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arXiv:2408.02655 · Quantum Science and Technology

Local ergotropy and its fluctuations across a dissipative quantum phase transition

G. Di Bello, Donato Farina, D. J. Jansen, C. A. Perroni, V. Cataudella, G. De Filippis

Published Dec 10, 2024• 13 citations
arXivHTMLPDF

Abstract

Abstract We investigate a two-qubit open Rabi model, focusing on local ergotropy-the maximum extractable work by acting solely on the two qubits-within a parameter regime where a Berezinskii–Kosterlitz–Thouless dissipative phase transition occurs. First, we aim to define a protocol for charging, storing, and discharging the two-qubit subsystem, interpreted as the working principle of an open quantum battery. Second, we examine the impact of the phase transition on ergotropy and identify potential markers. To achieve these goals, we construct an ad-hoc charging unitary operator, leveraging our knowledge of the ground state near the transition to bring it into a decoherence-free state (DFS) during storage. Using state-of-the-art numerics based on matrix product state representation, we reveal that high couplings to an external bath approximately double the local ergotropy immediately post-charging. Over time we observe oscillatory behaviors in ergotropy and its fluctuations, which undergo significant changes near the transition, signaling its occurrence. Furthermore, we optimize local ergotropy over time using a physically inspired ansatz, enabling work extraction at a generic time (local ergotropy never reaches zero). Our work proposes a tunable, experimentally realizable protocol for work extraction, leveraging DFS and phase transitions. Additionally, it sheds light on the complex interaction between local ergotropy and quantum phase transitions.

