Enhancing low-temperature quantum thermometry and magnetometry via quadratic interactions in optomechanical-like systems

Abstract

Standard optomechanical sensors operating in the low-temperature regime often face fundamental precision limits imposed by vacuum fluctuations. Here, we demonstrate that moving beyond conventional radiation-pressure interactions and exploiting quadratic coupling can surpass these limits, generating intrinsic squeezing and non-Gaussian features in the probe state. We study quantum thermometry and magnetometry in a coupled two-resonator system, focusing on the estimation of a thermal bath temperature and an external magnetic field. The resonators are assumed to be in thermal equilibrium with a common bath, while a weak magnetic field acts on one of the resonators. We perform measurements on a single resonator, which serves as the probe for estimating both parameters. We compute the quantum Fisher information of the probe for two different interaction models between the resonators. Our results show that the counter-rotating terms in the quadratic interaction naturally induce squeezing at intermediate coupling and strong non-Gaussian correlations as the coupling increases further. These effects yield orders-of-magnitude enhancement in sensitivity in the low-temperature and weak-field regimes compared to standard radiation-pressure couplings. Finally, we investigate multiparameter estimation and find that, although the optimal measurements remain compatible, statistical correlations between parameters prevent the simultaneous estimation of temperature and magnetic field from attaining single-parameter precision.

Figures (9)

• Figure 1: Schematic of quantum sensing system consisting of resonator A and resonator B via an effective optomechanical-like coupling with strength $g$. Both resonators are immersed in a common thermal bath at temperature $T$, while an external magnetic field $B_{\text{ext}}$ is applied to resonator B.
• Figure 2: (a) Wigner function of the probe (resonator A) obtained under the radiation-pressure interaction \ref{['mod2']} for coupling strength $g=0.08$. (b)–(c) Wigner functions of the probe under the quadratic interaction Hamiltonian \ref{['mod1']} for coupling strengths $g=0.04$ and $g=0.08$, respectively. The remaining parameters are set to $\omega_A=1$, $\omega_B=0.04$, $T=0.01$, and $B_{\text{ext}}=0.06$. For the quadratic interaction Hamiltonian \ref{['mod2']}, squeezing in the probe state is observed, and when the coupling strength $g$ is increased, it forms two symmetric lobes with interference fringes, whereas no squeezing is generated when the radiation pressure interaction \ref{['mod2']} is considered.
• Figure 3: Panels (d)–(f) display the non-Gaussianity $\delta$ and the quadrature kurtoses $\kappa(X)$ and $\kappa(P)$ of the probe state as functions of the coupling strength $g$ for the quadratic interaction. The parameters are fixed at $\omega_A=1$, $\omega_B=0.04$, $T=0.08$, and $B=0.06$.
• Figure 4: QFI as a function of the temperature $T$ and magnetic field $B_{\text{ext}}$, obtained using Resonator A as the local probe under the effective interaction Hamiltonian \ref{['mod2']}. The parameters are set to $\omega_A=1$ and $\omega_B=0.04$. Panels (a) and (b) correspond to coupling strengths $g=0.02$ and $g=0.08$, respectively.
• Figure 5: QFI as a function of the bath temperature $T$ and the external magnetic field $B_{\text{ext}}$, evaluated using using resonator A as the local probe under the quadratic interaction Hamiltonian \ref{['mod1']}. The other parameters are set to $\omega_A=1$ and $\omega_B=0.04$. Panels (a)-(c) correspond to coupling strengths $g=0.02$, $g=0.06$, and $g=0.08$, respectively.