Squeezing-enhanced dual-channel interference for ground-state cooling of a levitated micromagnet with low quality factor

Abstract

Cooling the center-of-mass (CM) motion of a macroscopic oscillator to its quantum ground state is a fundamental prerequisite for testing quantum mechanics at macroscopic scales. However, achieving this goal is currently hindered by the stringent requirement for an ultrahigh mechanical quality factor ($Q_c$). Here, we propose a dual-channel cooling scheme based on squeezing-enhanced quantum interference within a hybrid levitated cavity-magnomechanical system to overcome this limitation. By synergizing squeezing effects with quantum interference between the magnon-CM and cavity-CM channels, our scheme simultaneously suppresses Stokes (heating) scattering while enhancing anti-Stokes (cooling) scattering.~We demonstrate that this cooling mechanism reduces the critical $Q_c$ required for ground-state cooling by three orders of magnitude, making it achievable in the experimentally accessible regime of $Q_c \sim 10^4$. Furthermore, the net cooling rate is enhanced by nearly 180-fold compared to that of conventional single-channel cooling. This improvement is accompanied by a two orders of magnitude reduction in both the steady-state CM occupancy and the cooling time. Importantly, this enhanced performance remains robust even deep within the unresolved-sideband regime. Our results provide a feasible path toward preparing macroscopic quantum states by actively controlling the cooling dynamics, thereby relaxing the constraints on intrinsic material properties.

Figures (6)

• Figure 1: (a) Sketch of the hybrid CMM system: A YIG sphere is levitated and trapped at the potential minimum $V(x)$ in a cavity. The cavity contains a YIG sphere and a second-order nonlinear crystalline medium. (b) Schematic illustration of the quantum interference between scattering channels in the CMI cooling mechanism.
• Figure 2: Spectral characteristics and cooling performance comparison. (a, d) The PSD $S_{F_o}(\omega)$ versus the normalized frequency $\omega/\omega_c$. (b, e) Net cooling rates $\Gamma_c$ and (c, f) $n_c$ as a function of the normalized detuning $\Delta/\omega_c$ (where $\Delta \equiv \Delta_a = \Delta_m$). Panels (a--c) correspond to the MCM mechanism, while (d--f) correspond to the CMI mechanism. Note the orders-of-magnitude enhancement in the cooling rate scale in (e). System parameters: $\omega_c/2\pi = 50$ kHz, $\gamma_a = 8\omega_c/3$, $\gamma_m = 2\omega_c$, $\bar{n}_m = 0.31$, $J_{ac} = 0.09\omega_c$, $J_{mc} = 0.05\omega_c$, $J_{am} = 0.03\omega_c$, $\gamma_c = 10^{-7}\omega_c$, $r_s = 2$, $\phi_s = 94^{\circ}$, and $\varepsilon_a \approx (0.575 - 0.142i)\omega_c$.
• Figure 3: (a) $n_c$ versus the normalized cavity decay rate $\gamma_a/\omega_c$ for the CMI dual-channel (blue dashed curve) cooling mechanisms. (b) $n_c$ versus the normalized magnon decay rate $\gamma_m/\omega_c$ for the MCM single-channel (red solid curve) and CMI dual-channel (blue dashed curve) cooling mechanisms. The CM quality factor is $Q_c = 10^7$; all other parameters are the same as in Fig. \ref{['fig:SF-wc']}.
• Figure 4: (a) Time evolution of the CM occupancy $n_c(t)$ for the MCM and CMI mechanisms. The curves correspond to $Q_c = 5 \times 10^7$ (MCM: yellow circles; CMI: light blue triangles) and $Q_c = 10^{11}$ (MCM: red squares; CMI: blue diamonds). Specific parameters for (a) are $J_{ac} = 0.3\omega_c$, $J_{mc} = 0.025\omega_c$, and optimal detunings $\Delta_a = \sqrt{\gamma_a^2 + 4\omega_c^2}/2$, $\Delta_m = \sqrt{\gamma_m^2 + 4\omega_c^2}/2$. (b) $n_c$ versus the CM quality factor $Q_c$. The red solid curve denotes the MCM mechanism. The CMI mechanism is shown for squeezing parameters $r_s = 1.6$ (green diamonds), $2.0$ (blue triangles), and $2.6$ (orange squares) with triangular markers. Coupling parameters are $J_{ac} = 0.09\omega_c$, $J_{mc} = 0.05\omega_c$, and $J_{am} = 0.03\omega_c$. The inset highlights the ground-state cooling threshold $n_c \approx 1$. All other parameters are the same as in Fig. \ref{['fig:SF-wc']}.
• Figure 5: $n_c$ versus $Q_c$ for different values of (a) the CCM coupling strength $J_{ac}$, with fixed parameters $J_{mc} = 0.09\omega_c$, $J_{am} = 0.05\omega_c$; (b) the MCM coupling strength $J_{mc}$, with $J_{ac} = 0.2\omega_c$ and $J_{am} = 0.05\omega_c$ fixed; (c) the cavity-magnon coupling strength $J_{am}$, with the coupling strengths fixed at $J_{ac} = 0.2\omega_c$ and $J_{mc} = 0.09\omega_c$. The insets in (b) and (c) show zoomed-in views near $n_c\approx1$. The squeeze parameter is $r_s=2.6$, compared to Fig. \ref{['fig:SF-wc']}, with other parameters identical to those in Fig. \ref{['fig:SF-wc']}.