric. It is observed that the maximum work will be extracted in the situation where the coupled qubits within both boson and fermion reservoirs be symmetric .
This study investigates the thermodynamic behavior of a two-qubit quantum system, where each qubit is coupled to an independent thermal reservoir, either bosonic or fermionic. Using a master equation approach, we analyze both steady-state and time-dependent ergotropy to understand how different reservoir statistics affect work extraction. In bosonic environments, ergotropy consistently declines with increasing temperature due to thermal noise. In contrast, fermionic reservoirs exhibit more complex behavior, with ergotropy enhanced by particle transport under non-equilibrium conditions. Our results reveal a threshold-like sensitivity to the chemical potential configuration, leading to qualitatively distinct regimes of energy storage performance. Time-resolved analyses show that the system's approach to steady state varies depending on the type of reservoir and the coupling strength between qubits. These insights highlight how carefully engineered reservoir properties and non-equilibrium driving can be leveraged to optimize quantum battery performance.
Understanding the generation and activation of ergotropy, the maximum work extractable by cyclic unitary operations, is central to quantum battery research. Positive-temperature thermal states are passive, whereas nonequilibrium environments can sustain nonpassive steady states with nonzero ergotropy. However, the full secular approximation commonly used in Lindblad descriptions can suppress steady-state coherence and obscure its contribution to ergotropy. Using a Bloch-Redfield master equation beyond the full secular approximation, we investigate the ergotropy of the nonequilibrium steady state (NESS) of two exchange-coupled qubits connected to independent thermal reservoirs. The NESS ergotropy of two qubits with the same frequency is entirely coherent and grows quadratically with temperature bias near equilibrium. In contrast, detuned qubits can exhibit incoherent ergotropy. We derive an exact analytical criterion for its activation and show that activation requires the hotter reservoir to be coupled to the qubit with the higher bare frequency. Comparing NESSs obtained with and without full secularization reveals quantitative and qualitative differences in ergotropy that reflect changes in both its coherent and incoherent contributions. The results clarify the mechanisms of NESS ergotropy activation and demonstrate the importance of retaining steady-state coherence beyond the full secular approximation when characterizing stationary work resources.
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.
We study the ergotropy and the thermodynamic potentials of a qubit battery charged by repeated interactions with clusters of thermal ancillas, qubits or oscillators, through a composite system-bath coupling that generates steady-state coherence in the energy basis. A single parameter encoding the bath quantum statistics yields the coherence and ergotropy in closed form for any cluster size. For large clusters, the ergotropy becomes independent of the bath statistics and, at optimal couplings, reaches a universal fraction of the equilibrium internal energy of the qubit at the bath temperature. Since the charged state has no population inversion, all extractable work comes from coherence. The ergotropy is flat at low temperatures. We trace this plateau to the third law, and show that the ergotropy is proportional to the equilibrium enthalpy of the qubit, whose slope vanishes with the heat capacity. For a battery composed of multiple qubits, the coherence grows exponentially with the number of qubits while the ergotropy grows linearly, both remaining a nearly constant fraction of their respective maxima. The charged state is a non-equilibrium steady state with finite entropy at zero temperature, sustained by the work of switching the collisional interaction on and off. The cost is nonzero whenever the parallel coupling is nonzero, and, unlike the ergotropy, it depends on the bath statistics.
Ergotropy, which represents the maximum amount of work that can be extracted from a quantum system, has become a focal point of interest in the fields of quantum thermodynamics and information processing. In practical scenarios, the interaction of quantum systems with their surrounding environment is unavoidable. Recent studies have increasingly focused on analyzing open quantum systems affected by non-stationary environmental fluctuations due to their significant impact on various physical scenarios. While much research has concentrated on work extraction from these systems, it often assumes that the environmental degrees of freedom are substantial and that the environment is effectively in equilibrium. This has led us to explore work extraction from quantum systems under non-stationary environmental conditions. In this work, the dynamics of ergotropy will be investigated in a non-equilibrium environment for both Markovian and non-Markovian regime. In this study, both the coherent and incoherent parts of the ergotropy will be considered. It will be shown that for a non-equilibrium environment, the extraction of work is more efficient compared to when the environment is in equilibrium.
Coupling of a quantum battery (QB) to two thermal reservoirs brings it to a nonequilibrium steady-state (NESS). In this situation, although, the QB can be charged through the NESS heat current, no work may be extracted from it through unitary cyclic processes. We exemplify this statement by studying the two- and three-qubit XXZXXZXXZ spin-chain QBs coupled weakly to two different thermal reservoirs in a symmetric configuration wherein each end of chain interacts with an individual reservoir. We show that the work can be extracted at positive temperature bias when two ends of a XXZXXZXXZ chain are collectively coupled to the hot reservoir.