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Coherent feedback in optomechanical systems in the sideband-unresolved regime


Jingkun Guo and Simon Gröblacher

Kavli Institute of Nanoscience, Department of Quantum Nanoscience, Delft University of Technology, 2628CJ Delft, The Netherlands

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Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme, which is particularly well suited for systems in the sideband-unresolved regime, based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. We find that, by introducing an additional passive element – either a narrow linewidth cavity or a mirror with a delay line – an optomechanical system in the deeply sideband-unresolved regime will exhibit dynamics similar to one that is sideband-resolved. With this new approach, the experimental realization of groundstate cooling and optomechanical entanglement is well within reach of current integrated state-of-the-art high-Q mechanical resonators.

Preparing macroscopic mechanical resonators close to their motional quantum groundstate and generating entanglement with light offers great opportunities in studying fundamental physics and in developing a new generation of quantum applications. Here we propose an experimentally interesting scheme based on coherent feedback with linear, passive optical components to achieve groundstate cooling and photon-phonon entanglement generation with optomechanical devices. Our approach is particularly well suited for systems in the sideband-unresolved regime, where the linewidth of the cavity is larger than the mechanical frequency. With our scheme, the experimental realization of groundstate cooling and optomechanical entanglement is well within reach of current integrated state-of-the-art high-Q mechanical resonators.

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[1] K. Stannigel, P. Rabl, A. S. Sørensen, P. Zoller, and M. D. Lukin, Optomechanical Transducers for Long-Distance Quantum Communication, Phys. Rev. Lett. 105, 220501 (2010).

[2] A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, A high-resolution microchip optomechanical accelerometer, Nature Photon. 6, 768 (2012).

[3] I. Marinković, A. Wallucks, R. Riedinger, S. Hong, M. Aspelmeyer, and S. Gröblacher, An optomechanical Bell test, Phys. Rev. Lett. 121, 220404 (2018).

[4] M. Carlesso and S. Donadi, Collapse Models: Main Properties and the State of Art of the Experimental Tests, in Advances in Open Systems and Fundamental Tests of Quantum Mechanics, Springer Proceedings in Physics, edited by B. Vacchini, H.-P. Breuer, and A. Bassi (Springer International Publishing, 2019) pp. 1–13.

[5] P. E. Allain, L. Schwab, C. Mismer, M. Gely, E. Mairiaux, M. Hermouet, B. Walter, G. Leo, S. Hentz, M. Faucher, G. Jourdan, B. Legrand, and I. Favero, Optomechanical resonating probe for very high frequency sensing of atomic forces, Nanoscale 12, 2939 (2020).

[6] A. Wallucks, I. Marinković, B. Hensen, R. Stockill, and S. Gröblacher, A quantum memory at telecom wavelengths, Nat. Phys. 16, 772 (2020).

[7] N. Fiaschi, B. Hensen, A. Wallucks, R. Benevides, J. Li, T. P. M. Alegre, and S. Gröblacher, Optomechanical quantum teleportation, Nature Photon. 15, 817 (2021).

[8] W. J. Westerveld, M. Mahmud-Ul-Hasan, R. Shnaiderman, V. Ntziachristos, X. Rottenberg, S. Severi, and V. Rochus, Sensitive, small, broadband and scalable optomechanical ultrasound sensor in silicon photonics, Nature Photon. 15, 341 (2021).

[9] R. A. Norte, M. Forsch, A. Wallucks, I. Marinković, and S. Gröblacher, Platform for measurements of the casimir force between two superconductors, Phys. Rev. Lett. 121, 030405 (2018).

[10] J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, Nanomechanical coupling between microwave and optical photons, Nature Phys. 9, 712 (2013).

[11] O. Černotík and K. Hammerer, Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers, Phys. Rev. A 94, 012340 (2016).

[12] G. Arnold, M. Wulf, S. Barzanjeh, E. S. Redchenko, A. Rueda, W. J. Hease, F. Hassani, and J. M. Fink, Converting microwave and telecom photons with a silicon photonic nanomechanical interface, Nature Commun. 11, 4460 (2020).

