Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system

Abstract

In this paper, we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system. In the scheme, when the driving bichromatic laser beam is adjusted to the off-resonant j-order red- and blue-sideband, the interaction between the cavity and mechanical oscillator leads to a j-phonon resonance quantum Rabi model. Moreover, we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system. As a typical example, we theoretically analyze the two-phonon resonance quantum Rabi model, and derive an effective Hamiltonian of the six-phonon coupling. Finally, we present a method of six-phonon generation based on adiabatic passage across the resonance. Numerical simulations confirm the validity of the proposed scheme. Theoretically, the proposed scheme can be extended to the realization of 3j-phonon state.

Graphical abstract

Keywords

quantum Rabi model / cavity-optomechanical system / adiabatic passage

References

[1] M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Ha-gley, J. M. Raimond, and S. Haroche, Quantum Rabi oscillation: A direct test of field quantization in a cavity, Phys. Rev. Lett. 76(11), 1800 (1996)

[2] Q. Ai, Y. Li, H. Zheng, and C. P. Sun, Quantum anti-Zeno effect without rotating wave approximation, Phys. Rev. A 81(4), 042116 (2010)

[3] D. Z. Xu, Q. Ai, and C. P. Sun, Dispersive-coupling based quantum Zeno effect in a cavity-QED system, Phys. Rev. A 83(2), 022107 (2011)

[4] T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hmmer, E. Solano, A. Marx, and R.Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nat. Phys. 6, 772 (2010)

[5] P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. García-Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, Observation of the Bloch–Siegert shift in a qubit-oscillator system in the ultrastrong coupling regime, Phys. Rev. Lett. 105(23), 237001 (2010)

[6] J. Casanova, G. Romero, I. Lizuain, J. J. García-Ripoll, and E. Solano, Deep strong coupling regime of the Jaynes– Cummings model, Phys. Rev. Lett. 105(26), 263603 (2010)

[7] S. De Liberato, Light-matter decoupling in the deep strong coupling regime: The breakdown of the Purcell effect, Phys. Rev. Lett. 112(1), 016401 (2014)

[8] D. Braak, Q. H. Chen, M. T. Batchelor, and E. Solano, Semiclassical and quantum Rabi models: In celebration of 80 years, J. Phys. A Math. Theor. 49(30), 300301 (2016)

[9] J. F. Huang and C. K. Law, Photon emission via vacuum dressed intermediate states under ultrastrong coupling, Phys. Rev. A 89(3), 033827 (2014)

[10] L. Garziano, R. Stassi, A. Ridolfo, O. Di Stefano, and S. Savasta, Vacuum-induced symmetry breaking in a superconducting quantum circuit, Phys. Rev. A 90(4), 043817 (2014)

[11] L. T. Shen, Z. B. Yang, H. Z. Wu, and S. B. Zheng, Quantum phase transition and quench dynamics in the anisotropic Rabi model, Phys. Rev. A 95(1), 013819 (2017)

[12] S. Ashhab, Superradiance transition in a system with a single qubit and a single oscillator, Phys. Rev. A 87(1), 013826 (2013)

[13] T. H. Kyaw, S. Felicetti, G. Romero, E. Solano, and L. C. Kwek, Scalable quantum memory in the ultrastrong coupling regime, Sci. Rep. 5(1), 8621 (2015)

[14] S. Felicetti, E. Rico, C. Sabin, T. Ockenfels, J. Koch, M. Leder, C. Grossert, M. Weitz, and E. Solano, Quantum Rabi model in the Brillouin zone with ultracold atoms, Phys. Rev. A 95(1), 013827 (2017)

[15] A. Mezzacapo, U. Las Heras, J. S. Pedernales, L. DiCarlo, E. Solano, and L. Lamata, Digital quantum Rabi and Dicke models in superconducting circuits, Sci. Rep. 4(1), 7482 (2015)

[16] C. H. Alderete and B. M. Rodríguez-Lara, Crosscavity quantum Rabi model, J. Phys. A Math. Theor. 49(41), 414001 (2016)

[17] R. Puebla, J. Casanova, and M. B. Plenio, A robust scheme for the implementation of the quantum Rabi model in trapped ions, New J. Phys. 18(11), 113039 (2016)

[18] K. K. W. Ma and C. K. Law, Three-photon resonance and adiabatic passage in the large-detuning Rabi model, Phys. Rev. A 92(2), 023842 (2015)

