Kerr-enhanced optomechanical entanglement generation via reservoir design

TL;DR

This work tackles the fragility of optomechanical entanglement by combining a Kerr nonlinearity in the optical cavity with a deliberately engineered squeezed vacuum reservoir. Through displacement and squeezing transformations, the driven Kerr–cavity system maps to an effective linearized optomechanical model with a Kerr-induced modification of the detuning $\Delta_{sd}$ and the coupling $G_{sd}$, while the squeezed reservoir cancels the two-photon noise introduced by the Kerr term. The authors show that, in the single stable regime, the entanglement measure $E_N$ is enhanced over a broad range of $\chi$ and can extend into blue-sideband parameter regions, remaining robust to mechanical bath occupancies as high as $\bar{n}_{th}\approx 3000$. Experimentally feasible implementations across optical, microwave, and magnon–cavity platforms are discussed, highlighting reservoir engineering as a versatile tool to bolster fragile quantum resources in hybrid systems.

Abstract

Quantum entanglement is a crucial resource in quantum technologies, enabling advancements in quantum computing, quantum communication, and quantum precision measurement. Here, we propose a method to enhance optomechanical entanglement by introducing an optical Kerr nonlinear medium and a squeezed vacuum reservoir of the optomechanical cavity. By performing the displacement and squeezing transformations, the system can be reduced to a standard linearized optomechanical system with normalized driving detuning and linearized-coupling strength, in which the optical and mechanical modes are, respectively, coupled to an optical vacuum bath and a mechanical heat bath. We focus on the entanglement generation in the single stable regime of the system. By evaluating the steady-state logarithm negativity, we find that the optomechanical entanglement can be enhanced within a wide range of the Kerr constant. In addition, the Kerr nonlinearity can extend the stable region, enabling considerable entanglement generation in the blue-sideband parameter region. We also investigate the dependence of the entanglement generation on the average thermal phonon occupation of the mechanical bath and the optical driving amplitude. It is found that the presence of the Kerr nonlinearity allows the generation of optomechanical entanglement even when the thermal phonon occupation of the mechanical bath is as high as 3000. Our findings will provide valuable insights into enhancing fragile quantum resources in quantum systems.

Figures (7)

• Figure 1: Schematic of the Kerr-cavity optomechanical system consisting of a mechanical mode $b$ optomechanically coupled to a optical mode $a$ containing a Kerr nonlinear medium with nonlinear constant $\chi$. The $g_{0}$ is the single-photon optomechancial coupling strength. The cavity field and the mechanical resonator are, respectively, contacted to a squeezed vacuum reservoir (with decay rate $\kappa_{a}$, squeezing parameter $r_{e}$, and reference phase $\theta_{e}$) and a heat bath (with decay rate $\kappa_{b}$ and average thermal phonon occupation $\bar{n}_{th}$). In addition, the cavity field is driven by a monochromatic field with driving amplitude $\Omega$ and frequency $\omega_d$.
• Figure 2: The normalized detuning $\Delta_{sd}/\omega_m$ vs the scaled bare driving detuning $\Delta_{c}/\omega_m$ and the scaled Kerr constant $\chi/\omega_m$ when the cavity-field decay rate $\kappa_{a}$ takes different values: (a) $\kappa_{a}/\omega_m=0.5$, (b) $\kappa_{a}/\omega_m=0.8$, (c) $\kappa_{a}/\omega_m=1.2$, and (d) $\kappa_{a}/\omega_m=1.5$. Other parameters used are $g_{0}/\omega_{m}=0.005$, $\kappa_{b}/\omega_{m}=10^{-5}$, $\Omega/\omega_{m}=50$, and $\bar{n}_{th}=0$. Here, we also show the surfaces corresponding to $\Delta_{sd}/\omega_m=1$ and $\Delta_{sd}=\Delta_{c}$ for comparison.
• Figure 3: The scaled effective coupling strength $G_{sd}$ vs the scaled bare driving detuning $\Delta_{c}/\omega_m$ and the scaled Kerr constant $\chi/\omega_m$ when the cavity-field decay rate $\kappa_{a}$ takes different values: (a) $\kappa_a/\omega_m=0.5$, (b) $\kappa_a/\omega_m=0.8$, (c) $\kappa_a/\omega_m=1.2$, and (d) $\kappa_a/\omega_m=1.5$. Other parameters are the same as Fig. \ref{['Fig3']}.
• Figure 4: Stability phase diagram of the optomechanical system as a function of $\Delta_c/\omega_{m}$ and $\chi/\omega_{m}$ when (a) $\kappa_{a}/\omega_m=0.5$, (b) $\kappa_{a}/\omega_m=0.8$, (c) $\kappa_{a}/\omega_m=1.2$, and (d) $\kappa_{a}/\omega_m=1.5$. The regions are color-coded as follows: the blue area (region I) corresponds to the single-valued unstable region, the green area (region II) represents the multi-valued region, and the orange area (region III) represents the single-valued stable region. Other parameters are the same as Fig. \ref{['Fig3']}.
• Figure 5: The logarithmic negativity $E_N$ as a function of $\Delta_{c}/\omega_m$ and $\chi/\omega_m$ when (a) $\kappa_a/\omega_m=0.5$, (b) $\kappa_a/\omega_m=0.8$, (c) $\kappa_a/\omega_m=1.2$, and (d) $\kappa_a/\omega_m=1.5$. Other parameters are the same as those in Fig. \ref{['Fig3']}.