Kerr enhanced optomechanical cooling in the unresolved sideband regime

TL;DR

This work addresses cooling a low-frequency mechanical oscillator into its quantum ground state in the unresolved sideband regime by employing a Kerr-nonlinear cavity. The authors develop a detailed theoretical framework showing that Kerr nonlinearity induces a highly asymmetric photon-number spectrum, enhancing dynamical backaction cooling and enabling far stronger cooling than linear-cavity counterparts at the same drive power. They demonstrate that near bifurcation, the nonlinear cavity achieves large effective cooperativity, with substantial reductions in mechanical occupancy (example: from ~2778 to ~12 phonons in parameters inspired by Zoepfl et al.), and that injecting squeezed vacuum further suppresses backaction heating, potentially reaching ground state with reduced squeezing requirements. The results imply practical pathways for cooling large, low-frequency mechanical systems and highlight the synergy between nonlinearity and quantum-engineering techniques (squeezing) for quantum control of macroscopic motion.

Abstract

Dynamical backaction cooling has been demonstrated to be a successful method for achieving the motional quantum ground state of a mechanical oscillator in the resolved sideband regime, where the mechanical frequency is significantly larger than the cavity decay rate. Nevertheless, as mechanical systems increase in size, their frequencies naturally decrease, thus bringing them into the unresolved sideband regime, where the effectiveness of the sideband cooling approach decreases. Here, we will demonstrate, however, that this cooling technique in the unresolved sideband regime can be significantly enhanced by utilizing a nonlinear cavity as shown in the experimental work of Zoepfl et. al. (PRL, 2023). The above arises due to the increased asymmetry between the cooling and heating processes, thereby improving the cooling efficiency.

Figures (12)

• Figure 1: Optomechanical setup consisting of a driven Kerr-cavity coupled via radiation-pressure force to a mechanical resonator. Due to the presence of the nonlinearity, the average photon number circulating in the cavity exhibits a very prominent asymmetry.
• Figure 2: Average cavity photon number as a function of the detuning $\Delta = \omega_p - \omega_c$. The orange solid line shows the intracavity photon number obtained using a nonlinear cavity ($\mathcal{K} \neq 0$) near the point of bifurcation, namely at a drive amplitude of $\bar{n}_\text{in} = \bar{n}_\text{in,crit}$. In contrast, the grey-dashed line results from the linear cavity setup ($\mathcal{K} = 0$) at the same input power. The vertical dotted line denotes the critical detuning $\Delta_\text{bi}$, where the system becomes bistable.
• Figure 3: The black solid line depicts the effective Kerr nonlinearity defined in Eq. \ref{['effective_kerr']} normalized by $\mathcal{K}$ as a function of the optomechanical coupling strength $g_0/2\pi$. For given parameters (see Table \ref{['table_param']}), the intrinsic cavity nonlinearity dominates for weak coupling strengths, and the critical input power (red line) is dominated by $\mathcal{K}$. Increasing the coupling strength further the mechanical Kerr kicks in and the critical input power decreases as the effective Kerr is enhanced. Dashed lines (color) correspond to the case without the induced mechanical Kerr, i.e. $g_0 = 0$.
• Figure 4: a) Poles of the driven Kerr cavity in the absence of coupling to the mechanical mode as a function of the detuning. Here, we depict the real (solid) and imaginary (dashed-dotted) part of the poles given in Eq. \ref{['poles']}, which are associated with the system's resonance frequency and decay, respectively. Exceptional points are shown by the vertical grey-dotted lines, which delimit the interval where the system features two distinct decay rates at a single resonant frequency (red shaded and b). The EPs are found at the intersection of $\Lambda = \mathcal{K} \bar{n}_c$ with the lines $-\Delta/3$ and $-\Delta$. Outside this interval, the system exhibits split resonance frequencies for a single decay rate (green shaded) leading to a double peak structure in the photon number spectrum as shown in c). Note that, the decay rates' maxima/minima occur precisely at the bifurcation detuning $\Delta_\text{bi}$ shown here by the vertical blue line.
• Figure 5: Effective skewness of the photon number spectrum of a nonlinear cavity as a function of the detuning. Inset shows the corresponding photon number spectrum as a function of the driving frequency for detunings approaching the critical value $\Delta_\text{bi}$ (vertical dashed-blue line). These spectra follow a slightly asymmetric Lorentzian distribution, whose maximum asymmetry is found when the cavity is driven at $\Delta = \Delta_\text{bi}$. Thus, as the cavity is driven close to the critical detuning the photon number spectrum becomes increasingly peaked and asymmetric, so for illustrative purposes we chose $\Delta = - 8 \omega_m$ (solid) and $\Delta = - 8.3 \omega_m$ (dashed).