Sensing weak forces through observing a mechanical motion near or below its quantum zero-point fluctuation has been desired in diverse areas. While mechanical oscillators have played a crucial role in such studies, their application to free-fall-type sensing has been elusive, in particular in the quantum regime. Here, we demonstrate sensing a static force of the order of 10 zeptonewtons with a levitated nanomechanical oscillator below the zero-point fluctuation through the rapid modulation of its confining potential. We prepare a squeezed state with a reduced velocity uncertainty by abruptly decreasing the potential. Subsequently, we detect the exerted static force through time-of-flight measurements, where we release the nanoparticle from the potential and measure the displacement during a free fall. Furthermore, time-of-flight measurements allow us to perform quantum state tomography of the squeezed state, from which we reconstruct its Wigner quasiprobability distribution and evaluate the Fisher information for the position measurement to quantify the achievable force sensitivity of our protocol. Our results demonstrate that modulating the trap stiffness serves as a crucial technique for quantum-limited force sensing and paves the way to utilize a levitated nanoparticle as a promising sensing platform beyond the quantum limit with a capability of quantum state tomography.
According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion.
The sensitivity of a mechanical transducer is ultimately limited by its inherent quantum fluctuations. Here, we use an optically levitated nanoparticle to measure impulsive forces smaller than the particle's zero-point momentum uncertainty. Our approach relies on reversibly squeezing the levitated particle's center-of-mass motion to coherently amplify the perturbation. We demonstrate resolving single impulsive-force kicks as small as 6.9 keV/c, a value 0.6 dB below the sensor's zero-point value.