Strong mechanical squeezing in an optomechanical system based on Lyapunov control

Biao Xiong; Xun Li; Shi-Lei Chao; Zhen Yang; Wen-Zhao Zhang; Weiping Zhang; Ling Zhou

doi:10.1364/PRJ.8.000151

[1] E. E. Wollman, C. U. Lei, A. J. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, K. C. Schwab. Quantum squeezing of motion in a mechanical resonator. Science, 349, 952-955(2015).

[2] C.-S. Hu, Z.-B. Yang, H. Wu, Y. Li, S.-B. Zheng. Twofold mechanical squeezing in a cavity optomechanical system. Phys. Rev. A, 98, 023807(2018).

[3] W. H. Zurek. Decoherence and the transition from quantum to classical. Phys. Today, 44, 36-44(1991).

[4] S.-L. Ma, X.-K. Li, J.-K. Xie, F.-L. Li. Two-mode squeezed states of two separated nitrogen-vacancy-center ensembles coupled via dissipative photons of superconducting resonators. Phys. Rev. A, 99, 012325(2019).

[5] V. Peano, H. G. L. Schwefel, C. Marquardt, F. Marquardt. Intracavity squeezing can enhance quantum-limited optomechanical position detection through deamplification. Phys. Rev. Lett., 115, 243603(2015).

[6] B. Xie, S. Feng. Squeezing-enhanced heterodyne detection of 10 Hz atto-Watt optical signals. Opt. Lett., 43, 6073-6076(2018).

[7] A. Motazedifard, F. Bemani, M. H. Naderi, R. Roknizadeh, D. Vitali. Force sensing based on coherent quantum noise cancellation in a hybrid optomechanical cavity with squeezed-vacuum injection. New J. Phys., 18, 073040(2016).

[8] J. Aasi, J. Abadie, B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, C. Adams, T. Adams, P. Addesso, R. X. Adhikari. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photonics, 7, 613-619(2013).

[9] M. A. Lemonde, N. Didier, A. A. Clerk. Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification. Nat. Commun., 7, 11338(2016).

[10] Y. Wang, C. Li, E. M. Sampuli, J. Song, Y. Jiang, Y. Xia. Enhancement of coherent dipole coupling between two atoms via squeezing a cavity mode. Phys. Rev. A, 99, 023833(2019).

[11] X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, F. Nori. Squeezed optomechanics with phase-matched amplification and dissipation. Phys. Rev. Lett., 114, 093602(2015).

[12] D. Rugar, P. Grütter. Mechanical parametric amplification and thermomechanical noise squeezing. Phys. Rev. Lett., 67, 699-702(1991).

[13] W. Ge, M. Bhattacharya. Single and two-mode mechanical squeezing of an optically levitated nanodiamond via dressed-state coherence. New J. Phys., 18, 103002(2016).

[14] A. Serafini, A. Retzker, M. B. Plenio. Generation of continuous variable squeezing and entanglement of trapped ions in time-varying potentials. Quantum Inform. Process., 8, 619(2009).

[15] W.-Z. Zhang, Y. Han, B. Xiong, L. Zhou. Optomechanical force sensor in a non-Markovian regime. New J. Phys., 19, 083022(2017).

[16] J. Liu, K.-D. Zhu. Coupled quantum molecular cavity optomechanics with surface plasmon enhancement. Photon. Res., 5, 450-456(2017).

[17] B. Xiong, X. Li, X.-Y. Wang, L. Zhou. Improve microwave quantum illumination via optical parametric amplifier. Ann. Phys., 385, 757-768(2017).

[18] J. Liu, K.-D. Zhu. Room temperature optical mass sensor with an artificial molecular structure based on surface plasmon optomechanics. Photon. Res., 6, 867-874(2018).

[19] A. Motazedifard, A. Dalafi, M. Naderi, R. Roknizadeh. Strong quadrature squeezing and quantum amplification in a coupled Bose-Einstein condensate-optomechanical cavity based on parametric modulation. Ann. Phys., 405, 202-219(2019).

[20] B. A. Levitan, A. Metelmann, A. A. Clerk. Optomechanics with two-phonon driving. New J. Phys., 18, 093014(2016).

