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arXiv:2205.06897 · Physical Review A

Collective effects and quantum coherence in dissipative charging of quantum batteries

Franco Mayo, Augusto J. Roncaglia

Published Jun 6, 2022• 72 citations
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Abstract

We consider the dissipative charging process of quantum batteries in terms of a collisional model, where the batteries are coupled to a heat bath using nonenergy preserving interactions. First, we show that for low temperatures, the collective process can attain a charging power that increases polynomially with the number of batteries. The scaling we find is ${N}^{3}$ which, while being greater than the bound obtained for unitary processes, has a lower efficiency. Then, we study the dissipative charging process of a single battery using a time-dependent Hamiltonian that generates coherences in the energy basis. In this case, we find that the presence of coherence could enhance the charging power and also its efficiency. Finally, we show how this process can be used in a quantum heat engine that contains the charging process as one of its open strokes.

DOI
10.1103/physreva.105.062203

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We consider the dissipative charging process of quantum batteries in terms of a collisional model, where the batteries are coupled to a heat bath using nonenergy preserving interactions. First, we show that for low temperatures, the collective process can attain a charging power that increases polynomially with the number of batteries. The scaling we find is N3{N}^{3}N3 which, while being greater than the bound obtained for unitary processes, has a lower efficiency. Then, we study the dissipative charging process of a single battery using a time-dependent Hamiltonian that generates coherences in the energy basis. In this case, we find that the presence of coherence could enhance the charging power and also its efficiency. Finally, we show how this process can be used in a quantum heat engine that contains the charging process as one of its open strokes.
We study the connection between the charging power of quantum batteries and the fluctuations of the extractable work. We prove that in order to have a nonzero rate of change of the extractable work, the state ${\ensuremath{\rho}}_{\mathcal{W}}$ of the battery cannot be an eigenstate of a ``free energy operator,'' defined by $\mathcal{F}\ensuremath{\equiv}{H}_{\mathcal{W}}+{\ensuremath{\beta}}^{\ensuremath{-}1}\mathrm{log}({\ensuremath{\rho}}_{\mathcal{W}})$, where HW{H}_{\mathcal{W}}HW​ is the Hamiltonian of the battery and $\ensuremath{\beta}$ is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the free energy operator upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.
In this dissertation, we investigate the charging and discharging dynamics of a quantum battery composed of a collectively driven ensemble of NNN identical two level systems coupled to a structured electromagnetic environment. The system is described using collective angular momentum operators in the Dicke basis, which provides a compact and physically transparent framework for analyzing collective light-matter interactions. Rather than treating dissipation as an unwanted source of loss, we explicitly use it as a mechanism for energy storage and work extraction. Starting from a coherently driven ensemble coupled to common reservoirs, we derive a master equation in Lindblad form under the Born-Markov and secular approximations. In the dressed-state basis, spontaneous emission induces irreversible transitions that can increase the energy stored in the bare basis. We obtain analytic expressions for the steady state, including the stored energy and the ergotropy, and identify parameter regimes where substantial collective coherence is generated. A central result of this work is the demonstration that, in the extensive regime where the total energy scales linearly with NNN and relative fluctuations vanish, the charging power scales as N2N^2N2. This quadratic enhancement scaling exceeds the N3/2N^{3/2}N3/2 limit previously established for purely Hamiltonian charging protocols of noninteracting Dicke batteries in the same regime. We show that this enhancement is consistent with quantum speed limits for open-system dynamics and originates from collectively enhanced dissipative processes analogous to superradiance. We further analyze the extraction process and show that the charged steady state stores not only energy but a macroscopic collective dipole moment. This coherence enables rapid energy release through either collective spontaneous emission or stimulated emission driven by an external coherent field. In the appropriate large NNN extensive regime, the stored energy can become fully extractable in principle, and the discharging power also exhibits N2N^2N2 scaling. These results establish that dissipative protocols can provide a genuine collective advantage over Hamiltonian schemes in the extensive regime, while also highlighting the interplay between enhanced collective power and the conditions required to achieve high extractable energy.
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.
An open quantum battery (QB) model of a single qubit system charging in a coherent auxiliary bath (CAB) consisting of a series of independent coherent ancillae is considered. According to the collision charging protocol we derive a quantum master equation and obtain the analytical solution of QB in a steady state. We find that the full charging capacity (or the maximal extractable work (MEW)) of QB, in the weak QB-ancilla coupling limit, is positively correlated with the coherence magnitude of ancilla. Combining with the numerical simulations we compare with the charging properties of QB at finite coupling strength, such as the MEW, average charging power and the charging efficiency, when considering the bath to be a thermal auxiliary bath (TAB) and a CAB, respectively. We find that when the QB with CAB, in the weak coupling regime, is in fully charging, both its capacity and charging efficiency can go beyond its classical counterpart, and they increase with the increase of coherence magnitude of ancilla. In addition, the MEW of QB in the regime of relative strong coupling and strong coherent magnitude shows the oscillatory behavior with the charging time increasing, and the first peak value can even be larger than the full charging MEW of QB. This also leads to a much larger average charging power than that of QB with TAB in a short-time charging process. These features suggest that with the help of quantum coherence of CAB it becomes feasible to switch the charging schemes between the long-time slow charging protocol with large capacity and high efficiency and the short-time rapid charging protocol with highly charging power only by adjusting the coupling strength of QB-ancilla. This work clearly demonstrates that the quantum coherence of bath can not only serve as the role of “fuel” of QB to be utilized to improve the QB’s charging performance but also provide an alternative way to integrate the different charging protocols into a single QB.
The collective charge of NNN two-level atoms interacting in an open system is investigated. In contrast to a no atomic dissipation quantum battery, the battery remains at a steady state after reaching the moment of full charge. Considering the interactions between atoms, we find that the energy storage of quantum batteries will be significantly enhanced with the increase of atomic repulsion, and the attraction between atoms will exacerbate the dissipation of batteries in the environment. We extend this conclusion to two-level batteries in the drive field and three-level atom quantum batteries. In addition, we also investigate the dissipative charging process of multiatom quantum batteries and find that the number of atoms during the charging process can to some extent affect the energy conversion efficiency during the charging process. Under extreme conditions, the inverse temperature $\ensuremath{\beta}$ can disrupt the energy storage of the battery.
Thermodynamics of information identifies information flow as a thermodynamic resource, but whether quantum coherence and collective coupling can enhance it at low entropy-production cost remains unresolved. We address this question for interacting open quantum systems by deriving a thermodynamic uncertainty relation that bounds information flow in terms of entropy production in nonequilibrium steady states. We construct a quantum engine in which N-fold degenerate ground and excited states are collectively coupled to heat baths. Collective jumps enhance heat currents and information flow linearly with N, while entropy production remains independent of N, realizing a high-power, low-dissipation autonomous quantum Maxwell's demon that leverages collectively enhanced information flow to pump heat against a temperature gradient. Beyond steady states, collective interactions amplify the unitary component of quantum information flow, yielding a quadratic enhancement of the free-energy charging power of quantum batteries. Our results reveal scalable advantages of quantum coherence and collective effects in quantum engines.