Ultra-strong coupling regime in cavity quantum electrodynamics

    1. S. Ashhab, F. Nori
      Qubit-oscillator systems in the ultrastrong-coupling regime and their potential for preparing nonclassical states
      Phys. Rev. A 81, 042311 (2010). [PDF][Link][arXiv]

    2. X. Cao, J.Q. You, H. Zheng, A.G. Kofman, F. Nori
      Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation
      Phys. Rev. A 82, 022119 (2010). [PDF][Link][arXiv]

    3. X. Cao, J.Q. You, H. Zheng, F. Nori
      A qubit strongly coupled to a resonant cavity: asymmetry of the spontaneous emission spectrum beyond the rotating wave approximation
      New Journal of Physics 13, 073002 (2011). [PDF][Link][arXiv]

    4. X. Cao, Q. Ai, C.P. Sun, F. Nori
      The transition from quantum Zeno to anti-Zeno effects for a qubit in a cavity by varying the cavity frequency
      Phys. Lett. A 376, pp. 349-357 (2012). [PDF][Link][arXiv]

    5. L. Garziano, R. Stassi, V. Macri, A.F. Kockum, S. Savasta, F. Nori
      Multiphoton quantum Rabi oscillations in ultrastrong cavity QED
      Phys. Rev. A 92, 063830 (2015). [PDF][Link][arXiv]

    6. M. Cirio, S. De Liberato, N. Lambert, F. Nori
      Ground State Electroluminescence
      Phys. Rev. Lett. 116, 113601 (2016). [PDF][Link][arXiv][Suppl. Info.]

    7. L. Garziano, V. Macri, R. Stassi, O. Di Stefano, F. Nori, S. Savasta
      One Photon Can Simultaneously Excite Two or More Atoms
      Phys. Rev. Lett. 117, 043601 (2016). [PDF][Link][arXiv][Suppl. Info.]
      Featured in Physics, Editors' Suggestion

    8. R. Stassi, S. Savasta, L. Garziano, B. Spagnolo, F. Nori
      Output field-quadrature measurements and squeezing in ultrastrong cavity-QED
      New Journal of Physics 18, 123005 (2016). [PDF][Link][arXiv]

    9. O. Di Stefano, R. Stassi, L. Garziano, A.F. Kockum, S. Savasta, F. Nori
      Feynman-diagrams approach to the quantum Rabi model for ultrastrong cavity QED: stimulated emission and reabsorption of virtual particles dressing a physical excitation
      New Journal of Physics 19, 053010 (2017). [PDF][Link][arXiv]

    10. A.F. Kockum, A. Miranowicz, V. Macri, S. Savasta, F. Nori
      Deterministic quantum nonlinear optics with single atoms and virtual photons
      Phys. Rev. A 95, 063849 (2017). [PDF][Link][arXiv]

    11. A.F. Kockum, V. Macri, L. Garziano, S. Savasta, F. Nori
      Frequency conversion in ultrastrong cavity QED
      Scientific Reports 7, 5313 (2017). [PDF][Link][arXiv][Suppl. Info.]

    12. Z. Chen, Y. Wang, T. Li, L. Tian, Y. Qiu, K. Inomata, F. Yoshihara, S. Han, F. Nori, J.S. Tsai, J.Q. You
      Single-photon-driven high-order sideband transitions in an ultrastrongly coupled circuit-quantum-electrodynamics system
      Phys. Rev. A 96, 012325 (2017). [PDF][Link][arXiv]

    13. M. Cirio, K. Debnath, N. Lambert, F. Nori
      Amplified Optomechanical Transduction of Virtual Radiation Pressure
      Phys. Rev. Lett. 119, 053601 (2017). [PDF][Link][arXiv][Suppl. Info.]

    14. R. Stassi, V. Macri, A.F. Kockum, O. Di Stefano, A. Miranowicz, S. Savasta, F. Nori
      Quantum Nonlinear Optics without Photons
      Phys. Rev. A 96, 023818 (2017). [PDF][Link][arXiv]

    15. X. Wang, A. Miranowicz, H.R. Li, F. Nori
      Observing pure effects of counter-rotating terms without ultrastrong coupling: A single photon can simultaneously excite two qubits
      Phys. Rev. A 96, 063820 (2017). [PDF][Link][arXiv]

    16. V. Macri, A. Ridolfo, O. Di Stefano, A.F. Kockum, F. Nori, S. Savasta
      Nonperturbative Dynamical Casimir Effect in Optomechanical Systems: Vacuum Casimir-Rabi Splittings
      Phys. Rev. X 8, 011031 (2018). [PDF][Link][arXiv]

    17. W. Qin, A. Miranowicz, P.B. Li, X.Y. Lu, J.Q. You, F. Nori
      Exponentially Enhanced Light-Matter Interaction, Cooperativities, and Steady-State Entanglement Using Parametric Amplification
      Phys. Rev. Lett. 120, 093601 (2018). [PDF][Link][arXiv][Suppl. Info.]

