Exact solution of time-dependent Lindblad equations with closed algebras

Abstract

Time-dependent Lindblad master equations have important applications in areas ranging from quantum thermodynamics to dissipative quantum computing. In this paper we outline a general method for writing down exact solutions of time-dependent Lindblad equations whose superoperators form closed algebras. We focus on the particular case of a single qubit and study the exact solution generated by both coherent and incoherent mechanisms. We also show that if the time dependence is periodic, the problem may be recast in terms of Floquet theory. As an application, we give an exact solution for a two-level quantum heat engine operating in a finite time.