Nonclassical correlations in non-Markovian continuous-variable systems

We consider two identical and noninteracting harmonic oscillators coupled to either two independent bosonic baths or to a common bosonic bath. Under the only assumption, weak coupling, we analyze in detail the non-Markovian short-time-scale evolution of intensity correlations, entanglement, and quantum discord for initial two-mode squeezed-thermal vacuum states. In the independent reservoirs case, we observe the detrimental effect of the environment for all these quantities and we establish a hierarchy for their robustness against the environmental noise. In the common reservoir case, for initial uncorrelated states, we find that only quantum discord can be created via interaction with the bath, while entanglement and subshot noise intensity correlations remain absent.

Figure 1

Evolution of intensity correlations marker ${\mathcal{I}}_{\mathrm{corr}}$ below the SNL [dot-dashed (blue) line], logarithmic negativity $\mathcal{N}(\varrho )$ [dashed (purple) line], and quantum discord $\mathcal{D}(\varrho )$ [solid (yellow) line] in the independent reservoir case as a function of ${\omega }_{c}t$. Parameters: $\alpha =0.1$, $k_{B}T/\hslash {\omega }_c=100;$ (left) $x=10$, $r=2$, $N=0$; (right) $x=0.2$, $r=0.5$, $N=0$.

Figure 2

Evolution of quantum discord $\mathcal{D}(\varrho )$ as a function of the scaled time ${\omega }_{c}t$ in the independent reservoir scenario. Parameters: $\alpha =0.1$, $k_{B}T/\hslash {\omega }_c=100$, $x=10$, and $r=2$. Different lines represent different values of the thermal parameter: $N=0$ [solid (blue) line], $N=1$ [dashed (purple) line], $N=5$ [dash-dotted (yellow) line], and $N=10$ [dotted (green) line].

Figure 3

Evolution of quantum discord $\mathcal{D}(\varrho )$ as a function of the scaled time ${\omega }_{c}t$ in the common reservoir scenario. Parameters: $\alpha =0.1$, $k_{B}T/\hslash {\omega }_c=100$, $x=10$, and $r=0$ (initially uncorrelated state). Different lines represent different values of the thermal parameter: $N=0$ [solid (blue) line], $N=0.05$ [dashed (purple) line], and $N=0.1$ [dash-dotted (yellow) line].

Figure 4

Dynamics of the intensity correlations marker ${\mathcal{I}}_{\mathrm{corr}}$ for a common reservoir as a function of ${\omega }_{c}t$. Parameters: $\alpha =0.1$, $k_{B}T/\hslash {\omega }_c=100$, $N=0$; (top) $x=10$; (bottom) $x=0.3$. $r=0.5$ [solid (blue) line], $r=1$ [dashed (purple) line], $r=1.5$ [dot-dashed (yellow) line], $r=5$ [dotted (green) line].

Figure 5

Evolution of quantum discord $\mathcal{D}(\varrho )$ as a function of the scaled time ${\omega }_{c}t$ in the common reservoir scenario. Parameters: $\alpha =0.1$, $k_{B}T/\hslash {\omega }_c=100$, $x=10$, and $N=0$. Different lines represent different values of the squeezing parameter: $r=0$ [solid (blue) line], $r=0.2$ [dashed (purple) line], $r=0.4$ [dash-dotted (yellow) line], and $r=1$ [dotted (green) line].