Random quantum batteries

Abstract

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.Introduction.-Quantum batteries[1-8] are a fundamental concept in quantum thermodynamics[9-17], and they have attracted interest as part of research in nano-devices that can operate at the quantum level [18][19][20]. Tools and insights from quantum information theory have provided a natural bedrock for the description of quantum nano-devices and quantum batteries from the point of view of resource and information theory [21][22][23][24][25][26][27][29][30][31].In a closed quantum system, a battery can be modeled by a time-dependent Hamiltonian H(t) evolving from an initial H 0 to a final H 1 . The system is initialized in a state ρ and, given that the entropy of the battery is constant under unitary evolution, the work extracted is given by the difference between the initial and final energies as measured in H 0 [2].In this paper, we lay down the theory of Random Quantum Batteries (RQB). The randomness lies in the initial state ρ, the Hamitonian defining the units of the energy H 0 , and the time-evolution operator U t . We are concerned with the average work extractable by (or storable in) such a device and its fluctuations.The main results of this paper are: (i) proving a typicality result for the extracted work in a large class of time dependent quantum systems. We show that -as the dimension n of the Hilbert space becomes large -the extracted work is almost always given by the difference in energy between the initial state and the completely mixed state, amplified by a quantum efficiency factor 1 + Q/n 2 that depends solely on the distribution of the eigenvalues of the exponential of the time-dependent perturbation operator K. For Q = 0, this result can be obtained by a classical system at infinite temperature. A random quantum battery can do it with limited energy resources. A non vanishing Q is a contribution that is purely quantum and depends on the constructive interference between different eigenvalues of K. The second main result is (ii) to provide a general method to study the average extractable work and its fluctuations in perturbation theory, which is essential to ...

Random matrix theory of the isospectral twirling

“…The average 〈•〉 G is the average over all the unitary channels with a given spectrum. The quantityR (2k) (U) is the Isospectral twirling of U, that is, the average over its 2k-fold channel [1,104,105]. TheT (2k) π = T (2k) π /tr (T (2k) π ) is a rescaled permutation operator corresponding to the element π of the permutation group S 2k (in the cycle representation, see App.…”

“…Moreover, an important topic in quantum thermodynamics is the understanding of quantum engines [129] and their capability of storing energy or performing work, e.g. quantum batteries [105]. These systems are discussed under the lens of the Isospectral twirling in Sec.…”

“…Among the quantum devices capable of performing work, quantum batteries are of central importance, also in view of the fact of the possible technological applications of nanoscale devices, and of possible quantum advantages in storing and extracting energy from the systems. Quantum batteries thus play a relevant role in the study of thermal machines and are an area of intense study [105,[188][189][190][191][192][193][194][195]. We apply the formalism of the Isospectral twirling to quantum batteries following the setup of [105] calculating average work and fluctuations.…”

“…A quantum battery can be modeled by a Hamiltonian of the form H = H 0 + V (t). Let ψ t = U(ρ) = UψU † the state at the time t obtained by unitary evolution U induced by the Hamiltonian H(t) [105]. The work extracted by (or stored in) the quantum battery is defined as the difference between expectation value of H 0 at time 0 and t: Following [105], one has that in the interaction picture the work can be written as…”

Ultra-stable charging of fast-scrambling SYK quantum batteries

“…Although manybody effects can enhance charging performances [24,30], strong and nonlocal correlations are required to achieve a true quantum advantage for QBs. Recently, the role of random disorder and its impact on charging performances have been also inspected, showing that QBs exhibit typical behavior in the large N limit given the spectral properties of the driving systems [32,33].…”