Computable negativity in two-mode squeezing subject to dissipation

We study a system of two bosonic fields subject to two-mode squeezing in the presence of dissipation. We find the Lie algebra governing the dynamics of the problem and use the Wei-Norman method to determine the solutions. Using this scheme, we arrive at a closed-form expression for an infinitely dimensional density operator which we use to calculate the degree of entanglement (quantified by Horodeckis' negativity) between the modes. We compare our result to the known continuous variable entanglement measures. We analyze the conditions for entanglement generation and the influence of thermal environments on the state formed. The problem is relevant, in particular, for understanding of quantum dynamics of coupled optical and/or mechanical modes in optomechanical and nanomechanical systems.