Exploiting non-linear effects in optomechanical sensors with continuous photon-counting
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
|Published:||2022-09-20, volume 6, page 812|
|Citation:||Quantum 6, 812 (2022).|
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
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.
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.
► BibTeX data
 C. K. Law, ``Interaction between a moving mirror and radiation pressure: A Hamiltonian formulation,'' Phys. Rev. A 51, 2537 (1995).
 M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, ``Cavity optomechanics,'' Rev. Mod. Phys. 86, 1391 (2014a).
 M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity Optomechanics: Nano- and Micromechanical Resonators Interacting with Light (Springer, 2014).
 W. P. Bowen and G. J. Milburn, Quantum Optomechanics (CRC Press, 2015).
 S. Barzanjeh, et al., ``Optomechanics for quantum technologies,'' Nat. Phys. 18, 15 (2022).
 C. Whittle, et al., ``Approaching the motional ground state of a 10-kg object,'' Science 372, 1333 (2021).
 S. Mancini, V. I. Man'ko, and P. Tombesi, ``Ponderomotive control of quantum macroscopic coherence,'' Phys. Rev. A 55, 3042 (1997).
 S. Bose, K. Jacobs, and P. L. Knight, ``Preparation of nonclassical states in cavities with a moving mirror,'' Phys. Rev. A 56, 4175 (1997).
 A. A. Clerk and F. Marquardt, ``Basic theory of cavity optomechanics,'' (2014).
 C. Gonzalez-Ballestero, et al., ``Levitodynamics: Levitation and control of microscopic objects in vacuum,'' Science 374, eabg3027 (2021).
 F. Tebbenjohanns, et al., ``Quantum control of a nanoparticle optically levitated in cryogenic free space,'' Nature 595, 378 (2021).
 N. Kiesel, et al., ``Cavity cooling of an optically levitated submicron particle,'' PNAS 110, 14180 (2013).
 F. Brennecke, et al., ``Cavity optomechanics with a bose-einstein condensate,'' Science 322, 235 (2008).
 K. W. Murch, et al., ``Observation of quantum-measurement backaction with an ultracold atomic gas,'' Nature Phys 4, 561 (2008).
 D. W. C. Brooks, et al., ``Non-classical light generated by quantum-noise-driven cavity optomechanics,'' Nature 488, 476 (2012).
 M. Eichenfield, et al., ``Optomechanical crystals,'' Nature 462, 78 (2009).
 J. Chan, et al., ``Laser cooling of a nanomechanical oscillator into its quantum ground state,'' Nature 478, 89 (2011).
 R. Riedinger, et al., ``Remote quantum entanglement between two micromechanical oscillators,'' Nature 556, 473 (2018).
 D. K. Armani, et al., ``Ultra-high-Q toroid microcavity on a chip,'' Nature 421, 925 (2003).
 D. J. Wilson, et al., ``Measurement-based control of a mechanical oscillator at its thermal decoherence rate,'' Nature 524, 325 (2015).
 V. Sudhir, et al., ``Appearance and disappearance of quantum correlations in measurement-based feedback control of a mechanical oscillator,'' Phys. Rev. X 7, 011001 (2017).
 M. Rossi, et al., ``Measurement-based quantum control of mechanical motion,'' Nature 563, 53 (2018).
 K. Iwasawa, et al., ``Quantum-limited mirror-motion estimation,'' Phys. Rev. Lett. 111, 163602 (2013).
 W. Wieczorek, et al., ``Optimal State Estimation for Cavity Optomechanical Systems,'' Phys. Rev. Lett. 114, 223601 (2015).
 M. Rossi, et al., ``Observing and Verifying the Quantum Trajectory of a Mechanical Resonator,'' Phys. Rev. Lett. 123, 163601 (2019).
 A. Setter, et al., ``Real-time kalman filter: Cooling of an optically levitated nanoparticle,'' Phys. Rev. A 97, 033822 (2018).
 D. Mason, et al., ``Continuous force and displacement measurement below the standard quantum limit,'' Nat. Phys. 15, 745 (2019).
 L. Magrini, et al., ``Real-time optimal quantum control of mechanical motion at room temperature,'' Nature 595, 373 (2021).
 D. Vitali, et al., ``Optomechanical Entanglement between a Movable Mirror and a Cavity Field,'' Phys. Rev. Lett. 98, 030405 (2007).
 C. Genes, et al., ``Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes,'' Phys. Rev. A 77, 033804 (2008a).
 I. Wilson-Rae, et al., ``Cavity-assisted backaction cooling of mechanical resonators,'' New J. Phys. 10, 095007 (2008).
 Y.-C. Liu, et al., ``Dynamic Dissipative Cooling of a Mechanical Resonator in Strong Coupling Optomechanics,'' Phys. Rev. Lett. 110, 153606 (2013).
