Nanomechanical Sensor Achieves Force Measurement 0.6 dB below Zero-Point Fluctuations

Scientists have, for the first time, demonstrated the ability to measure impulsive forces acting on an object at a scale below the limits previously imposed by quantum fluctuations. Led by Martynas Skrabulis, Martin Colombano Sosa, and Nicola Carlon Zambon , from ETH Z urich, Universit`a di Padova, and with contributions from Andrei Militaru et al , this research details a novel technique utilising an optically levitated nanoparticle to detect forces as small as 6.9 keV/c, surpassing the standard quantum limit by 0.6 dB. This breakthrough, achieved through coherent amplification of motion via reversible squeezing, promises to revolutionise precision measurement in fields ranging from fundamental physics to advanced sensing applications , opening doors to probing previously inaccessible phenomena and enhancing the sensitivity of nanomechanical devices. This breakthrough, achieved through coherent amplification of motion via reversible squeezing, promises to revolutionise precision measurement in fields ranging from fundamental physics to advanced sensing applications, opening doors to probing previously inaccessible phenomena and enhancing the sensitivity of nanomechanical devices. Squeezed light detects forces below zero-point limit Researchers at ETH Zurich and collaborating institutions have achieved a groundbreaking advancement in nanomechanical sensing, resolving impulsive forces acting on an optically levitated nanoparticle that are smaller than the particle’s zero-point fluctuations.

The team successfully measured impulsive force kicks as small as 6.9 keV/c, a value 0.6 dB below the sensor’s zero-point value, representing a significant leap in precision. This unlocks new possibilities for detecting incredibly weak forces and exploring fundamental physics at the nanoscale. The study centres on an optically levitated nanoparticle, a promising candidate for refining the standard model of particle physics and detecting elusive dark matter candidates. Instead of focusing on the probe field used in traditional measurements, the researchers engineered quantum correlations of the nanoparticle’s motion to coherently amplify the perturbation caused by impulsive forces. This innovative approach involved rapidly switching the stiffness of the optical potential trapping the particle, creating a squeezing operation that enhances the detection of minute momentum changes. By reversibly squeezing the nanoparticle’s center-of-mass motion, the team effectively amplified the signal generated by the impulsive force, allowing them to resolve forces previously hidden within the noise floor. Experiments involved modulating the nanoparticle’s resonant frequency in a step-like fashion, initially squeezing the momentum uncertainty before an impulsive force acted upon the system. This squeezing process elongated the phase-space representation of the particle’s motion, preparing it for enhanced sensitivity. The subsequent application of an impulsive force displaced the squeezed state along the momentum axis, and a final anti-squeezing operation transformed this momentum displacement into a measurable position displacement, amplified by a factor of ‘r’. This coherent amplification protocol, adapted for a levitated oscillator system, enabled the detection of forces below the fundamental quantum limit. The research establishes a new paradigm for impulsive force sensing, surpassing the limitations imposed by zero-point fluctuations. By carefully controlling the nanoparticle’s quantum state and exploiting the principles of levitodynamics, the team achieved a sensitivity improvement of 0.6 dB, demonstrating the power of engineered quantum correlations for enhancing measurement precision. This work opens exciting avenues for exploring fundamental interactions, searching for new physics beyond the standard model, and developing ultra-sensitive sensors for a wide range of applications, from materials science to biophysics. Optical Levitation and Reversible Squeezing for Force Detection Scientists have demonstrated a novel method for measuring incredibly weak impulsive forces, successfully detecting kicks as small as 6.9 keV/c, a value 0.6 dB below the zero-point limit. This breakthrough hinges on the optical levitation of a nanoparticle and a technique called reversible squeezing, coherently amplifying minute perturbations in the particle’s motion. The research team engineered a system where a nanoparticle is held in place by an optical trap, allowing for precise monitoring of its center-of-mass motion. Crucially, they implemented a method to reversibly squeeze this motion, effectively increasing the sensitivity to external impulses. Experiments employed a high-vacuum environment and a carefully calibrated optical trap to isolate the nanoparticle and minimise external disturbances.

The team then induced known impulsive forces onto the levitated particle and measured the resulting changes in its motion using sensitive position detection. Data acquisition involved sophisticated signal processing techniques, including a Kalman filter, to extract the weak force signals from the background noise. This innovative approach achieves an impulsive-force sensitivity that is 2.1 dB smaller than the quantum limit achievable with an ideal system lacking reversible squeezing. The study pioneered the use of reversible squeezing not merely as a theoretical enhancement, but as a practical tool for surpassing the standard quantum limit in force measurements. Scientists harnessed frequency jumps to manipulate the nanoparticle’s motion, creating a squeezed state where the uncertainty in one direction is reduced at the expense of increased uncertainty in another. This technique enables the coherent amplification of the impulsive force signal, making it detectable amidst the inherent fluctuations of the system.

