[Paper Review] Injection locking of a levitated optomechanical oscillator for precision force sensing

Siamak Dadras, Robert M. Pettit+4 more|arXiv (Cornell University)|Dec 22, 2020

Mechanical and Optical Resonators62 references4 citations

TL;DR

This paper demonstrates injection locking of a levitated silica nanosphere optomechanical oscillator to resonant intensity modulations of an external laser, achieving a force sensitivity of ~23 zN/√Hz. By leveraging injection locking to narrow the oscillation linewidth and reduce noise, the system enables high-precision force sensing at the zeptonewton scale, suitable for probing short-range forces and optically induced interactions in nanoscale systems.

ABSTRACT

We report on the injection locking of an optically levitated nanomechanical oscillator (a silica nanosphere) to resonant intensity modulations of an external optical signal. We explore the characteristic features of injection locking in this system, e.g. the phase pull-in effect and the injection-induced reduction of the oscillation linewidth. Our measurements are in good agreement with theoretical predictions and deepen the analogy of injection locking in levitated optomechanical systems to that in optical systems (lasers). By measuring the force noise of our feedback cooled free-running oscillator, we attain a force sensitivity of $\sim23~ m{zN}/\sqrt{ m{Hz}}$. This can readily allow, in fairly short integration times, for tests of violations of Newtonian gravity and searching for new small-scale forces. As a proof of concept, we show that the injection locking can be exploited to measure the forces optically induced on levitated nanoparticles, with potential applications in explorations of optical binding and entanglement between optically coupled nanomechanical oscillators.

Motivation & Objective

• To achieve sub-zeptonewton force sensitivity in a room-temperature levitated optomechanical system using injection locking.
• To explore the analogies between injection locking in levitated optomechanics and in optical systems such as lasers.
• To demonstrate a practical method for measuring small optical forces on nanoparticles via injection locking.
• To enable testing of non-Newtonian gravity and new small-scale forces using a high-Q, feedback-cooled levitated nanosphere.

Proposed method

• A silica nanosphere (73.2 nm radius, 3.6 fg mass) is optically levitated in high vacuum and feedback-cooled to an effective temperature of 23.9 mK.
• An external laser is intensity-modulated at the mechanical resonance frequency (128 kHz) to inject a coherent signal into the oscillator.
• Injection locking is achieved by phase-locking the nanosphere's mechanical oscillation to the modulated signal, reducing the linewidth and enhancing signal-to-noise ratio.
• The system's force sensitivity is measured via displacement spectral density and noise analysis, with contributions from thermal, shot, and feedback noise modeled using a Langevin equation framework.
• The injected force is calibrated using the DFT amplitude of the oscillation and the known force noise floor, enabling quantitative force measurement.
• Theoretical predictions for injection locking dynamics, including phase pull-in and linewidth narrowing, are compared with experimental data to validate the model.

Experimental results

Research questions

• RQ1 Can injection locking be effectively implemented in a levitated optomechanical oscillator to enhance force sensitivity?
• RQ2 To what extent does injection locking reduce the mechanical oscillation linewidth and improve signal-to-noise ratio in a high-Q levitated system?
• RQ3 What is the force sensitivity of the system in the free-running and injection-locked regimes, and can it reach the zeptonewton scale?
• RQ4 Can injection locking be used to measure small, optically induced forces on levitated nanoparticles?
• RQ5 How does the system’s performance compare to theoretical models of injection-locked oscillators?

Key findings

• The system achieves a force sensitivity of ~23.12 zN/√Hz in the free-running, feedback-cooled state, with dominant noise contributions from shot noise and thermal fluctuations.
• Injection locking reduces the mechanical oscillation linewidth significantly, as evidenced by a narrower peak in the DFT spectrum compared to free-running oscillations.
• The measured force noise averages down as t^(-1/2), confirming the expected scaling for a stochastic process and enabling detection of forces as small as ~1 zN in integration times of ~300 s.
• The injected optical force of 127 zN is successfully measured via calibration of the DFT amplitude increase under injection locking, validating the sensing protocol.
• Theoretical predictions for phase pull-in and linewidth narrowing in injection-locked systems are in good agreement with experimental observations.
• The system demonstrates potential for detecting forces at the 1 zN level in moderate bandwidths, enabling tests of non-Newtonian gravity and short-range interactions.