Generation of robust tripartite entanglement with a single-cavity optomechanical system

We present a proposal to generate robust tripartite optomechanical entanglement with a single-cavity optomechanical system driven by a single input laser field. The produced stationary tripartite entanglement among two longitudinal cavity modes and a mirror oscillation mode via radiation pressure force exhibits robustness to the variation of the environment temperature when the cavity free spectral range is close to the mechanical oscillation frequency. The present optomechanical system can serve as an alternative intermediary for quantum-state exchange between two microwave (or optical) fields as well as between photons and the macroscopic mechanical oscillator, and may be potentially useful for quantum information processing and quantum networks.

Figure 1

(a) The single-cavity optomechanical system with a movable mirror (MM) driven by a single input laser field with frequency ${\omega }_{\mathrm{L}}$, where $a_1$ and $a_2$ represent the two longitudinal cavity field modes 1 and 2 with frequencies ${\omega }_1$ and ${\omega }_2$, respectively. (b) The relevant frequencies of the driving field and two cavity modes 1 and 2, where the cavity free spectral range is equal to twice the oscillating frequency of the mirror and the input field is tuned around the midfrequency of the two cavity modes.

Figure 2

The evolution of the logarithmic negativity $E_N^{a_1{a}_2}$ (solid line), $E_N^{a_{1}c}$ (dotted line), and $E_N^{a_2\mathrm{c}}$ (dotted-dashed line) as a function of the normalized detuning ${\mathrm{\Delta }}_2/{\omega }_m$ of the cavity field 2 with respect to the input laser field, where $E_N^{a_1{a}_2}$ presents for the entanglement between the two cavity fields 1 and 2, and $E_N^{a_{1}c}$ ($E_N^{a_2\mathrm{c}}$) for that between the cavity field 1 (2) and the vibrating mirror, respectively. The relevant parameters are $L=0.01\mathrm{m}, T=0.1\mathrm{K}, {\omega }_m=\pi c/2L, k=100{\gamma }_m=1\mathrm{MHz}, \lambda =1.33\mu \mathrm{m}, m=5\times {10}^{-9}\mathrm{kg}, P=20\mathrm{mW}$.

Figure 3

The 3D plots of the evolution of logarithmic negativity $E_N^{a_1{a}_2}, E_N^{a_{1}c}$, and $E_N^{a_2\mathrm{c}}$ with respect to the environmental temperature and the quality factor $Q_m$ of the vibrating mirror, where ${\mathrm{\Delta }}_1=-{\mathrm{\Delta }}_2=-{\omega }_m$ and we set $k=100{\gamma }_m$ (so the quality factor $Q$ of the cavity simultaneously varies with $Q_m$), and the other parameters are the same as those in Fig. 2.