[13] Y. Chen, Macroscopic quantum mechanics: theory and experimental concepts of optomechanics, J. Phys. B At. Mol. Opt. Phys. 46, 104001 (2013).

[14] S. G. Hofer, W. Wieczorek, M. Aspelmeyer, and K. Hammerer, Quantum entanglement and teleportation in pulsed cavity optomechanics, Phys. Rev. A 84, 52327 (2011).

[15] M. Paternostro, Engineering Nonclassicality in a Mechanical System through Photon Subtraction, Phys. Rev. Lett. 106, 183601 (2011).

[16] T. Palomaki, J. Teufel, R. Simmonds, and K. Lehnert, Entangling mechanical motion with microwave fields, Science 342, 710 (2013).

[17] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).

[18] A. A. Rakhubovsky and R. Filip, Robust entanglement with a thermal mechanical oscillator, Phys. Rev. A 91, 062317 (2015).

[19] M. Rossi, D. Mason, J. Chen, Y. Tsaturyan, and A. Schliesser, Measurement-based quantum control of mechanical motion, Nature 563, 53 (2018).

[20] L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, A. Kugi, and M. Aspelmeyer, Real-time optimal quantum control of mechanical motion at room temperature, Nature 595, 373 (2021).

[21] J. Chen, M. Rossi, D. Mason, and A. Schliesser, Entanglement of propagating optical modes via a mechanical interface, Nature Commun. 11, 943 (2020).

[22] Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution, Nature Nanotechn. 12, 776 (2017).

[23] A. H. Ghadimi, S. A. Fedorov, N. J. Engelsen, M. J. Bereyhi, R. Schilling, D. J. Wilson, and T. J. Kippenberg, Elastic strain engineering for ultralow mechanical dissipation, Science 360, 764 (2018).

[24] J. Guo, R. Norte, and S. Gröblacher, Feedback Cooling of a Room Temperature Mechanical Oscillator close to its Motional Ground State, Phys. Rev. Lett. 123, 223602 (2019).

[25] A. Beccari, M. J. Bereyhi, R. Groth, S. A. Fedorov, A. Arabmoheghi, N. J. Engelsen, and T. J. Kippenberg, Hierarchical tensile structures with ultralow mechanical dissipation, arXiv:2103.09785 (2021).

[26] R. Leijssen and E. Verhagen, Strong optomechanical interactions in a sliced photonic crystal nanobeam, Sci. Rep. 5, 15974 (2015).

[27] J. Guo and S. Gröblacher, Integrated optical-readout of a high-q mechanical out-of-plane mode, Light Sci. Appl. 11, 282 (2022).

[28] M. R. Vanner, I. Pikovski, G. D. Cole, M. S. Kim, C. Brukner, K. Hammerer, G. J. Milburn, and M. Aspelmeyer, Pulsed quantum optomechanics, Proc. Natl. Acad. Sci. 108, 16182 (2011).

[29] J. S. Bennett, K. Khosla, L. S. Madsen, M. R. Vanner, H. Rubinsztein-Dunlop, and W. P. Bowen, A quantum optomechanical interface beyond the resolved sideband limit, New J. Phys. 18, 053030 (2016).

[30] K. E. Khosla, G. A. Brawley, M. R. Vanner, and W. P. Bowen, Quantum optomechanics beyond the quantum coherent oscillation regime, Optica 4, 1382 (2017).

[31] J. Clarke, P. Sahium, K. E. Khosla, I. Pikovski, M. S. Kim, and M. R. Vanner, Generating mechanical and optomechanical entanglement via pulsed interaction and measurement, New J. Phys. 22, 063001 (2020).

[32] C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, Ground-state cooling of a micromechanical oscillator: comparing cold damping and cavity-assisted cooling schemes, Phys. Rev. A 77, 033804 (2008).

