Pulsed Position Measurements of a Nano-optomechanical Resonator to Evade the Standard Quantum Limit

Instantaneous measurements of a resonator`s displacement can have precision beyond the standard quantum limit. We show how we approach this regime through pulsed measurements on a cryogenic nano-optomechanical system with extreme photon-phonon coupling strength.

In optomechanical systems, co-localizing light and mechanical oscillations at the nanoscale enables ultraprecise sensing and optical control of nanoscale motion.
Continuous position measurements are limited by the standard quantum limit (SQL), since they simultaneously measure the two non-commuting motional quadratures. In contrast, pulsed measurements take ‘snapshots’ of a resonator`s position that measure only one quadrature, allowing in principle to achieve unlimited precision.
With sufficient measurement precision and low thermal decoherence the mechanical resonator can then be prepared to a squeezed conditional state where the uncertainty in one of the quadratures is below the zero-point fluctuation amplitude. In this regime significant quantum back-action would be introduced to the orthogonal quadrature [1]. Beating the SQL with pulsed measurements, requires resolving the position of the resonator with accuracy smaller than the ground state size in a time much shorter than the oscillation period. Systems that could potentially achieve this require a large measurement bandwidth while maintaining a high ratio of optomechanical coupling rate to cavity linewidth.
We thus explore pulsed optomechanical measurement in nanoscale resonators with high photon-phonon coupling strengths. We use subwavelength confinement of optical fields in sliced photonic crystal structures to yield record-high optomechanical interaction strengths and single-photon cooperativities exceeding unity [2]. Moreover we `purify` the mechanical response through mechanical mode spectrum design, to approach the ideal scenario of a single MHz mechanical mode coupled to the optical cavity.
We report position measurements with an accuracy of 16 times the mechanical ground state size. We show how the ability to perform strong and fast measurements can be used for efficient optomechanical transduction, and how pulsed measurements provide a path to controlling the motional quantum state. We quantify the limiting factors of decoherence and additional mechanical modes to the ability to predict future measurement outcomes. We show that single pulses resolve the resonator`s thermal motion and can prepare thermally squeezed and purified (cooled) conditional mechanical states, and perform full state tomography on these states.
We thus demonstrate that pulsed backaction-evading nano-optomechanical measurement can be brought close to the quantum regime. We discuss promising routes to advance and exploit this regime of `time-domain quantum optomechanics`. Notably, a modest increase of the coupling efficiency of the input/output laser field to the optical cavity mode would be enough to bring the uncertainty in one quadrature below the zero-point fluctuation size, allowing squeezed state preparation and studying quantum backaction.
[1] M.R. Vanner et al., PNAS 108, 16182 (2011).
[2] R. Leijssen et al., Nat. Commun. 8, 16024 (2017).