    18. R. Stassi, F. Nori
      Long-lasting quantum memories: Extending the coherence time of superconducting artificial atoms in the ultrastrong-coupling regime
      Phys. Rev. A 97, 033823 (2018). [PDF][Link][arXiv]

    19. C.S. Munoz, F. Nori, S. De Liberato
      Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics
      Nature Communications 9, 1924 (2018). [PDF][Link][arXiv][Suppl. Info.][Reviewers' Comments]

    20. A. Settineri, V. Macrí, A. Ridolfo, O. Di Stefano, A.F. Kockum, F. Nori, S. Savasta
      Dissipation and thermal noise in hybrid quantum systems in the ultrastrong-coupling regime
      Phys. Rev. A 98, 053834 (2018). [PDF][Link][arXiv]

    21. O. Di Stefano, A.F. Kockum, A. Ridolfo, S. Savasta, F. Nori
      Photodetection probability in quantum systems with arbitrarily strong light-matter interaction
      Scientific Reports 8, 17825 (2018). [PDF][Link_1][Link_2][arXiv]

    22. V. Macri, F. Nori, A.F. Kockum
      Simple preparation of Bell and Greenberger-Horne-Zeilinger states using ultrastrong-coupling circuit QED
      Phys. Rev. A 98, 062327 (2018). [PDF][Link][arXiv]

    23. A.F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, F. Nori
      Ultrastrong coupling between light and matter
      Nature Reviews Physics 1, pp. 19–40 (2019). [PDF][Link][arXiv]
      This is the only review (plus three technical reviews) of the first issue of this journal.

    24. O. Di Stefano, A. Settineri, V. Macri, A. Ridolfo, R. Stassi, A.F. Kockum, S. Savasta, F. Nori
      Interaction of Mechanical Oscillators Mediated by the Exchange of Virtual Photon Pairs
      Phys. Rev. Lett. 122, 030402 (2019). [PDF][Link][arXiv][Suppl. Info.]

    25. M. Cirio, N. Shammah, N. Lambert, S.D. Liberato, F. Nori
      Multielectron Ground State Electroluminescence
      Phys. Rev. Lett. 122, 190403 (2019). [PDF][Link][arXiv][Suppl. Info.]

    26. O. Di Stefano, A. Settineri, V. Macri, L. Garziano, R. Stassi, S. Savasta, F. Nori
      Resolution of gauge ambiguities in ultrastrong-coupling cavity quantum electrodynamics
      Nature Physics 15, pp. 803–808 (2019). [PDF][Link_1][Link_2][arXiv][Suppl. Info.]

    27. A. Settineri, V. Macri, L. Garziano, O. Di Stefano, F. Nori, S. Savasta
      Conversion of mechanical noise into correlated photon pairs: Dynamical Casimir effect from an incoherent mechanical drive
      Phys. Rev. A 100, 022501 (2019). [PDF][Link][arXiv]

    28. N. Lambert, S. Ahmed, M. Cirio, F. Nori
      Modelling the ultra-strongly coupled spin-boson model with unphysical modes
      Nature Communications 10, 3721 (2019). [PDF][Link_1][Link_2][arXiv][Suppl. Info.][Reviewers' Comments]

    29. S. Endo, Y. Matsuzaki, K. Kakuyanagi, S. Saito, N. Lambert, F. Nori
      Projecting an ultra-strongly-coupled system in a non-energy-eigenbasis with a driven nonlinear resonator
      Scientific Reports 10, 1751 (2020). [PDF][Link_1][Link_2][arXiv]

    30. V. Macri, F. Nori, S. Savasta, D. Zueco
      Spin squeezing by one-photon–two-atom excitation processes in atomic ensembles
      Phys. Rev. A 101, 053818 (2020). [PDF][Link][arXiv]

    31. R. Stassi, M. Cirio, F. Nori
      Scalable quantum computer with superconducting circuits in the ultrastrong coupling regime
      npj Quantum Information 6, 67 (2020). [PDF][Link_1][Link_2][arXiv]

    32. L. Garziano, A. Settineri, O. Di Stefano, S. Savasta, F. Nori
      Gauge invariance of the Dicke and Hopfield models
      Phys. Rev. A 102, 023718 (2020). [PDF][Link][arXiv]

    33. C.S. Munoz, A.F. Kockum, A. Miranowicz, F. Nori
      Simulating ultrastrong-coupling processes breaking parity conservation in Jaynes-Cummings systems
      Phys. Rev. A 102, 033716 (2020). [PDF][Link][arXiv]