[19] L. Garziano, R. Stassi, V. Macrì, A. F. Kockum, S. Savasta, and F. Nori, Multiphoton quantum Rabi oscillations in ultrastrong cavity QED, Phys. Rev. A 92(6), 063830 (2015)

[20] M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86(4), 1391 (2014)

[21] S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Entangling macroscopic oscillators exploiting radiation pressure, Phys. Rev. Lett. 88(12), 120401 (2002)

[22] X. W. Xu, Y. J. Zhao, and Y. X. Liu, Entangled-state engineering of vibrational modes in a multimembrane optomechanical system, Phys. Rev. A 88(2), 022325 (2013)

[23] Z. R. Zhong, X. Wang, and W.Qin, Towards quantum entanglement of micromirrors via a two-level atom and radiation pressure, Front. Phys. 13(5), 130319 (2018)

[24] Y. H. Chen, Z. C. Shi, J. Song, and Y. Xia, Invariantbased inverse engineering for fluctuation transfer between membranes in an optomechanical cavity system, Phys. Rev. A 97(2), 023841 (2018)

[25] C. S. Hu, Z. Q. Liu, Y. Liu, L. T. Shen, H. Wu, and S. B. Zheng, Entanglement beating in a cavity optomechanical system under two-field driving, Phys. Rev. A 101(3), 033810 (2020)

[26] S. S. Chen, H. Zhang, Q. Ai, and G. J. Yang, Phononic entanglement concentration via optomechanical interactions, Phys. Rev. A 100(5), 052306 (2019)

[27] X. B. Yan, H. L. Lu, F. Gao, F. Gao, and L. Yang, Perfect optical nonreciprocity in a double-cavity optomechanical system, Front. Phys. 14(5), 52601 (2019)

[28] L. Qi, G. L. Wang, S. Liu, S. Zhang, and H. F. Wang, Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice, Front. Phys. 16(1), 12503 (2021)

[29] Z. Zhang, J. Pei, Y. P. Wang, and X. Wang, Measuring orbital angular momentum of vortex beams in optomechanics, Front. Phys. 16(3), 32503 (2021)

[30] K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Wein-stein, and N. Mavalvala, A quantum-enhanced prototype gravitational-wave detector, Nat. Phys. 4(6), 472 (2008)

[31] U. B. Hoff, G. I. Harris, L. S. Madsen, H. Kerdoncuff, M. Lassen, B. M. Nielsen, W. P. Bowen, and U. L. Andersen, Quantum-enhanced micromechanical displacement sensi-tivity, Opt. Lett. 38(9), 1413 (2013)

[32] R. C. Pooser and B. Lawrie, Ultrasensitive measurement of microcantilever displacement below the shotnoise limit, Optica 2(5), 393 (2015)

[33] C. M. Caves, Quantum-mechanical noise in an interferom-eter, Phys. Rev. D 23(8), 1693 (1981)

[34] D. Kienzler, C. Flühmann, V. Negnevitsky, H. Y. Lo, M. Marinelli, D. Nadlinger, and J. P. Home, Observation of quantum interference between separated mechanical oscil-lator wave packets, Phys. Rev. Lett. 116(14), 140402 (2016)

[35] J. Q. Liao, Q. Q. Wu, and F. Nori, Entangling two macroscopic mechanical mirrors in a two-cavity optomechanical system, Phys. Rev. A 89(1), 014302 (2014)

[36] T. Hong, H. Yang, H. Miao, and Y. Chen, Open quantum dynamics of single-photon optomechanical devices, Phys. Rev. A 88(2), 023812 (2013)

[37] J. Q. Liao, H. K. Cheung, and C. K. Law, Spectrum of single-photon emission and scattering in cavity optome-chanics, Phys. Rev. A 85(2), 025803 (2012)

[38] B. He, Quantum optomechanics beyond linearization, Phys. Rev. A 85(6), 063820 (2012)

[39] H. Xie, G. W. Lin, X. Chen, Z. H. Chen, and X. M. Lin, Single-photon nonlinearities in a strongly driven optome-chanical system with quadratic coupling, Phys. Rev. A 93(6), 063860 (2016)

[40] X. W. Xu, Y. J. Li, and Y. X. Liu, Photon-induced tunnel-ing in optomechanical systems, Phys. Rev. A 87(2), 025803 (2013)

