Memory-effect-induced macroscopic-microscopic entanglement

We study optomechanical entanglement between an optical cavity field and a movable mirror coupled to a non-Markovian environment. The non-Markovian quantum-state diffusion approach and the non-Markovian master equation are shown to be useful in investigating entanglement generation between the cavity field and the movable mirror. The simple model presented in this paper demonstrates several interesting properties of optomechanical entanglement that are associated with environment memory effects. It is evident that the effective environment central frequency can be used to modulate the optomechanical entanglement. In addition, we show that the maximum entanglement may be achieved by properly choosing the effective detuning, which is significantly dependent on the strength of the memory effect of the environment.

Figure 1

Schematic of a typical optomechanical system, in which an optical cavity driven by a coherent laser is coupled to a mechanical mode.

Figure 2

Time evolution of the coefficients in the $O$ operator. For the case $\gamma =0.6,\frac{|F_5|}{|F_1|}\approx 0.43\%$ at ${\omega }_{m}t=15$.

Figure 3

Memory-effect-enhanced entanglement generation. Solid red, dashed green, and dotted blue lines are plotted with different memory times $1/\gamma$. The other parameters are chosen as ${\omega }_m=1,\mathrm{\Delta }=1,G=0.1,\mathrm{\Omega }=0, \mathrm{\Gamma }=2$. The initial state is chosen as $|{\psi }_i\rangle =|00\rangle$. As a comparison, the Markov case is also plotted, as the dash-dotted black line.

Figure 4

Time evolution of entanglement for different $\mathrm{\Omega }$'s. (a) Contour plot of the time evolution of the entanglement indicator En for various values of $\mathrm{\Omega }$. (b) Two-dimensional plot of the entanglement generation for different values of $\mathrm{\Omega }$ at the fixed time ${\omega }_{m}t=20$. The initial state is chosen as $|{\psi }_i\rangle =|00\rangle$. The other parameters are chosen as ${\omega }_m=1,\mathrm{\Delta }=1,G=0.1$, and $\gamma =1$.

Figure 5

Time evolution of entanglement for different effective detunings $\mathrm{\Delta }/{\omega }_m$. The initial state is chosen as $|{\psi }_i\rangle =|00\rangle$. (a) The memory time is (a) $\gamma =1.5$ and (b) $\gamma =0.8$. The other parameters are chosen as ${\omega }_m=1,\mathrm{\Omega }=0,G=0.1$, and $\mathrm{\Gamma }=4$.