Fig. 1. Hybrid quantum systems awarded the Nobel Prize in Physics

Fig. 2. Typical microcavity optomechanical systems^[20]

Fig. 3. Squeezing in the phase quadrature component of the optical field^[36]

Fig. 4. Balance of radiant pressure noise and shot noise. (a) Squeezing of the amplitude and phase component for the frequency-dependent optical field^[36]; (b) suppression of quantum noise by squeezing angle^[40]

Fig. 5. Important experiments of LIGO. (a) Reduction of quantum radiation pressure noise via squeezed light injection^[40]; (b) quantum correlation between light and the kilogram-mass mirror^[36]; (c) room-temperature optomechanical squeezing^[42]; (d) frequency-dependent quantum squeezing^[41]

Fig. 6. Entangled atomic clock beyond the SQL based on squeezed light^[44]. (a) Entanglement on an optical atomic-clock transition; (b) tomographic measurements of the squeezed spin state

Fig. 7. Cooling a 10 kg mirror to near its ground state^[48]. (a) Schematic diagram of the experimental set-up; (b) displacement spectrum of the oscillator as the damping increased

Fig. 8. Noise spectral density in linear optomechanical system^[64]. (a) When the second-order nonlinear medium is absent or its phase is fixed at 0, the weak force detection sensitivity is always above the SQL (yellow solid line); (b) by tuning the phaseof the second-order nonlinear medium, the system sensitivity achieves significant enhancement beyond the SQL due to quantum squeezing

Fig. 9. Schematic diagram of squeezing-enhanced quadratic cavity optomechanical sensing^[88]

Fig. 10. Backaction noise cancellation is achieved by introducing an antinoise path (path 2) through intracavity squeezing^[88]

Fig. 11. Performances of the squeezing-enhanced quadratic optomechanical sensor^[88]. (a) Quantum noise below the SQL; (b) comparison of the optimal mechanical responses for standard and squeezing-enhanced quadratic optomechanical sensors; (c) sensitivity enhanced by intracavity squeezing

Fig. 12. Schematic diagram of hybrid cavity magnomechanical system^[137]

Fig. 13. Weak force measurements below the SQL with magnon squeezing^[137]

Fig. 14. Quantum noise is further reduced by optimizing the homodyne detection angle^[137]