[33] J. T. Muhonen, G. R. L. Gala, R. Leijssen, and E. Verhagen, State Preparation and Tomography of a Nanomechanical Resonator with Fast Light Pulses, Phys. Rev. Lett. 123, 113601 (2019).

[34] C. Gut, K. Winkler, J. Hoelscher-Obermaier, S. G. Hofer, R. M. Nia, N. Walk, A. Steffens, J. Eisert, W. Wieczorek, J. A. Slater, M. Aspelmeyer, and K. Hammerer, Stationary optomechanical entanglement between a mechanical oscillator and its measurement apparatus, Phys. Rev. Research 2, 033244 (2020).

[35] W. P. Bowen and G. J. Milburn, Quantum optomechanics (CRC press, 2015).

[36] M. Yanagisawa, Quantum feedback control for deterministic entangled photon generation, Phys. Rev. Lett. 97, 190201 (2006).

[37] M. R. James, H. I. Nurdin, and I. R. Petersen, $H^∞$ control of linear quantum stochastic systems, IEEE Trans. Automat. Contr. 53, 1787 (2008).

[38] R. Hamerly and H. Mabuchi, Advantages of coherent feedback for cooling quantum oscillators, Phys. Rev. Lett. 109, 173602 (2012).

[39] N. Yamamoto, Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information, Phys. Rev. X 4, 041029 (2014).

[40] J. Combes, J. Kerckhoff, and M. Sarovar, The SLH framework for modeling quantum input-output networks, Adv. Phys-X 2, 784 (2017).

[41] T. Ojanen and K. Børkje, Ground-state cooling of mechanical motion in the unresolved sideband regime by use of optomechanically induced transparency, Phys. Rev. A 90, 013824 (2014).

[42] J. S. Bennett, L. S. Madsen, M. Baker, H. Rubinsztein-Dunlop, and W. P. Bowen, Coherent control and feedback cooling in a remotely coupled hybrid atom–optomechanical system, New J. Phys 16, 083036 (2014).

[43] T. M. Karg, B. Gouraud, P. Treutlein, and K. Hammerer, Remote Hamiltonian interactions mediated by light, Phys. Rev. A 99, 063829 (2019).

[44] J. Li, G. Li, S. Zippilli, D. Vitali, and T. Zhang, Enhanced entanglement of two different mechanical resonators via coherent feedback, Phys. Rev. A 95, 043819 (2017).

[45] J.-S. Feng, L. Tan, H.-Q. Gu, and W.-M. Liu, Auxiliary-cavity-assisted ground-state cooling of an optically levitated nanosphere in the unresolved-sideband regime, Phys. Rev. A 96, 063818 (2017).

[46] Z. Wang and A. H. Safavi-Naeini, Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback, Nature Commun. 8, 15886 (2017).

[47] H.-K. Lau, A. Eisfeld, and J.-M. Rost, Cavity-free quantum optomechanical cooling by atom-modulated radiation, Phys. Rev. A 98, 043827 (2018).

[48] T. M. Karg, B. Gouraud, C. T. Ngai, G.-L. Schmid, K. Hammerer, and P. Treutlein, Light-mediated strong coupling between a mechanical oscillator and atomic spins 1 meter apart, Science 369, 174 (2020).

[49] A. Harwood, M. Brunelli, and A. Serafini, Cavity optomechanics assisted by optical coherent feedback, Phys. Rev. A 103, 023509 (2021).

[50] G.-L. Schmid, C. T. Ngai, M. Ernzer, M. B. Aguilera, T. M. Karg, and P. Treutlein, Coherent feedback cooling of a nanomechanical membrane with atomic spins, Phys. Rev. X 12, 011020 (2022).

[51] J. Louisell, A matrix method for determining the imaginary axis eigenvalues of a delay system, IEEE Trans. Automat. Contr. 46, 2008 (2001).

[52] N. Olgac and R. Sipahi, A practical method for analyzing the stability of neutral type LTI-time delayed systems, Automatica 40, 847 (2004).

