Efficiency fluctuations in a quantum battery charged by a repeated interaction process

Abstract

A repeated interaction process assisted by auxiliary thermal systems charges a quantum battery. The charging energy is supplied by switching on and off the interaction between the battery and the thermal systems. The charged state is an equilibrium state for the repeated interaction process, and the ergotropy characterizes its charge. The working cycle consists in extracting the ergotropy and charging the battery again. We discuss the fluctuating efficiency of the process, among other fluctuating properties. These fluctuations are dominated by the equilibrium distribution and depend weakly on other process properties. I. INTRODUCTIONRepeated interaction schemes, a.k.a collisional models [1-6], have played a vital role in the development of quantum optics [7-10] and the rapid evolution of quantum thermodynamics [11][12][13][14][15]. The idealized and straightforward formalism has been crucial to designing and understanding quantum devices such as information engines [16][17][18][19], heat engines [12,[20][21][22][23], and quantum batteries [24][25][26][27][28][29][30][31][32][33]. Recently, it was realized that the framework can be extended to deal with macroscopic reservoirs [23,34], expanding the reach of applications in quantum thermodynamics. For comprehensive reviews of the method and its applications, see [35] and [36].In the simplest scenario, many copies of an auxiliary system in the Gibbs equilibrium thermal state interact sequentially with a system of interest. Each interaction step is described by a completely-positive trace-preserving (CPTP) map [37]. The repeated interaction process corresponds to concatenations of the map, which eventually will bring the system to a nonequilibrium steady-state or an equilibrium state. In equilibrium, heat does not flow to the environment, and entropy is not produced. They are not sustained by work. When the repeated interaction brings the system to an equilibrium state, we say that we iterate a map with equilibrium.The thermodynamic quantities characterizing the process can be considered the average over stochastic versions of them defined on trajectories. These quantities satisfy fluctuation theorems [38][39][40][41] that reveal essential properties of the process. Particular attention has been drawn to efficiency fluctuations in different classical [42][43][44][45][46][47][48][49][50][51][52] or quantum [21] engines due to their remarkable properties.This paper will study a quantum battery charged by a repeated interaction process. A quantum battery is a system that stores energy. The battery's charge is characterized by its ergotropy [53], i.e., the maximum amount of energy extracted with a unitary process. Once the energy is removed, the battery is recharged with a repeated interaction process that starts from the discharged state. In this way, we have a working cycle, and we analyze its thermodynamics. The most straightforward charging protocol considers the auxiliary systems in a nonequilibrium state. However, the process of sustaining the charged state is diss...