01255nas a2200169 4500008004100000245007000041210006900111260001400180300000800194490000600202520075000208100002500958700001300983700003200996700002001028856003701048 2021 eng d00aEnergy storage and coherence in closed and open quantum batteries0 aEnergy storage and coherence in closed and open quantum batterie c7/15/2021 a5050 v53 a

We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery's Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case. 

1 aCaravelli, Francesco1 aYan, Bin1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia uhttps://arxiv.org/abs/2012.1502600815nas a2200157 4500008004100000245004700041210004400088260001300132300001100145490000800156520033100164100003200495700002000527700002200547856008800569 2021 eng d00aGarcía-Pintos, Hamma, and del Campo Reply0 aGarcíaPintos Hamma and del Campo Reply c7/9/2021 a0289020 v1273 a

We acknowledge that a derivation reported in Phys. Rev. Lett. 125, 040601 (2020) is incorrect as pointed out by Cusumano and Rudnicki. We respond by giving a correct proof of the claim “fluctuations in the free energy operator upper bound the charging power of a quantum battery” that we made in the Letter.

1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia1 adel Campo, Adolfo uhttps://www.quics.umd.edu/publications/garc%C3%ADa-pintos-hamma-and-del-campo-reply01237nas a2200145 4500008004100000245008300041210006900124260001400193490000800207520076500215100003200980700002001012700002201032856003701054 2020 eng d00aFluctuations in Extractable Work Bound the Charging Power of Quantum Batteries0 aFluctuations in Extractable Work Bound the Charging Power of Qua c7/22/20200 v1253 a

We study the connection between the charging power of quantum batteries and the fluctuations of the stored work. We prove that in order to have a non-zero rate of change of the extractable work, the state ρW of the battery cannot be an eigenstate of a `\emph{work operator}', defined by F ≡ HW + β−1log(ρW), where HW is the Hamiltonian of the battery and β 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 stored work 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. 

1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia1 adel Campo, Adolfo uhttps://arxiv.org/abs/1909.0355801387nas a2200157 4500008004100000245002900041210002900070260001300099490000600112520096500118100002501083700003201108700003201140700002001172856003701192 2020 eng d00aRandom Quantum Batteries0 aRandom Quantum Batteries c5/5/20200 v23 a

Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.

1 aCaravelli, Francesco1 aDe Wit, Ghislaine, Coulter-1 aGarcía-Pintos, Luis, Pedro1 aHamma, Alioscia uhttps://arxiv.org/abs/1908.08064