Quantum jump model for a system with a finite-size environment

Abstract

Measuring the thermodynamic properties of open quantum systems poses a major challenge. A calorimetric detection has been proposed as a feasible experimental scheme to measure work and fluctuation relations in open quantum systems. However, the detection requires a finite size for the environment, which influences the system dynamics. This process cannot be modeled with the standard stochastic approaches. We develop a quantum jump model suitable for systems coupled to a finite-size environment. With the method we study the common fluctuation relations and prove that they are satisfied.

Comparison between quantum jumps and master equation in the presence of a finite environment

“…The work of a trajectory is then obtained as the change in the internal energy of the qubit plus the total heat released to the calorimeter. This leads to a work distribution equivalent to that of the double projective measurements for both the qubit and the calorimeter [36].…”

“…We denote the probability of a quantum trajectory with N jumps by Using the calorimeter traced jump operators, the trajectory's probability can be written as [36] P …”

“…For a two-level quantum system (qubit), the internal energy change of the system can also be obtained from the heat emitted (see, for example, Appendix C in Ref. [36]). As the environment is large and coupled to a detector, it is assumed to be decohered into a set of energy eigenstates, called microstates [36].…”

“…[36]). As the environment is large and coupled to a detector, it is assumed to be decohered into a set of energy eigenstates, called microstates [36].…”

“…In a recent paper [36], a finite-environment quantum jump (FEQJ) model was introduced to describe the calorimetric process. In the model, a jump changes both the system and the environment states.…”