 A. Ferraro, S. Olivares, and M. G. A. Paris, Gaussian states in continuous variable quantum information (Bibliopolis, Napoli, 2005).
 S. G. Hofer and K. Hammerer, in Advances In Atomic, Molecular, and Optical Physics, Vol. 66, edited by E. Arimondo, C. C. Lin, and S. F. Yelin (Academic Press, 2017) pp. 263–374.
 A. D. O’Connell, et al., ``Quantum ground state and single-phonon control of a mechanical resonator,'' Nature 464, 697 (2010).
 K. Stannigel, et al., ``Optomechanical Quantum Information Processing with Photons and Phonons,'' Phys. Rev. Lett. 109, 013603 (2012).
 T. Ramos, et al., ``Nonlinear Quantum Optomechanics via Individual Intrinsic Two-Level Defects,'' Phys. Rev. Lett. 110, 193602 (2013).
 A. P. Reed, et al., ``Faithful conversion of propagating quantum information to mechanical motion,'' Nature Phys 13, 1163 (2017).
 J. D. Teufel, et al., ``Circuit cavity electromechanics in the strong-coupling regime,'' Nature 471, 204 (2011).
 S. Qvarfort, et al., ``Master-equation treatment of nonlinear optomechanical systems with optical loss,'' Phys. Rev. A 104, 013501 (2021a).
 X. Wang, et al., ``Ultraefficient cooling of resonators: Beating sideband cooling with quantum control,'' Phys. Rev. Lett. 107, 177204 (2011).
 V. Bergholm, et al., ``Optimal control of hybrid optomechanical systems for generating non-classical states of mechanical motion,'' Quantum Sci. Technol. 4, 034001 (2019).
 A. Nunnenkamp, K. Børkje, and S. M. Girvin, ``Single-photon optomechanics,'' Phys. Rev. Lett. 107, 063602 (2011).
 P. Rabl, ``Photon blockade effect in optomechanical systems,'' Phys. Rev. Lett. 107, 063601 (2011).
 X.-W. Xu, Y.-J. Li, and Y.-x. Liu, ``Photon-induced tunneling in optomechanical systems,'' Phys. Rev. A 87, 025803 (2013).
 A. Kronwald, M. Ludwig, and F. Marquardt, ``Full photon statistics of a light beam transmitted through an optomechanical system,'' Phys. Rev. A 87, 013847 (2013).
 L. A. Clark, A. Stokes, and A. Beige, ``Quantum jump metrology,'' Phys. Rev. A 99, 022102 (2019).
 S. Qvarfort, et al., ``Gravimetry through non-linear optomechanics,'' Nat. Commun. 9, 1 (2018).
 S. Qvarfort, et al., ``Optimal estimation of time-dependent gravitational fields with quantum optomechanical systems,'' Phys. Rev. Res. 3, 013159 (2021b).
 S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, 1993).
 M. G. A. Paris, ``Quantum estimation for quantum technology,'' Int. J. Quantum Inf. 07, 125 (2009).
 J. D. Cohen, et al., ``Phonon counting and intensity interferometry of a nanomechanical resonator,'' Nature 520, 522 (2015).
 I. Galinskiy, et al., ``Phonon counting thermometry of an ultracoherent membrane resonator near its motional ground state,'' Optica 7, 718 (2020).
 N. Fiaschi, et al., ``Optomechanical quantum teleportation,'' Nat. Photon. 15, 817 (2021).
 K. Jacobs, Quantum Measurement Theory and its Applications (Cambridge University Press, Cambridge, 2014).
 S. Gammelmark and K. Molmer, ``Bayesian parameter inference from continuously monitored quantum systems,'' Phys. Rev. A 87, 032115 (2013).
 J. Z. Bernád, C. Sanavio, and A. Xuereb, ``Optimal estimation of the optomechanical coupling strength,'' Phys. Rev. A 97, 063821 (2018).
 D. Hälg, et al., ``Membrane-Based Scanning Force Microscopy,'' Phys. Rev. Appl. 15, L021001 (2021).
 H. L. Van Trees and K. L. Bell, Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking (Wiley, 2007).
 F. Albarelli, et al., ``Ultimate limits for quantum magnetometry via time-continuous measurements,'' New J. Phys. 19, 123011 (2017).
 A. H. Kiilerich and K. Mølmer, ``Estimation of atomic interaction parameters by photon counting,'' Phys. Rev. A 89, 052110 (2014).