[53] A. G. Krause, T. D. Blasius, and O. Painter, Optical read out and feedback cooling of a nanostring optomechanical cavity, arXiv:1506.01249 (2015).

[54] M. Eichenfield, R. Camacho, J. Chan, K. J. Vahala, and O. Painter, A picogram- and nanometre-scale photonic-crystal optomechanical cavity, Nature 459, 550 (2009).

[55] L. Wu, H. Wang, Q. Yang, Q.-x. Ji, B. Shen, C. Bao, M. Gao, and K. Vahala, Greater than one billion Q factor for on-chip microresonators, Opt. Lett. 45, 5129 (2020).

[56] M. W. Puckett, K. Liu, N. Chauhan, Q. Zhao, N. Jin, H. Cheng, J. Wu, R. O. Behunin, P. T. Rakich, K. D. Nelson, and D. J. Blumenthal, 422 Million intrinsic quality factor planar integrated all-waveguide resonator with sub-MHz linewidth, Nature Commun. 12, 934 (2021).

[57] J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, Laser cooling of a nanomechanical oscillator into its quantum ground state, Nature 478, 89 (2011).

[58] H. Ren, M. H. Matheny, G. S. MacCabe, J. Luo, H. Pfeifer, M. Mirhosseini, and O. Painter, Two-dimensional optomechanical crystal cavity with high quantum cooperativity, Nature Commun. 11, 3373 (2020).

[59] A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, Quantum ground state and single-phonon control of a mechanical resonator, Nature 464, 697 (2010).

[60] J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, Sideband cooling of micromechanical motion to the quantum ground state, Nature 475, 359 (2011).

[61] C. Whittle, E. D. Hall, S. Dwyer, N. Mavalvala, V. Sudhir, R. Abbott, A. Ananyeva, C. Austin, L. Barsotti, J. Betzwieser, C. D. Blair, A. F. Brooks, D. D. Brown, A. Buikema, C. Cahillane, J. C. Driggers, A. Effler, A. Fernandez-Galiana, P. Fritschel, V. V. Frolov, T. Hardwick, M. Kasprzack, K. Kawabe, N. Kijbunchoo, J. S. Kissel, G. L. Mansell, F. Matichard, L. McCuller, T. McRae, A. Mullavey, A. Pele, R. M. S. Schofield, D. Sigg, M. Tse, G. Vajente, D. C. Vander-Hyde, H. Yu, H. Yu, C. Adams, R. X. Adhikari, S. Appert, K. Arai, J. S. Areeda, Y. Asali, S. M. Aston, A. M. Baer, M. Ball, S. W. Ballmer, S. Banagiri, D. Barker, J. Bartlett, B. K. Berger, D. Bhattacharjee, G. Billingsley, S. Biscans, R. M. Blair, N. Bode, P. Booker, R. Bork, A. Bramley, K. C. Cannon, X. Chen, A. A. Ciobanu, F. Clara, C. M. Compton, S. J. Cooper, K. R. Corley, S. T. Countryman, P. B. Covas, D. C. Coyne, L. E. H. Datrier, D. Davis, C. Di Fronzo, K. L. Dooley, P. Dupej, T. Etzel, M. Evans, T. M. Evans, J. Feicht, P. Fulda, M. Fyffe, J. A. Giaime, K. D. Giardina, P. Godwin, E. Goetz, S. Gras, C. Gray, R. Gray, A. C. Green, E. K. Gustafson, R. Gustafson, J. Hanks, J. Hanson, R. K. Hasskew, M. C. Heintze, A. F. Helmling-Cornell, N. A. Holland, J. D. Jones, S. Kandhasamy, S. Karki, P. J. King, R. Kumar, M. Landry, B. B. Lane, B. Lantz, M. Laxen, Y. K. Lecoeuche, J. Leviton, J. Liu, M. Lormand, A. P. Lundgren, R. Macas, M. MacInnis, D. M. Macleod, S. Márka, Z. Márka, D. V. Martynov, K. Mason, T. J. Massinger, R. McCarthy, D. E. McClelland, S. McCormick, J. McIver, G. Mendell, K. Merfeld, E. L. Merilh, F. Meylahn, T. Mistry, R. Mittleman, G. Moreno, C. M. Mow-Lowry, S. Mozzon, T. J. N. Nelson, P. Nguyen, L. K. Nuttall, J. Oberling, R. J. Oram, C. Osthelder, D. J. Ottaway, H. Overmier, J. R. Palamos, W. Parker, E. Payne, R. Penhorwood, C. J. Perez, M. Pirello, H. Radkins, K. E. Ramirez, J. W. Richardson, K. Riles, N. A. Robertson, J. G. Rollins, C. L. Romel, J. H. Romie, M. P. Ross, K. Ryan, T. Sadecki, E. J. Sanchez, L. E. Sanchez, T. R. Saravanan, R. L. Savage, D. Schaetz, R. Schnabel, E. Schwartz, D. Sellers, T. Shaffer, B. J. J. Slagmolen, J. R. Smith, S. Soni, B. Sorazu, A. P. Spencer, K. A. Strain, L. Sun, M. J. Szczepańczyk, M. Thomas, P. Thomas, K. A. Thorne, K. Toland, C. I. Torrie, G. Traylor, A. L. Urban, G. Valdes, P. J. Veitch, K. Venkateswara, G. Venugopalan, A. D. Viets, T. Vo, C. Vorvick, M. Wade, R. L. Ward, J. Warner, B. Weaver, R. Weiss, B. Willke, C. C. Wipf, L. Xiao, H. Yamamoto, L. Zhang, M. E. Zucker, and J. Zweizig, Approaching the motional ground state of a 10-kg object, Science 372, 1333 (2021).

