Analytical framework for describing non-trivial quantum dissipation

Recent works have shown how quantum correlations can be harnessed for Hamiltonian amplification in cavity-QED and circuit-QED setups. However, interplay of such correlations with noise still remains an active area of study. Specifically driven-dissipative dynamics of a system, coupled to a reservoir with strong correlations, remains insufficiently understood. This is partly due to the fact that well-established methods such as adiabatic elimination need to be revisited in the presence of strongly correlated quantum reservoirs. In this talk, we will present the progress towards a self-consistent derivation of quantum master equation in the presence of strong quantum correlations. Applying it to quantum reservoir with Gaussian correlations, we will first discuss how both the effective Hamiltonian and dissipator get modified. Using exact simulations to benchmark the analytical description of the reduced system, we will then comment on the implications of reservoir correlations on the validity of adiabatic elimination.