[41] A. Kronwald, M. Ludwig, and F. Marquardt, Full photon statistics of a light beam transmitted through an optome-chanical system, Phys. Rev. A 87(1), 013847 (2013)

[42] G. F. Xu and C. K. Law, Dark states of a moving mirror in the single-photon strong-coupling regime, Phys. Rev. A 87(5), 053849 (2013)

[43] P. Rabl, Photon blockade effect in optomechanical sys-tems, Phys. Rev. Lett. 107(6), 063601 (2011)

[44] A. Miranowicz, J. Bajer, N. Lambert, Y. X. Liu, and F. Nori, Tunable multiphonon blockade in coupled nanome-chanical resonators, Phys. Rev. A 93(1), 013808 (2016)

[45] A. Miranowicz, J. Bajer, M. Paprzycka, Y. X. Liu, A. M. Zagoskin, and F. Nori, State-dependent photon blockade via quantum-reservoir engineering, Phys. Rev. A 90(3), 033831 (2015)

[46] V. Macrì, A. Ridolfo, O. Di Stefano, A. F. Kockum, F. Nori, and S. Savasta, Nonperturbative dynamical casimir effect in optomechanical systems: Vacuum Casimir-Rabi splittings, Phys. Rev. X 8(1), 011031 (2018)

[47] T. Holz, R. Betzholz, and M. Bienert, Suppression of Rabi oscillations in hybrid optomechanical systems, Phys. Rev. A 92(4), 043822 (2015)

[48] E. Solano, R. L. de Matos Filho, and N. Zagury, Meso-scopic superpositions of vibronic collective states of n trapped ions, Phys. Rev. Lett. 87, 060402(4) (2001)

[49] P. C. Haljan, K.-A. Brickman, L. Deslauriers, P. J. Lee, and C. Monroe, Spin-dependent forces on trapped ions for phase-stable quantum gates and entangled states of spin and motion, Phys. Rev. Lett. 94, 153602(4) (2005)

[50] A. Sorensen and K. Molmer, Entanglement and quantum computation with ions in thermal motion, Phys. Rev. A 62(2), 022311 (2000)

[51] A. Nunnenkamp, K. Børkje, and S. M. Girvin, Single-photon optomechanics, Phys. Rev. Lett. 107(6), 063602 (2011)

[52] X. H. Cheng, I. Arrazola, J. S. Pedernales, L. Lamata, X. Chen, and E. Solano, Nonlinear quantum Rabi model in trapped ions, Phys. Rev. A 97(2), 023624 (2018)

[53] R. G. Unanyan, N. V. Vitanov, and K. Bergmann, Prepa-ration of entangled states by adiabatic passage, Phys. Rev. Lett. 87(13), 137902 (2001)

[54] P. Král, I. Thanopulos, and M. Shapiro, Coherently con-trolled adiabatic passage, Rev. Mod. Phys. 79(1), 53 (2007)

[55] M. Weitz, B. C. Young, and S. Chu, Atomic interferometer based on adiabatic population transfer, Phys. Rev. Lett. 73(19), 2563 (1994)

[56] A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, Syn-thesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence, Phys. Rev. Lett. 71(19), 3095 (1993)

[57] W. Lange and H. J. Kimble, Dynamic generation of max-imally entangled photon multiplets by adiabatic passage, Phys. Rev. A 61(6), 063817 (2000)

[58] M. Amniat-Talab, S. Lagrange, S. Guérin, and H. R. Jauslin, Generation of multiphoton Fock states by bichro-matic adiabatic passage: Topological analysis, Phys. Rev. A 70(1), 013807 (2004)

[59] S. Y. Ye, Z. R. Zhong, and S. B. Zheng, Deterministic gen-eration of three-dimensional entanglement for two atoms separately trapped in two optical cavities, Phys. Rev. A 77(1), 014303 (2007)

[60] C. Marr, A. Beige, and G. Rempe, Entangled-state prepa-ration via dissipation-assisted adiabatic passages, Phys. Rev. A 68(3), 033817 (2003)

[61] K. Toyoda, T. Watanabe, T. Kimura, S. Nomura, S. Haze, and S. Urabe, Generation of Dicke states using adiabatic passage, Phys. Rev. A 83(2), 022315 (2011)

[62] F. Beaudoin, J. M. Gambetta, and A. Blais, Dissipation and ultrastrong coupling in circuit QED, Phys. Rev. A 84(4), 043832 (2011)