[62] S. Barzanjeh, A. Xuereb, S. Gröblacher, M. Paternostro, C. A. Regal, and E. M. Weig, Optomechanics for quantum technologies, Nature Physics 18, 15 (2022).

[63] C. Schäfermeier, H. Kerdoncuff, U. B. Hoff, H. Fu, A. Huck, J. Bilek, G. I. Harris, W. P. Bowen, T. Gehring, and U. L. Andersen, Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light, Nature Commun. 7, 13628 (2016).

[64] C. Galland, N. Sangouard, N. Piro, N. Gisin, and T. J. Kippenberg, Heralded Single-Phonon Preparation, Storage, and Readout in Cavity Optomechanics, Phys. Rev. Lett. 112, 143602 (2014).

[65] R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, Non-classical correlations between single photons and phonons from a mechanical oscillator, Nature 530, 313 (2016).

[66] R. Y. Teh, S. Kiesewetter, M. D. Reid, and P. D. Drummond, Simulation of an optomechanical quantum memory in the nonlinear regime, Phys. Rev. A 96, 013854 (2017).

[67] S. Abdalla, S. Ng, P. Barrios, D. Celo, A. Delage, S. El-Mougy, I. Golub, J.-J. He, S. Janz, R. McKinnon, P. Poole, S. Raymond, T. Smy, and B. Syrett, Carrier injection-based digital optical switch with reconfigurable output waveguide arms, IEEE Photon. Technol. Lett. 16, 1038 (2004).

[68] C. Sun, W. Wu, Y. Yu, G. Chen, X. Zhang, X. Chen, D. J. Thomson, and G. T. Reed, De-multiplexing free on-chip low-loss multimode switch enabling reconfigurable inter-mode and inter-path routing, Nanophotonics 7, 1571 (2018).

[69] P. Hyllus and J. Eisert, Optimal entanglement witnesses for continuous-variable systems, New J. Phys. 8, 51 (2006).

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[1] Maryse Ernzer, Manel Bosch Aguilera, Matteo Brunelli, Gian-Luca Schmid, Christoph Bruder, Patrick P. Potts, and Philipp Treutlein, “Optical coherent feedback control of a mechanical oscillator”, arXiv:2210.07674.

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