[21] X. Xu, J. M. Taylor. Squeezing in a coupled two-mode optomechanical system for force sensing below the standard quantum limit. Phys. Rev. A, 90, 043848(2014).

[22] J.-Q. Liao, C. K. Law. Parametric generation of quadrature squeezing of mirrors in cavity optomechanics. Phys. Rev. A, 83, 033820(2011).

[23] C.-H. Bai, D.-Y. Wang, S. Zhang, H.-F. Wang. Qubit-assisted squeezing of mirror motion in a dissipative cavity optomechanical system. Sci. China Phys. Mech. Astron., 62, 970311(2019).

[24] B. Xiong, X. Li, S.-L. Chao, L. Zhou. Optomechanical quadrature squeezing in the non-Markovian regime. Opt. Lett., 43, 6053-6056(2018).

[25] Z.-C. Zhang, Y.-P. Wang, Y.-F. Yu, Z.-M. Zhang. Quantum squeezing in a modulated optomechanical system. Opt. Express, 26, 11915-11927(2018).

[26] M. Rashid, T. Tufarelli, J. Bateman, J. Vovrosh, D. Hempston, M. S. Kim, H. Ulbricht. Experimental realization of a thermal squeezed state of levitated optomechanics. Phys. Rev. Lett., 117, 273601(2016).

[27] D. Y. Wang, C. H. Bai, H. F. Wang, A. D. Zhu, S. Zhang. Steady-state mechanical squeezing in a double-cavity optomechanical system. Sci. Rep., 6, 38559(2016).

[28] G. Milburn, D. Walls. Production of squeezed states in a degenerate parametric amplifier. Opt. Commun., 39, 401-404(1981).

[29] M. O. Scully, M. S. Zubairy. Quantum Optics(1997).

[30] G. S. Agarwal, S. Huang. Strong mechanical squeezing and its detection. Phys. Rev. A, 93, 043844(2016).

[31] K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. S. Polzik, P. Zoller. Cavity-assisted squeezing of a mechanical oscillator. Phys. Rev. A, 79, 063819(2009).

[32] A. Dalafi, M. H. Naderi, A. Motazedifard. Effects of quadratic coupling and squeezed vacuum injection in an optomechanical cavity assisted with a Bose-Einstein condensate. Phys. Rev. A, 97, 043619(2018).

[33] M. Asjad, G. S. Agarwal, M. S. Kim, P. Tombesi, G. D. Giuseppe, D. Vitali. Robust stationary mechanical squeezing in a kicked quadratic optomechanical system. Phys. Rev. A, 89, 023849(2014).

[34] C.-H. Bai, D.-Y. Wang, S. Zhang, S. Liu, H.-F. Wang. Engineering of strong mechanical squeezing via the joint effect between duffing nonlinearity and parametric pump driving. Photon. Res., 7, 1229-1239(2019).

[35] A. Szorkovszky, A. C. Doherty, G. I. Harris, W. P. Bowen. Mechanical squeezing via parametric amplification and weak measurement. Phys. Rev. Lett., 107, 213603(2011).

[36] A. Kronwald, F. Marquardt, A. A. Clerk. Arbitrarily large steady-state bosonic squeezing via dissipation. Phys. Rev. A, 88, 063833(2013).

[37] C. U. Lei, A. J. Weinstein, J. Suh, E. E. Wollman, A. Kronwald, F. Marquardt, A. A. Clerk, K. C. Schwab. Quantum nondemolition measurement of a quantum squeezed state beyond the 3 dB limit. Phys. Rev. Lett., 117, 100801(2016).

[38] X. You, Z. Li, Y. Li. Strong quantum squeezing of mechanical resonator via parametric amplification and coherent feedback. Phys. Rev. A, 96, 063811(2017).

[39] R. Zhang, Y. Fang, Y.-Y. Wang, S. Chesi, Y.-D. Wang. Strong mechanical squeezing in an unresolved-sideband optomechanical system. Phys. Rev. A, 99, 043805(2019).

[40] J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, M. A. Sillanpää. Squeezing of quantum noise of motion in a micromechanical resonator. Phys. Rev. Lett., 115, 243601(2015).

