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arXiv:2209.13868 · Physical Review Applied

Charging by Quantum Measurement

Jia‐shun Yan, Jun Jing

Published Jun 23, 2023• 32 citations
arXivHTMLPDF

Abstract

We propose a quantum charging scheme fueled by measurements on ancillary qubits serving as disposable chargers. A stream of identical qubits are sequentially coupled to a quantum battery of $N+1$ levels and measured by projective operations after joint unitary evolutions of optimized intervals. If charger qubits are prepared in excited state and measured on ground state, then their excitations (energy) can be near perfectly transferred to battery by iteratively updating the optimized measurement intervals. Starting from its ground state, the battery could be constantly charged to an even higher energy level. Starting from a thermal state, the battery could also achieve a near-unit ratio of ergotropy and energy through less than $N$ measurements, when a population inversion is realized by measurements. If charger qubits are prepared in ground state and measured on excited state, useful work extracted by measurements alone could transform the battery from a thermal state to a high-ergotropy state before the success probability vanishes. Our operations in charging are more efficient than those without measurements and do not invoke the initial coherence in both battery and chargers. Particularly, our finding features quantum measurement in shaping nonequilibrium systems.

DOI
10.1103/physrevapplied.19.064069

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We propose a quantum charging scheme fueled by measurements on ancillary qubits serving as disposable chargers. A stream of identical qubits are sequentially coupled to a quantum battery of N+1N+1N+1 levels and measured by projective operations after joint unitary evolutions of optimized intervals. If charger qubits are prepared in excited state and measured on ground state, then their excitations (energy) can be near perfectly transferred to battery by iteratively updating the optimized measurement intervals. Starting from its ground state, the battery could be constantly charged to an even higher energy level. Starting from a thermal state, the battery could also achieve a near-unit ratio of ergotropy and energy through less than NNN measurements, when a population inversion is realized by measurements. If charger qubits are prepared in ground state and measured on excited state, useful work extracted by measurements alone could transform the battery from a thermal state to a high-ergotropy state before the success probability vanishes. Our operations in charging are more efficient than those without measurements and do not invoke the initial coherence in both battery and chargers. Particularly, our finding features quantum measurement in shaping nonequilibrium systems.
We present a collision model for the charging of a quantum battery by identical nonequilibrium qubit units. When the units are prepared in a mixture of energy eigenstates, the energy gain in the battery can be described by a classical random walk, where both average energy and variance grow linearly with time. Conversely, when the qubits contain quantum coherence, interference effects buildup in the battery and lead to a faster spreading of the energy distribution, reminiscent of a quantum random walk. This can be exploited for faster and more efficient charging of a battery initialized in the ground state. Specifically, we show that coherent protocols can yield higher charging power than any possible incoherent strategy, demonstrating a quantum speed-up at the level of a single battery. Finally, we characterize the amount of extractable work from the battery through the notion of ergotropy.
Abstract The reduced state of a small system strongly coupled to a charger in thermal equilibrium may be athermal and used as a small battery once disconnected. By harnessing the battery-charger correlations, the battery’s extractable energy can increase above the ergotropy. We introduce a protocol that uses a quantum system as a memory that measures the charger and leaves the battery intact in its charged state. Using the information gained from the measurement, the daemonic ergotropy of the battery is extracted. Then the battery is reconnected to the charger, thermalizing and charging it. However, the memory should return to its initial standard state to close the thermodynamic cycle. Thus, on the one hand, the work cost of the cycle is the sum of the disconnecting and reconnecting battery-charger work plus the measurement and erasure work. On the other hand, the extracted energy is the daemonic ergotropy of the battery plus the ergotropy of the memory. The ratio of these quantities defines the efficiency of the cycle. The protocol is exemplified by a modified transverse spin 1/2 Ising chain, one spin functioning as the battery and the others as the charger. The memory is another auxiliary spin 1/2. We found pairs of measurement schemes from which we extract the same daemonic ergotropy from the battery, they dissipate the same amount of energy, and one leaves the memory in an active state, the other in a passive state. We study the memory’s ergotropy and the daemonic ergotropy of the battery. We find that with measurements, the efficiency can surpass that of the unmeasured protocol, given conditions on temperature, coupling, and choice of the measurement operators.
We reconsider the quantum energetics and quantum thermodynamics of the charging process of a simple, two-component quantum battery model made up of a charger qubit and a single--cell battery qubit. We allow for the initial quantum state of the charger to lie anywhere on the surface of the Bloch sphere, and find the generalized analytical expressions describing the stored energy, ergotropy and capacity of the battery, all of which depend upon the initial Bloch sphere polar angle in a manner evocative of the quantum area theorem. The origin of the ergotropy produced, as well as the genesis of the battery capacity, can be readily traced back to the quantum coherences and population inversions generated (and the balance between these two mechanisms is contingent upon the starting Bloch polar angle). Importantly, the ergotropic charging power and its associated optimal charging time display notable deviations from standard results which disregard thermodynamic considerations. Our theoretical groundwork may be useful for guiding forthcoming experiments in quantum energy science based upon coupled two-level systems.
Abstract Quantum batteries (QBs)—small-scale energy storage devices based on quantum systems—offer the potential for enhanced charging performance through quantum effects such as coherence and collectivity. In this work, we study the collective charging of QBs consisting of N qubits, coupled to a driven qubit charger in a star configuration, with controlled pure dephasing acting on the charger. We investigate how an ‘asymptotic freedom’-like behavior—in which all the energy deposited into the battery can be extracted as work, resulting in the ergotropy-to-energy ratio approaching unity—can emerge in the steady state of the battery. We show that the ergotropy-to-energy ratio increases with the number of qubits and approaches unity asymptotically as 1 − O ( 1 / N ) . In the large- N limit, the emergence of approximate ground-state degeneracy of the collective battery system leads to this asymptotic freedom behavior, despite the battery state remaining mixed. We also discuss the scaling behavior of the charging time of the battery with N .
We explore the wireless charging of a quantum battery (QB) via nnn charging units, whose coupling is mediated by a common bosonic reservoir. We consider the general scenarios in which the charger energy is not maximal and the QB has residual ergotropy initially. It is found that the charging performance improves with the increase of the coupling strength. In the strong coupling regime, the charging time is insensitive to the charger energy, the number of charging units, and the residual ergotropy in the QB, while the ergotropy charged on the QB strongly depends on the charger energy and ergotropy, and the residual ergotropy in the QB does not help to enhance its performance. Moreover, the multiple charging units help to enhance the charging performance in the weak and moderate coupling regimes, while they are less efficient in the strong coupling regime.
The performance of open quantum batteries (QBs) is severely limited by decoherence due to the interaction with the surrounding environment. So, protecting the charging processes against decoherence is of great importance for realizing QBs. In this work we address this issue by developing a charging process of a qubit-based open QB composed of a qubit-battery and a qubit-charger, where each qubit moves inside an independent cavity reservoir. Our results show that, in both the Markovian and non-Markovian dynamics, the charging characteristics, including the charging energy, efficiency and ergotropy, regularly increase with increasing the speed of charger and battery qubits. Interestingly, when the charger and battery move with higher velocities, the initial energy of the charger is completely transferred to the battery in the Markovian dynamics. In this situation, it is possible to extract the total stored energy as work for a long time. Our findings show that open moving-qubit systems are robust and reliable QBs, thus making them a promising candidate for experimental implementations.