Distribution of energy dissipated by a driven two-level system

TL;DR

This paper analyzes the energy exchange distribution in a driven two-level quantum system, incorporating quantum corrections and confirming fluctuation relation symmetries, with implications for solid-state qubit experiments.

Contribution

It introduces a method to calculate energy exchange distributions in a driven two-level system with quantum corrections, extending the spin-boson model.

Findings

Distribution function of energy exchange derived

Conditional distributions confirmed to obey fluctuation symmetry

Quantum corrections significant at short times

Abstract

In the context of fluctuation relations, we study the distribution of energy dissipated by a driven two-level system. Incorporating an energy counting field into the well known spin-boson model enables us to calculate the distribution function of the amount of energy exchanged between the system and the bath. We also derive the conditional distribution functions of the energy exchanged with the bath for particular initial and/or final states of the two-level system. We confirm the symmetry of the conditional distribution function expected from the theory of fluctuation relations. We also find that the conditional distribution functions acquire considerable quantum corrections at times shorter or of the order of the dephasing time. Our findings can be tested using solid-state qubits.