    34. W. Qin, Y.H. Chen, X. Wang, A. Miranowicz, F. Nori
      Strong spin squeezing induced by weak squeezing of light inside a cavity
      Nanophotonics 9, pp. 4853–4868 (2020). [PDF][Link][arXiv]

    35. S. Savasta, O. Di Stefano, F. Nori
      Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons
      Nanophotonics 10, pp. 465–476 (2020). [PDF][Link][arXiv]

    36. L. Garziano, A. Ridolfo, A. Miranowicz, G. Falci, S. Savasta, F. Nori
      Atoms in separated resonators can jointly absorb a single photon
      Scientific Reports 10, 21660 (2020). [PDF][Link_1][Link_2][arXiv]

    37. Y.H. Chen, W. Qin, X. Wang, A. Miranowicz, 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). [PDF][Link][arXiv][Suppl. Info.]

    38. A. Settineri, O. Di Stefano, D. Zueco, S. Hughes, S. Savasta, F. Nori
      Gauge freedom, quantum measurements, and time-dependent interactions in cavity QED
      Phys. Rev. Research 3, 023079 (2021). [PDF][Link][arXiv]

    39. F. Minganti, V. Macri, A. Settineri, S. Savasta, F. Nori
      Dissipative state transfer and Maxwell's demon in single quantum trajectories: Excitation transfer between two noninteracting qubits via unbalanced dissipation rates
      Phys. Rev. A 103, 052201 (2021). [PDF][Link][arXiv]

    40. S. Savasta, O. Di Stefano, A. Settineri, D. Zueco, S. Hughes, F. Nori
      Gauge principle and gauge invariance in two-level systems
      Phys. Rev. A 103, 053703 (2021). [PDF][Link][arXiv]

    41. X.L. Dong, P.B. Li, T. Liu, F. Nori
      Unconventional Quantum Sound-Matter Interactions in Spin-Optomechanical-Crystal Hybrid Systems
      Phys. Rev. Lett. 126, 203601 (2021). [PDF][Link][arXiv][Suppl. Info.]

    42. I.I. Arkhipov, F. Minganti, A. Miranowicz, F. Nori
      Generating high-order quantum exceptional points in synthetic dimensions
      Phys. Rev. A 104, 012205 (2021). [PDF][Link][arXiv]

    43. S. Hughes, A. Settineri, S. Savasta, F. Nori
      Resonant Raman scattering of single molecules under simultaneous strong cavity coupling and ultrastrong optomechanical coupling in plasmonic resonators: Phonon-dressed polaritons
      Phys. Rev. B 104, 045431 (2021). [PDF][Link][arXiv]

    44. W. Qin, A. Miranowicz, H. Jing, F. Nori
      Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles
      Phys. Rev. Lett. 127, 093602 (2021). [PDF][Link][arXiv][Suppl. Info.]

    45. Y.H. Chen, W. Qin, R. Stassi, X. Wang, F. Nori
      Fast binomial-code holonomic quantum computation with ultrastrong light-matter coupling
      Phys. Rev. Research 3, 033275 (2021). [PDF][Link][arXiv]

    46. V. Macri, F. Minganti, A.F. Kockum, A. Ridolfo, S. Savasta, F. Nori
      Revealing higher-order light and matter energy exchanges using quantum trajectories in ultrastrong coupling
      Phys. Rev. A 105, 023720 (2022). [PDF][Link][arXiv]

    47. W. Salmon, C. Gustin, A. Settineri, O. Di Stefano, D. Zueco, S. Savasta, F. Nori, S. Hughes
      Gauge-independent emission spectra and quantum correlations in the ultrastrong coupling regime of open system cavity-QED
      Nanophotonics 11, pp. 1573-1590 (2022). [PDF][Link][arXiv][Erratum]

    48. A. Mercurio, V. Macri, C. Gustin, S. Hughes, S. Savasta, F. Nori
      Regimes of cavity QED under incoherent excitation: From weak to deep strong coupling
      Phys. Rev. Research 4, 023048 (2022). [PDF][Link][arXiv]

    49. Y.H. Chen, A. Miranowicz, X. Chen, Y. Xia, F. Nori
      Enhanced-Fidelity Ultrafast Geometric Quantum Computation Using Strong Classical Drives
      Phys. Rev. Applied 18, 064059 (2022). [PDF][Link][arXiv]

    50. S. Terradas-Brianso, C.A. Gonzalez-Gutierrez, F. Nori, L. Martín-Moreno, D. Zueco
      Ultrastrong waveguide QED with giant atoms
      Phys. Rev. A 106, 063717 (2022). [PDF][Link][arXiv]

    51. V. Macri, A. Mercurio, F. Nori, S. Savasta, C.S. Munoz
      Spontaneous Scattering of Raman Photons from Cavity-QED Systems in the Ultrastrong Coupling Regime
      Phys. Rev. Lett. 129, 273602 (2022). [PDF][Link][arXiv][Suppl. Info.]

