Finite coupling effects in double quantum dots near equilibrium

Abstract

A weak coupling quantum master equation provides reliable steady-state results only in the van Hove limit, i.e., when the system-lead coupling approaches zero. Recently, J. Thingna et al. [Phys. Rev. E 88, 052127 (2013)PLEEE81539-375510.1103/PhysRevE.88.052127] proposed an alternative approach, based on an analytic continuation of the Redfield solution, to evaluate the steady-state reduced density matrix up to second order in the system-bath coupling. The approach provides accurate results for harmonic oscillator and spin-bosonic systems. We apply this approach to study steady-state fermionic systems and the calculation on an exactly solvable double quantum dot system shows that the method is rigorously valid up to second order in system-lead coupling only near equilibrium, i.e., linear response regime. We further compare to the Redfield and the secular Redfield (Lindblad-type) master equations that are inaccurate in all parameter regimes. Lastly, we consider the nontrivial problem of strong Coulomb interaction and illustrate the interplay between system-lead coupling, interdot tunneling, and Coulomb strength that can be captured only via the analytic continuation method.