The team’s meticulous control over the optical trap and the nanoparticle’s motion is central to the success of this method. Furthermore, the researchers acknowledge potential avenues for further improvement, including the implementation of hybrid traps utilising radio-frequency fields and exploring alternative squeezing methods like free-falls or evolution in inverted potentials. This work could contribute to scientific discoveries by enabling the detection of elusive particles, such as dark matter candidates or neutrinos, and enhancing the analysis of rarefied media through collision measurements.

This research was supported by grants from the Swiss SERI Quantum Initiative, the Swiss National Science Foundation, and the European Research Council.

Forces Below Zero-Point Limit Detected Scientists have achieved a breakthrough in precision measurement, successfully detecting impulsive forces acting on an optically levitated nanoparticle that are smaller than the particle’s zero-point fluctuations.

The team measured these forces at 6.9 ±0.8 keV/c, a value demonstrably 0.6+0.6 −0.4 dB below the fundamental zero-point limit, a remarkable feat in sensitive force detection. This work establishes a new standard for measuring minuscule interactions at the nanoscale, opening doors to previously inaccessible realms of physics. Experiments revealed a coherent amplification protocol, utilising reversible and coherent squeezing operations implemented by rapidly switching the stiffness of the optical potential trapping the nanoparticle. The researchers modulated the oscillator’s eigenfrequency in a step-like fashion, initially reducing it from Ω to Ω/r, with r exceeding 1, at time t = −πr/Ω. This manipulation elongated phase space along the position axis, maximally squeezing the momentum uncertainty to σ²P,i/r² at t = −πr/(2Ω) and simultaneously anti-squeezing the position variance to r²σ²Q,i. Crucially, an impulsive force applied at this moment displaced the squeezed state along the momentum axis by ∆P, and subsequent evolution reversed the squeezing, transforming the momentum displacement into a boosted position displacement of ∆Q = r∆P. Data shows this amplification technique effectively enhances the signal from the impulsive force without introducing additional uncertainty, allowing for the detection of incredibly weak interactions. The system, employing a silica nanoparticle with a nominal diameter of 100nm and a mass of 1.2 fg, operates within a cryogenic ultra-high vacuum environment. Measurements confirm characteristic frequencies of (Ωz, Ωx, Ωy)/(2π) = (52, 141, 175) kHz for the particle’s motion along the three axes, with the study focusing on the z-axis (Ω = Ωz). Interferometric detection, with an efficiency of η = 0.14 ±0.02, and cold-damping feedback reduced the phonon occupation to n = 1.2±0.6 quanta, minimising thermal noise. Voltage pulses of constant amplitude Up = 2V were applied to electrodes, generating controlled impulsive forces with pulse durations restricted by the transferred momentum ∆P. This breakthrough delivers a pathway towards exploring fundamental forces and interactions with unprecedented sensitivity.

Reversible Squeezing Beats Quantum Impulsive Force Limit, demonstrating Scientists have successfully measured impulsive forces acting on an optically levitated nanoparticle that are smaller than the particle’s zero-point momentum uncertainty. This achievement relies on a technique involving the reversible squeezing of the nanoparticle’s center-of-mass motion to coherently amplify the perturbation caused by these forces. The researchers demonstrated the ability to resolve single impulsive-force kicks as small as 6.9 keV/c, a value 0.6 dB below the zero-point fluctuation limit. This work represents a significant advance in the field of precision measurement, demonstrating an impulsive-force sensitivity 2.1 dB smaller than the quantum limit achievable without reversible squeezing. The method could potentially enable the detection of elusive particles, including dark matter candidates and neutrinos, as well as particles produced in nuclear decays. Furthermore, the technique may benefit the analysis of rarefied media through collision measurements, opening avenues for quantum-enhanced sensing applications. The authors acknowledge that the current sensitivity is primarily limited by the squeezing ratio employed, with excessively large values leading to increased mechanical vibrations and potential particle loss. Future research could explore hybrid traps utilising radio-frequency fields to provide low-stiffness potentials, or alternative squeezing methods like free-falls and evolution in inverted potentials, to further enhance the attainable amplification. 👉 More information 🗞 Nanomechanical sensor resolving impulsive forces below its zero-point fluctuations 🧠 ArXiv: https://arxiv.org/abs/2601.19392 Tags: