Enhanced optomechanical entanglement and cooling via dissipation engineering

We propose an optomechanical dissipation engineering scheme by introducing an ancillary mechanical mode with a large decay rate to control the density of states of the optical mode. The effective linewidth of the optical mode can be reduced or broadened, manifesting the dissipation engineering. To prove the ability of our scheme to improve the performances of the optomechanical system, we studied optomechanical entanglement and phonon cooling. It is demonstrated that the optomechanical entanglement overwhelmed by thermal phonon excitations could be restored via dissipation engineering. For the phonon cooling, an order-of-magnitude improvement could be achieved. Our scheme can be generalized to other systems with multiple bosonic modes, which is experimentally feasible with advances in materials and nanofabrication, including optical Fabry-Perot cavities, superconducting circuits, and nanobeam photonic crystals.

Figure 1

(a) Schematic of the multimode optomechanical system for dissipation engineering. Potential experimental systems: (b) the optical microresonator, where both the Brillouin mechanical mode $b$ and the breath mechanical mode $m$ are coupling to the common optical mode $a$, and (c) the Fabry-Perot cavity with two mechanical membranes inside; the optical mode $a$ can simultaneously couple with mechanical modes $b$ and $m$ in different membranes.

Figure 2

Intracavity power $P_a$ of optical mode $a$. (a) Engineering the linewidth of the optical mode via only stimulated Brillouin scattering. The intracavity power spectra for different control powers $G_b/\left(2\pi \right)=0$ (solid line), 2 (dashed line), and 3 (dotted line) $\mathrm{MHz}$, where the blue and red lines correspond to ${\mathrm{\Delta }}_j=0$ and ${\mathrm{\Delta }}_k=0$, respectively. (b) Optomechanically induced transparency and amplification are affected by the dissipation engineering, and (c) is the enlarged view of (b) around the detuning, $\delta /\left(2\pi \right)\in \left[-0.01,0.01\right]$ $\mathrm{MHz}$. The intracavity power spectra for the red detuning ${\mathrm{\Delta }}_{j\left(k\right)}={\omega }_m$ and the blue detuning ${\mathrm{\Delta }}_{j\left(k\right)}=-{\omega }_m$ with the control power $G_{m,j\left(k\right)}/2\pi =0.03\mathrm{MHz}$, where the blue and red arrows correspond to ${\mathrm{\Delta }}_j=0$ (Stokes process) and ${\mathrm{\Delta }}_k=0$ (anti-Stokes process), respectively. Other parameters are ${\kappa }_j/2\pi =2\mathrm{MHz}$, ${\kappa }_k/2\pi =2$ $\mathrm{MHz}$, ${\gamma }_b/2\pi =40\mathrm{MHz}$, ${\omega }_b/2\pi =10$ $\mathrm{GHz}$, ${\gamma }_m/2\pi =10\mathrm{kHz}$, and ${\omega }_m/2\pi =100$ $\mathrm{MHz}$.

Figure 3

Logarithmic negativity $E_{a,m}$ affected by the dissipation engineering. (a) The logarithmic negativity as a function of time $t$ with $G_{m,j}/\left(2\pi \right)=0.03$ MHz for $G_{b,k}/\left(2\pi \right)=0$ (black dashed line), 2 (blue line), 4 (red line), and 8 (green line) MHz. (b) The logarithmic negativity vs the dissipation engineering $G_{b,k}$ for $G_{m,j}/\left(2\pi \right)=0.03$ (solid line), 0.04 (dashed line), and 0.05 (dotted line) MHz. (a) and (b) are the results with the thermal noise $n_m=250$; (c) and (d) are the condition with $n_m=300$. Other parameters are the same as Fig. 2.

Figure 4

(a) Logarithmic negativity $E_{a,m}$ as a function of both ${\mathrm{\Delta }}_b$ and $G_{b,k}$ with $G_{m,j}/\left(2\pi \right)=0.05$ MHz. (b) Logarithmic negativity $E_{a,m}$ for both $G_{m,j}$ and $G_{b,k}$ with ${\mathrm{\Delta }}_b=-{\omega }_m$. Here we choose $n_m=250$. Other parameters are the same as Fig. 2.

Figure 5

(a) The thermal occupation as a function of $G_{m,j}$ for $G_{b,k}/\left(2\pi \right)=0$ (black dashed line), 20 (blue line), and 40 (red line) MHz. (b) The thermal occupation as a function of $G_{b,k}$ for $G_{m,j}/\left(2\pi \right)=1$ (black dashed line), 10 (blue line), and 20 (red line) MHz. (c) Cooling effect for both $G_{m,j}$ and $G_{b,k}$. Here we choose $n_m=100$. Other parameters are the same as Fig. 2.

Figure 6

(a) Thermal occupation $n_f$ and (b) the ratio as a function of $n_m$ for ${\omega }_m/\left(2\pi \right)=50$ (red line), 100 (blue line), and 200 (black line) MHz. Other parameters are the same as Fig. 2.