# Exploiting non-linear effects in optomechanical sensors with continuous photon-counting

Lewis A. Clark1, Bartosz Markowicz1,2, and Jan Kołodyński1

1Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Banacha 2c, 02-097 Warszawa, Poland
2Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland

### Abstract

Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter regimes of non-linear interactions between their constituent mechanical and optical degrees of freedom. In this work, we show how this novel opportunity may serve to construct a new generation of optomechanical sensors. We consider the canonical optomechanical setup with the detection scheme being based on time-resolved counting of photons leaking from the cavity. By performing simulations and resorting to Bayesian inference, we demonstrate that the non-classical correlations of the detected photons may crucially enhance the sensor performance in real time. We believe that our work may stimulate a new direction in the design of such devices, while our methods apply also to other platforms exploiting non-linear light-matter interactions and photon detection.

Optomechanics spans a wide variety of physical systems involving light coupling to mechanical motion. Moreover, they are typically some of the most accessible candidates for probing quantum effects in nature. Most often, optomechanical systems are considered in the linear regime, where the optical driving of the system is strong or the light-mechanics coupling is weak. However, such systems generally show less quantum characteristics. Moving into the non-linear regime, the quantum behaviour of the system is enhanced, which may also result in the production of highly non-classical light. While still experimentally challenging to achieve, the benefits of working within the non-linear regime are clear.

Meanwhile, techniques involving continuous monitoring of a system for quantum sensing tasks have been demonstrated to be highly effective. Here, instead of preparing the system in a specific state and performing an optimum single-shot measurement, the system is allowed to evolve over time and its emission statistics are monitored. By doing so, an unknown system parameter can be well estimated, even from a single quantum trajectory.

Here, we combine these two observations by using the photon statistics of a non-linear optomechanical system to estimate unknown parameters, such as the optomechanical coupling strength. We see how the non-classical statistics of the non-linear optomechanical system produce excellent results from just a single quantum trajectory, even with a relatively low number of photon emissions. Utilising the techniques of Bayesian inference, a posterior distribution can be obtained and compared with the sensing performance of an optimum single-shot measurement. We demonstrate that after a sufficient amount of time, our continuous monitored system is capable of outperforming a system measured with a single-shot measurement, and provide useful insight into designing potential novel sensing schemes for optomechanical devices.

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### Cited by

[1] Kawthar Al Rasbi, Almut Beige, and Lewis A. Clark, "Quantum jump metrology in a two-cavity network", arXiv:2201.04412.

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