[41] W.-J. Gu, Z. Yi, L.-H. Sun, Y. Yan. Generation of mechanical squeezing and entanglement via mechanical modulations. Opt. Express, 26, 30773-30785(2018).

[42] C. Li, J. Song, Y. Xia, W. Ding. Driving many distant atoms into high-fidelity steady state entanglement via Lyapunov control. Opt. Express, 26, 951-962(2018).

[43] S. Kuang, S. Cong. Lyapunov control methods of closed quantum systems. Automatica, 44, 98-108(2008).

[44] D. Ran, W.-J. Shan, Z.-C. Shi, Z.-B. Yang, J. Song, Y. Xia. High fidelity Dicke-state generation with Lyapunov control in circuit QED system. Ann. Phys., 396, 44-55(2018).

[45] W. Li, C. Li, H. Song. Quantum synchronization in an optomechanical system based on Lyapunov control. Phys. Rev. E, 93, 062221(2016).

[46] D. Ran, Z.-C. Shi, J. Song, Y. Xia. Speeding up adiabatic passage by adding Lyapunov control. Phys. Rev. A, 96, 033803(2017).

[47] Z. C. Shi, L. C. Wang, X. X. Yi. Preparing entangled states by Lyapunov control. Quantum Inform. Process., 15, 4939-4953(2016).

[48] Y.-X. Zeng, T. Gebremariam, M.-S. Ding, C. Li. Quantum optical diode based on Lyapunov control in a superconducting system. J. Opt. Soc. Am. B, 35, 2334-2341(2018).

[49] W.-M. Zhang, K.-M. Hu, Z.-K. Peng, G. Meng. Tunable micro- and nanomechanical resonators. Sensors, 15, 26478-26566(2015).

[50] D.-Y. Wang, C.-H. Bai, S. Liu, S. Zhang, H.-F. Wang. Optomechanical cooling beyond the quantum backaction limit with frequency modulation. Phys. Rev. A, 98, 023816(2018).

[51] A. Farace, V. Giovannetti. Enhancing quantum effects via periodic modulations in optomechanical systems. Phys. Rev. A, 86, 013820(2012).

[52] R. A. Barton, I. R. Storch, V. P. Adiga, R. Sakakibara, B. R. Cipriany, B. Ilic, S. P. Wang, P. Ong, P. L. McEuen, J. M. Parpia, H. G. Craighead. Photothermal self-oscillation and laser cooling of graphene optomechanical systems. Nano Lett., 12, 4681-4686(2012).

[53] C. Chen, S. Lee, V. V. Deshpande, G.-H. Lee, M. Lekas, K. Shepard, J. Hone. Graphene mechanical oscillators with tunable frequency. Nat. Nanotechnol., 8, 923-927(2013).

[54] V. Singh, S. Bosman, B. Schneider, Y. M. Blanter, A. Castellanos-Gomez, G. Steele. Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity. Nat. Nanotechnol., 9, 820-824(2014).

[55] J.-Q. Liao, C. K. Law. Cooling of a mirror in cavity optomechanics with a chirped pulse. Phys. Rev. A, 84, 053838(2011).

[56] Y.-D. Wang, A. A. Clerk. Using interference for high fidelity quantum state transfer in optomechanics. Phys. Rev. Lett., 108, 153603(2012).

[57] X.-Y. Lü, J.-Q. Liao, L. Tian, F. Nori. Steady-state mechanical squeezing in an optomechanical system via duffing nonlinearity. Phys. Rev. A, 91, 013834(2015).

[58] D. Vitali, S. Gigan, A. Ferreira, H. R. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, M. Aspelmeyer. Optomechanical entanglement between a movable mirror and a cavity field. Phys. Rev. Lett., 98, 030405(2007).

[59] M. Aspelmeyer, T. J. Kippenberg, F. Marquardt. Cavity optomechanics. Rev. Mod. Phys., 86, 1391-1452(2014).

[60] Y.-C. Liu, Y.-F. Xiao, X. Luan, Q. Gong, C. W. Wong. Coupled cavities for motional ground-state cooling and strong optomechanical coupling. Phys. Rev. A, 91, 033818(2015).