Nonequilibrium thermal effects on exciton time correlations in coupled semiconductor quantum dots

Abstract

Theoretical guides to test 'macroscopic realism' in solid-state systems under quantum control are highly desirable. Here, we report on the evolution of a Leggett-Garg inequality (LGI), a combination of two-time correlations, in an out-of-equilibrium set up consisting of two interacting excitons confined in separate semiconductor quantum dots which are coupled to independent baths at different temperatures (T1 ≠ T2). In a Markovian steady-state situation we found a rich variety of dynamical behaviors in different sectors of the average temperature (TM = (T1+T2)/2) vs. coupling strength to the reservoirs (Γ) space parameter. For high TM and Γ values the LGI is not violated, as expected. However, by decreasing TM or Γ a sector of parameters appears where the LGI is violated at thermal equilibrium (T1 = T2) and the violation starts decreasing when the system is moved out of the equilibrium. Surprisingly, at even lower TM values, for any Γ, there is an enhancement of the LGI violation by exposing the system to a temperature gradient, i.e. quantum correlations increase in a nonequilibrium thermal situation. Results on LGI violations in a steady-state regime are compared with other non-locality-dominated quantum correlation measurements, such as concurrence and quantum discord, between the two excitons under similar temperature gradients.