 D. E. Chang, V. Vuletić, and M. D. Lukin, ``Quantum nonlinear optics — photon by photon,'' Nat. Photonics 8, 685 (2014).
 A. Reiserer and G. Rempe, ``Cavity-based quantum networks with single atoms and optical photons,'' Rev. Mod. Phys. 87, 1379 (2015).
 T. Peyronel, et al., ``Quantum nonlinear optics with single photons enabled by strongly interacting atoms,'' Nature 488, 57 (2012).
 C. Möhl, et al., ``Photon correlation transients in a weakly blockaded rydberg ensemble,'' J. Phys. B: At. Mol. Opt. Phys. 53, 084005 (2020).
 A. S. Prasad, et al., ``Correlating photons using the collective nonlinear response of atoms weakly coupled to an optical mode,'' Nat. Photonics 14, 719 (2020).
 C. Genes, et al., ``Robust entanglement of a micromechanical resonator with output optical fields,'' Phys. Rev. A 78, 032316 (2008b).
 M. K. Schmidt, et al., ``Frequency-resolved photon correlations in cavity optomechanics,'' Quantum Science and Technology 6, 034005 (2021).
 K. Børkje, F. Massel, and J. G. E. Harris, ``Nonclassical photon statistics in two-tone continuously driven optomechanics,'' Phys. Rev. A 104, 063507 (2021).
 H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, 2002).
 J. Dalibard, Y. Castin, and K. Molmer, ``Wave-function approach to dissipative processes in quantum optics,'' Phys. Rev. Lett. 68, 580 (1992).
 K. Mølmer, Y. Castin, and J. Dalibard, ``Monte carlo wave-function method in quantum optics,'' J. Opt. Soc. Am. B 10, 524 (1993).
 G. C. Hegerfeldt, ``How to reset an atom after a photon detection: Applications to photon-counting processes,'' Phys. Rev. A 47, 449 (1993).
 H. Carmichael, An Open Systems Approach to Quantum Optics (Springer Berlin Heidelberg, 1993).
 M. B. Plenio and P. L. Knight, ``The quantum-jump approach to dissipative dynamics in quantum optics,'' Rev. Mod. Phys. 70, 101 (1998).
 K. Mølmer and Y. Castin, ``Monte Carlo wavefunctions in quantum optics,'' Quantum and Semiclassical Optics: Journal of the European Optical Society Part B 8, 49 (1996).
 R. Horodecki, et al., ``Quantum entanglement,'' Rev. Mod. Phys. 81, 865 (2009).
 O. Gühne and G. Tóth, ``Entanglement detection,'' Phys. Rep. 474, 1 (2009).
 C. Gardiner and P. Zoller, Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics (Springer Science & Business Media, 2004).
 K. P. Murphy, Machine Learning: A Probabilistic Perspective (MIT Press, 2012).
 Y. Li, et al., ``Frequentist and Bayesian Quantum Phase Estimation,'' Entropy 20, 628 (2018).
 H. L. van Trees, Detection, Estimation and Modulation Theory, Vol. I (Wiley, 1968).
 A. W. van der Vaart, Asymptotic Statistics (Cambridge University Press, 1998).
 S. L. Braunstein and C. M. Caves, ``Statistical distance and the geometry of quantum states,'' Phys. Rev. Lett. 72, 3439 (1994).
 H. Yuan and C.-H. F. Fung, ``Quantum parameter estimation with general dynamics,'' npj Quantum Inf. 3, 1 (2017).
 S. Zhou and L. Jiang, ``An exact correspondence between the quantum Fisher information and the Bures metric,'' arXiv:1910.08473 [quant-ph] (2019), arXiv: 1910.08473.
 S. Gammelmark and K. Mølmer, ``Fisher information and the quantum cramér-rao sensitivity limit of continuous measurements,'' Phys. Rev. Lett. 112, 170401 (2014).
 J. Amoros-Binefa and J. Kołodyński, ``Noisy atomic magnetometry in real time,'' New J. Phys. 23, 012030 (2021).
 M. Ludwig, B. Kubala, and F. Marquardt, ``The optomechanical instability in the quantum regime,'' New J. Phys. 10, 095013 (2008).
 Kawthar Al Rasbi, Almut Beige, and Lewis A. Clark, "Quantum jump metrology in a two-cavity network", Physical Review A 106 6, 062619 (2022).
The above citations are from Crossref's cited-by service (last updated successfully 2023-06-08 13:10:10) and SAO/NASA ADS (last updated successfully 2023-06-08 13:10:11). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.