Noise-tolerant tripartite entanglement and quantum coherence via saturation effects

TL;DR

The paper addresses the challenge of generating robust quantum resources against thermal environments by proposing a three-mode optomechanical system in which a mechanical resonator is driven by two phase-modulated, optically coupled cavities that incorporate saturable gain/loss. The analysis uses linearization to obtain a Gaussian-state description, with the stationary covariance matrix $V$ solved from the Lyapunov equation $M V + V M^{\top} = -D$, enabling quantitative measures of tripartite entanglement and quantum coherence. Key findings show that increasing the photon hopping rate $J$ and tuning the phase $\theta$ enhances both resources, and that saturable gain/loss can boost tripartite entanglement by up to an order of magnitude while postponing thermal decoherence by up to two orders of magnitude (quantified via $n_{th}$). These results indicate saturable nonlinearities as a versatile tool to engineer thermally immune quantum correlations with potential room-temperature quantum information processing applications, leveraging the interplay between $J$, $\theta$, $g_s$, and $f_s$.

Abstract

Engineering quantum resources that survive against environmental temperature is of great interest for modern quantum technologies. However, it is a tricky task to synthetize such quantum states. Here, we propose a scheme to generate highly resilient tripartite entanglement and quantum coherence against thermal fluctuations. Our benchmark model consists of a mechanical resonator driven by two electromagnetic fields, which are optically coupled. A modulated photon hopping $J$ captures the optical coupling, and each optical cavity hosts saturable gain or loss. When the saturable gain/loss are off, we observe a slightly enhancement of both tripartite entanglement and quantum coherence for an appropriate tuning of the phase modulation. When the saturation effects are turned on, we observe a significant enhancement of the tripartite entanglement, up to one order of magnitude, together with a moderate improvement of the quantum coherence. More interestingly, our results show that the threshold thermal phonon mumber for preserving tripartite entanglement in our proposal has been postponed up to two order of magnitude stronger than when the saturation effects are not accounted. The inclusion of saturable gain/loss in our proposal induces noise-tolerant quantum resources, and may lead to room temperature quantum applications such as quantum information processing, and quantum computional tasks. Our findings are quite general, and suggest saturation nonlinear effects as a tool for engineering thermal-immune quantum correlations.

Figures (9)

• Figure 1: Sketch of our benchmark model. Three mode optomechanical system made of two electromagnetic fields optically coupled, which are driving a mechanical resonator. The optical coupling is captured through the photon hopping $J$ that is phase modulated ($\theta$) under the synthetic magnetism. The optical and the mechanical dissipations are $\kappa_j$ and $\gamma_m$, respectively.
• Figure 2: Stability diagram versus the optical coupling $J$ and the effective coupling $G_j$. The dark (blue) area is stable, while the red (light) area is unstable. The other parameters are $\kappa_j=0.2\omega_m$, $\gamma_m=10^{-5}\omega_m$, $\Delta_j=\omega_m$, $g_s=0$, and $f_s=0$.
• Figure 3: Contour plot of tripartite entanglement (a) and quantum coherence (b) versus the optical coupling $J$ and its phase modulation $\theta$. (c) and (d) show $2D$-representations extracted from (a) and (b), respectively for $J=0.2\omega_m$. The other parameters are $\kappa_j=0.2\omega_m$, $\gamma_m=10^{-5}\omega_m$, $G_j=0.15\omega_m$, $n_{th}=100$, $\Delta_j=\omega_m$, $g_s=0$, and $f_s=0$.
• Figure 4: (a) Contour plot of tripartite entanglement, and (b) contour plot of the quantum coherence versus $J$ and $G_j$ for $\theta=\pi$. The other parameters are the same as those in \ref{['fig:Fig3']}.
• Figure 5: (a) one mode, and (b) multi-modes quantum coherences, versus the effective optomechanical coupling $G_j$ for $J=0.2\omega_m$. The other parameters are the same as those in \ref{['fig:Fig3']}.