DOI
10.1088/2058-9565/ad9cbb

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Abstract We investigate a two-qubit open Rabi model, focusing on local ergotropy-the maximum extractable work by acting solely on the two qubits-within a parameter regime where a Berezinskii–Kosterlitz–Thouless dissipative phase transition occurs. First, we aim to define a protocol for charging, storing, and discharging the two-qubit subsystem, interpreted as the working principle of an open quantum battery. Second, we examine the impact of the phase transition on ergotropy and identify potential markers. To achieve these goals, we construct an ad-hoc charging unitary operator, leveraging our knowledge of the ground state near the transition to bring it into a decoherence-free state (DFS) during storage. Using state-of-the-art numerics based on matrix product state representation, we reveal that high couplings to an external bath approximately double the local ergotropy immediately post-charging. Over time we observe oscillatory behaviors in ergotropy and its fluctuations, which undergo significant changes near the transition, signaling its occurrence. Furthermore, we optimize local ergotropy over time using a physically inspired ansatz, enabling work extraction at a generic time (local ergotropy never reaches zero). Our work proposes a tunable, experimentally realizable protocol for work extraction, leveraging DFS and phase transitions. Additionally, it sheds light on the complex interaction between local ergotropy and quantum phase transitions.
Abstract In this mini-review, we discuss work extraction under restricted control, where only the system is accessible while other degrees of freedom remain uncontrolled. In this setting, local ergotropy is the maximum work extractable by cyclic unitaries on the system, and it can differ strongly from “switch-off” extraction after quenching the system-environment coupling. We review two settings where correlations and many-body effects shape local work. First, in a two-qubit quantum Rabi model, dissipation induces a Berezinskii–Kosterlitz–Thouless quantum phase transition. A gate-based charge-store-extract protocol uses a decoherence-free state to stabilize storage and makes strong system-bath coupling a resource, yielding local ergotropy above switch-off extraction and making its dynamics transition-dependent, also in relative fluctuations. Second, in a disordered XXZ chain where the first two spins form a battery coupled to an interacting spin bath, local ergotropy shows distinct long-time behavior across Anderson, many-body localized, and ergodic regimes, linking extractable work to localization transitions. Overall, the examples reviewed here show that local ergotropic observables quantify quantum-battery performance under local control and probe collective phenomena.
We investigate a two-qubit quantum battery where coherent charger-battery coupling competes with non-Markovian environmental interactions. By tuning the coupling strengths and detuning, we identify regimes in which environmental memory enhances energy storage and charging power, while strong dissipation suppresses ergotropy by driving the battery into passive states. We show that detuning plays a dual role: reducing dissipation and inducing a phase shift in the memory kernel that controls the interference between coherent energy exchange and environment-induced backflow. As a result, although the stored energy varies smoothly, the extractable work exhibits a discontinuous onset at a critical detuning, signaling a first-order phase transition in ergotropy. The corresponding phase diagram in the coupling-detuning plane reveals a sharp boundary between thermodynamically inactive and work-producing regimes. Our results demonstrate that phase-controlled coherence and non-Markovianity provide a powerful mechanism for optimizing work extraction in open quantum batteries, offering practical strategies for noise-resilient quantum energy storage.
Decoherence and dissipation in open quantum systems generally drive quantum batteries toward passive states, thereby reducing their extractable work (ergotropy). Here, we study a driven qubit quantum battery coherently coupled to an auxiliary harmonic oscillator in the presence of dephasing and dissipation. Using the differential formulation of the first law of open quantum thermodynamics, we analyze the local energy-flow dynamics during the charging process. We find that the auxiliary oscillator induces a transient negative local energy current into the qubit subsystem, corresponding to a temporary inward energy backflow. This transient energy redistribution is accompanied by an enhancement of the qubit ergotropy and a partial suppression of decoherence-induced passivation. Moreover, the parameter regime exhibiting a more pronounced negative-current interval is consistently correlated with larger ergotropy enhancement. Our results suggest that transient inward energy flow provides a useful thermodynamic signature associated with enhanced energy storage in open quantum batteries.
We investigate the performance of a quantum battery exposed to local Markovian and non-Markovian dephasing noises. The battery is initially prepared as the ground state of a one-dimensional transverse XYXYXY model with open boundary condition and is charged (discharged) via interactions with local bosonic reservoirs. We show that in the transient regime, the quantum battery (QB) can store energy faster and has a higher maximum extractable work, quantified via ergotropy, when it is affected by local phase-flip or bit-flip Markovian noise compared to the case when there is no noise in the system. In both the charging and discharging processes, we report the enhancement in work output as well as in ergotropy when all the spins are affected by a non-Markovian Ohmic bath in both the transient and the steady-state regimes, thereby showing a counterintuitive advantage of decoherence in the QB. In both Markovian and non-Markovian cases, we identify the system parameters and the corresponding noise models which lead to maximum enhancement of work output and ergotropy. Moreover, we show that the benefit due to noise persists even with the initial state being prepared at a moderate temperature.
Many-body localization is a dynamical phenomenon characteristic of strongly interacting and disordered many-body quantum systems that fail to achieve thermal equilibrium. From a quantum information perspective, one of the most relevant fingerprints of this phenomenon is the logarithmic growth of the entanglement entropy over time. We perform intensive numerical simulations, applied to a paradigmatic model system, showing that the local ergotropy, the maximum extractable work via local unitary operations on a small subsystem in the presence of Hamiltonian coupling, dynamically witnesses the change from ergodic to localized phases. Within the many-body localized phase, both the local ergotropy and its quantum fluctuations slowly vary over time with a characteristic logarithmic law analogous to the behavior of entanglement entropy. This showcases how directly leveraging local control, instead of local observables or entropies analyzed in previous works, provides a thermodynamic marker of localization phenomena based on the locally extractable work.
We propose a simple realization of an open quantum battery powered by local dephasing. The setup consists of a triple-quantum-dot chain coupled at one end to a thermal reservoir, with the dot at the opposite end strongly detuned to form a high-energy storage element. Local dephasing populates this highly excited state and autonomously drives the system into a nonequilibrium steady state with high ergotropic efficiency. We find a limit where the ergotropic efficiency approaches unity, while the ergotropy itself approaches one-third of the energy detuning. We characterize the battery through its energy-storage performance, charging time, and stability, showing that the charged state remains long-lived after the dephasing source is switched off. We then demonstrate two complementary protocols for extracting the stored energy. First, nearly all the available ergotropy can be recovered through a simple cyclic unitary protocol involving only modulation of the detuned-dot gate. Second, coupling the detuned dot to an electronic load allows the extraction of electrochemical work exceeding the initial ergotropy, thereby accessing part of the battery's passive energy. Our results establish local dephasing as an autonomous resource for charging open quantum batteries and demonstrate simple routes for extracting the resulting stored energy in experimentally accessible mesoscopic platforms.