Constructive role of dissipation for driven coupled bosonic modes

We theoretically investigate a system of two coupled bosonic modes subject to both dissipation and external driving. We show that in the steady state the degree of entanglement between the coupled bosonic modes can be enhanced by dissipation. Nonmonotonic dependence of entanglement on the decay rates is observed when the bosonic modes are asymmetrically coupled to their local baths. This counterintuitive result opens a way to better understand the interplay between noise and coherence in continuous-variable systems driven away from equilibrium.

Figure 1

Steady-state negativity $\mathcal{N}$ calculated as a measure of the quantum entanglement between the studied two coupled bosonic modes and plotted as a function of their decay rates ${\zeta }_1$ and ${\zeta }_2$. In (a) and (b) black indicates regions with minimal and white regions with maximal entanglement. (a) shows the result for two symmetric modes ${\omega }_a={\omega }_b$, for which maximum entanglement $\mathcal{N}=0.2$ is achieved for ${\zeta }_1={\zeta }_2$. (b) shows the result for two asymmetric modes ${\omega }_b/{\omega }_a=0.6$, for which the maximum entanglement is obtained for ${\zeta }_1\ne {\zeta }_2$. In (c) $\mathcal{N}$ is plotted as a function of the decay rate ${\zeta }_1$ for the fixed value of ${\zeta }_2=0.01$. One notes that the negativity has a nonmonotonic dependence on ${\zeta }_1$ for both the symmetric (solid line) and the asymmetric (dashed line) cases. In (d), where the same data are plotted on an expanded scale, one sees that the maximum entanglement for the asymmetric case appears for ${\zeta }_1=0.003\ne {\zeta }_2=0.01$ [marked by thick vertical lines in (d)]. All parameters are given in units of ${\omega }_a$ with ${\omega }_{\mathrm{p}}=10$, ${\nu }_1={\nu }_2=1$, and $\kappa =|{\Delta }_1+{\Delta }_2|/10=1.84$.