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arXiv:2008.07089

Collectively enhanced high-power and high-capacity charging of quantum batteries via quantum heat engines

Kosuke Ito, Gentaro Watanabe A

Published Aug 17, 2020• 2 citations
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Abstract

As a model of so-called quantum battery (QB), quantum degrees of freedom as energy storage, we study a charging protocol of a many-body QB consisting of $N$ two-level systems (TLSs) using quantum heat engines (QHEs). We focus on the collective enhancement effects in the charging performance of QBs in comparison to the individual charging. It is a challenging goal of QBs to achieve large collective enhancements in the charging power and the capacity while keeping the experimental feasibility, the stability, and the cheapness of the required control and resources. We show that our model actually exhibits these features. In fact, our protocol simultaneously achieves the asymptotically-perfect charge and almost $N$-order average power enhancement with only thermal energy resource and simple local interactions in a stable manner. The capacity is collectively enhanced due to the emergent bosonic quantum statistics caused by the symmetry of the interaction between the engine and the batteries, which results in asymptotically perfect excitation of all the TLSs. The charging speed, and hence the average power are collectively enhanced by the superradiance-like cooperative excitation in the effective negative temperature. Our results suggest that QHEs actually fit for a charger of QBs, efficiently exploiting the collective enhancements, not only converting the disordered thermal energy to the ordered energy stored in quantum degrees of freedom.