[63] J. Kabuss, A. Carmele, T. Brandes, and A. Knorr, Op-tically driven quantum dots as source of coherent cavity phonons: A proposal for a phonon laser scheme, Phys. Rev. Lett. 109(5), 054301 (2012)

[64] W. Maryam, A. V. Akimov, R. P. Campion, and A. J. Kent, Dynamics of a vertical cavity quantum cascade phonon laser structure, Nat. Commun. 4(1), 2184 (2013)

[65] H. X. Han, B. W. Li, S. Volz, and Y. A. Kosevich, Ul-tracompact interference phonon nanocapacitor for storage and lasing of coherent terahertz lattice waves, Phys. Rev. Lett. 114(14), 145501 (2015)

[66] H. Jing, S. K. Özdemir, X.-Y. Lü, J. Zhang, L. Yang, and F. Nori, PT-symmetric phonon laser, Phys. Rev. Lett. 113, 053604 (2014)

[67] B. He, L. Yang, and M. Xiao, Dynamical phonon laser in coupled active-passive microresonators, Phys. Rev. A 109, 054301 (2012)

[68] I. S. Grudinin, H. Lee, O. Painter, and K. J. Vahala, Phonon laser action in a tunable two-level system, Phys. Rev. Lett. 104(8), 083901 (2010)

[69] M. A. Lemonde, S. Meesala, A. Sipahigil, M. J. A. Schuetz, M. D. Lukin, M. Loncar, and P. Rabl, Phonon networks with silicon-vacancy centers in diamond waveguides, Phys. Rev. Lett. 120(21), 213603 (2018)

[70] G. Calaj’ o, M. J. A. Schuetz, H. Pichler, M. D. Lukin, P. Schneeweiss, J. Volz, and P. Rabl, Quantum acoustooptic control of light-matter interactions in nanophotonic net-works, Phys. Rev. A 99(5), 053852 (2019)

[71] M. J. A. Schuetz, E. M. Kessler, G. Giedke, L. M. K. Van-dersypen, M. D. Lukin, and J. I. Cirac, Universal quantum transducers based on surface acoustic waves, Phys. Rev. X 5(3), 031031 (2015)

[72] R. Manenti, A. F. Kockum, A. Patterson, T. Behrle, J. Ra-hamim, G. Tancredi, F. Nori, and P. J. Leek, Circuit quan-tum acoustodynamics with surface acoustic waves, Nat. Commun. 8(1), 975 (2017)

[73] X. Y. Chu, X. Honga, P. Zou, J. Men, and Y. C. Liu, Ultrasensitive protein detection in terms of multiphonon resonance Raman scattering in ZnS nanocrystals, Appl. Phys. Lett. 98(25), 253703 (2011)

[74] J. J. Viennot, X. Ma, and K. W. Lehnert, Phonon number-sensitive electromechanics, Phys. Rev. Lett. 121(18), 183601 (2018)

[75] M. Kounalakis, Y. M. Blanter, and G. A. Steele, Synthe-sizing multi-phonon quantum superposition states using flux-mediated three-body interactions with superconduct-ing qubits, npj Quant. Inform. 5, 100, (2019)

[76] Y. Chu, P. Kharel, T. Yoon, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator, Nature 563(7733), 666 (2018)

[77] R. Ohira, T. Mukaiyama, and K. Toyoda, Phononnumber-resolving detection of multiple local phonon modes in trapped ions, Phys. Rev. A 100, 060301(R) (2019)

[78] Q. Bin, X. Y. Lü, F. P. Laussy, F. Nori, and Y. Wu, N-phonon bundle emission via the Stokes process, Phys. Rev. Lett. 124(5), 053601 (2020)

[79] M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Optomechanical crystals, Nature 462(7269), 78 (2009)

[80] 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(7356), 359 (2011)

[81] S. Gupta, K. L. Moore, K. W. Murch, and D. M. Stamper-Kurn, Cavity nonlinear optics at low photon numbers from collective atomic motion, Phys. Rev. Lett. 99(21), 213601 (2007)

[82] X. Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, Squeezed optomechanics with phase-matched am-plification and dissipation, Phys. Rev. Lett. 114(9), 093602 (2015)

[83] J. M. Pirkkalainen, S. U. Cho, F. Massel, J. Tuorila, T. T. Heikkilä, P. J. Hakonen, and M. A. Sillanpää, Cavity optomechanics mediated by a quantum two-level system, Nat. Commun. 6(1), 6981 (2015)

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