DOI
10.48550/arxiv.2008.07089

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As a model of so-called quantum battery (QB), quantum degrees of freedom as energy storage, we study a charging protocol of a many-body QB consisting of NNN two-level systems (TLSs) using quantum heat engines (QHEs). We focus on the collective enhancement effects in the charging performance of QBs in comparison to the individual charging. It is a challenging goal of QBs to achieve large collective enhancements in the charging power and the capacity while keeping the experimental feasibility, the stability, and the cheapness of the required control and resources. We show that our model actually exhibits these features. In fact, our protocol simultaneously achieves the asymptotically-perfect charge and almost NNN-order average power enhancement with only thermal energy resource and simple local interactions in a stable manner. The capacity is collectively enhanced due to the emergent bosonic quantum statistics caused by the symmetry of the interaction between the engine and the batteries, which results in asymptotically perfect excitation of all the TLSs. The charging speed, and hence the average power are collectively enhanced by the superradiance-like cooperative excitation in the effective negative temperature. Our results suggest that QHEs actually fit for a charger of QBs, efficiently exploiting the collective enhancements, not only converting the disordered thermal energy to the ordered energy stored in quantum degrees of freedom.
Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like sqrt[N] for N≫1.
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 .
Quantum batteries (QBs) exploit principles of quantum mechanics to accelerate the charging process and aim to achieve optimal energy storage. However, analytical results for investigating these problems remain lacking due to the challenges associated with nonequilibrium dynamics. In this work we analytically investigate a central-spin QB model in which Nb{N}_{b}Nb​ spin-12\frac{1}{2}21​ battery cells interact with Nc{N}_{c}Nc​ spin-12\frac{1}{2}21​ charger units, using mmm initially excited charger units as a resource. By employing the invariant subspace method and the shifted Holstein-Primakoff transformation, we identify four scenarios in which optimal energy storage can be achieved: (i) ${N}_{b}\ensuremath{\ll}m\ensuremath{\ll}{N}_{c}$, (ii) $m\ensuremath{\ll}{N}_{b}\ensuremath{\ll}{N}_{c}$, (iii) $m\ensuremath{\ll}{N}_{c}\ensuremath{\ll}{N}_{b}$, and (iv) ${N}_{b}\ensuremath{\ll}m=k{N}_{c} [k\ensuremath{\in}(0,1)]$. In these cases, optimal storage is ensured by the SU(2) symmetry emerging from the charging dynamics. The first three cases map the central-spin QB to different Tavis-Cummings (TC) QBs, while the fourth corresponds to the non-TC limit. We analytically determine the charging time and demonstrate that in the fully charging cases (i) and (iv), the collective charging exhibits an Nb{N}_{b}Nb​-fold enhancement in speedup compared to the parallel charging scheme. Additionally, we numerically observe a unified charging behavior when m=Ncm={N}_{c}m=Nc​, showing that asymptotically optimal energy storage is possible when Nb=m=Nc{N}_{b}=m={N}_{c}Nb​=m=Nc​. In this case, we find a collective charging enhancement scaling as Nb0.8264{N}_{b}^{0.8264}Nb0.8264​. The origin of the collective charging advantage in central-spin quantum batteries is also analyzed through the quantum speed limit and a multipartite entanglement witness. Our results highlight the crucial role of dynamically emergent SU(2) symmetry in providing an analytical understanding of nonequilibrium charging dynamics in QBs.
Quantum battery works as a micro- or nanodevice to store and redistribute energy at the quantum level. Here we propose a spin-charger protocol, in which the battery cells are charged by a finite number of spins through a general Heisenberg XY interaction. Under the isotropic interaction, the spin-charger protocol is endowed with a higher capacity in terms of the maximum stored energy than the conventional protocols, where the battery is charged by a continuous-variable system, e.g., a cavity mode. By tuning the charger size, a tradeoff between the maximum stored energy and the average charging power is found in comparison to the cavity-charger protocol in the Tavis-Cummings model. Quantum advantage of our protocol is manifested by the scaling behavior of the optimal average power with respect to the battery size, in comparing the collective charging scheme to its parallel counterpart. We also discuss the detrimental effect on the charging performance from the anisotropic interaction between the battery and the charger, the nonideal initial states for both of them, and the crosstalk among the charger spins. A strong charger-charger interaction can be used to decouple the battery and the charger. Our findings about the advantages of the spin-charger protocol over the conventional cavity-charger protocols, including the high capacity of energy storage and the superior power law in the collective charging, provide an insight to exploit an efficient quantum battery based on the spin-spin-environment model.
High-power Dicke quantum batteries (QBs) typically exploit collective superradiance, whereas intrinsic matter-matter interactions are conventionally considered detrimental. Here, we propose a counterintuitive paradigm: these interactions can be controlled and repurposed as a synergistic resource to enhance charging power and capacity. In the low-excitation limit, transverse interactions induce collective spin squeezing, causing critical mode softening and an exponential enhancement of effective coupling, which significantly boosts charging power. At higher excitations, these interactions act as a macroscopic nonlinear torque. By appropriately aligning this torque, we effectively lower phase-space dynamical barriers, guiding the system along optimal rapid-charging paths. Importantly, this cooperative enhancement remains highly robust under realistic dissipation, outperforming ideal, dissipationless Dicke QBs in specific regimes. Our results provide a blueprint for exploiting matter interactions to design dissipation-resistant, high-performance many-body QBs.
A bstract Collective behavior strongly influences the charging dynamics of quantum batteries (QBs). Here, we study the impact of nonlocal correlations on the energy stored in a system of N QBs. A unitary charging protocol based on a Sachdev-Ye-Kitaev (SYK) quench Hamiltonian is thus introduced and analyzed. SYK models describe strongly interacting systems with nonlocal correlations and fast thermalization properties. Here, we demonstrate that, once charged, the average energy stored in the QB is very stable, realizing an ultraprecise charging protocol. By studying fluctuations of the average energy stored, we show that temporal fluctuations are strongly suppressed by the presence of nonlocal correlations at all time scales. A comparison with other paradigmatic examples of many-body QBs shows that this is linked to the collective dynamics of the SYK model and its high level of entanglement. We argue that such feature relies on the fast scrambling property of the SYK Hamiltonian, and on its fast thermalization properties, promoting this as an ideal model for the ultimate temporal stability of a generic QB. Finally, we show that the temporal evolution of the ergotropy, a quantity that characterizes the amount of extractable work from a QB, can be a useful probe to infer the thermalization properties of a many-body quantum system.