    52. L.B. Fan, C.C. Shu, D. Dong, J. He, N.E. Henriksen, F. Nori
      Quantum Coherent Control of a Single Molecular-Polariton Rotation
      Phys. Rev. Lett. 130, 043604 (2023). [PDF][Link][arXiv][Suppl. Info.]

    53. B. Wang, J.M. Hu, V. Macri, Z.L. Xiang, F. Nori
      Coherent resonant coupling between atoms and a mechanical oscillator mediated by cavity-vacuum fluctuations
      Phys. Rev. Research 5, 013075 (2023). [PDF][Link][arXiv]

    54. E. Russo, A. Mercurio, F. Mauceri, R.L. Franco, F. Nori, S. Savasta, V. Macri
      Optomechanical two-photon hopping
      Phys. Rev. Research 5, 013221 (2023). [PDF][Link][arXiv]

    55. K. Akbari, W. Salmon, F. Nori, S. Hughes
      Generalized Dicke model and gauge-invariant master equations for two atoms in ultrastrongly-coupled cavity quantum electrodynamics
      Phys. Rev. Research 5, 033002 (2023). [PDF][Link][arXiv]

    56. X.L. Dong, P.B. Li, J.Q. Chen, F.L. Li, F. Nori
      Exotic quantum light-matter interactions in bilayer square lattices
      Phys. Rev. B 108, 045407 (2023). [PDF][Link]

    57. S.P. Wang, A. Ridolfo, T. Li, S. Savasta, F. Nori, Y. Nakamura, J.Q. You
      Probing the symmetry breaking of a light–matter system by an ancillary qubit
      Nature Communications 14, 4397 (2023). [PDF][Link][arXiv][Suppl. Info.][Reviewers' Comments]

    58. F. Nori
      Squeezed quantum hybrid system: Giant enhancement of magnon-phonon-spin interactions
      Science China: Physics, Mechanics & Astronomy 66, 110331 (2023). [PDF][Link]

    59. R. Stassi, M. Cirio, K. Funo, J. Puebla, N. Lambert, F. Nori
      Unveiling and veiling an entangled light-matter quantum state from the vacuum
      Phys. Rev. Research 5, 043095 (2023). [PDF][Link][arXiv]

    60. P.C. Kuo, N. Lambert, M. Cirio, Y.T. Huang, F. Nori, Y.N. Chen
      Kondo QED: The Kondo effect and photon trapping in a two-impurity Anderson model ultrastrongly coupled to light
      Phys. Rev. Research 5, 043177 (2023). [PDF][Link][arXiv]

    61. O. Di Stefano, A. Settineri, V. Macri, L. Garziano, R. Stassi, S. Savasta, F. Nori
      Gauge non-invariance due to material truncation in ultrastrong-coupling quantum electrodynamics
      Nature Physics 20, pp. 379–380 (2023). [PDF][Link]

    62. Y.H. Chen, Y. Qiu, A. Miranowicz, N. Lambert, W. Qin, R. Stassi, Y. Xia, S.B. Zheng, F. Nori
      Sudden change of the photon output field marks phase transitions in the quantum Rabi model
      Communications Physics 7, 5 (2024). [PDF][Link][arXiv][Suppl. Info.]

    63. B. Wang, F. Nori, Z.L. Xiang
      Quantum Phase Transitions in Optomechanical Systems
      Phys. Rev. Lett. 132, 053601 (2024). [PDF][Link][arXiv][Suppl. Info.]

    64. S. Hughes, C. Gustin, F. Nori
      Reconciling quantum and classical spectral theories of ultrastrong coupling: role of cavity bath coupling and gauge corrections
      Optica Quantum 2, pp. 133-139 (2024). [PDF][Link][arXiv][Suppl. Info.]
      Editors' Suggestion

    65. W. Qin, A.F. Kockum, C.S. Munoz, A. Miranowicz, F. Nori
      Quantum amplification and simulation of strong and ultrastrong coupling of light and matter
      Physics Reports 1078, pp. 1-59 (2024). [PDF][Link][arXiv] (published online May 23, 2024)


  • June 2022 pedagogical presentation to over 150 students at QIQT-2022: The “Summer School on Quantum Information and Quantum Technology – 2022”. URL: qiqt2022.org


    Title: Quantum nonlinear optics with virtual and real photons in the ultrastrong coupling regime of cavity QED.
    The pedagogical talk is about one hour and six minutes, plus 20 minutes for the Q&A period.
    The video of the talk is available on YouTube at: https://youtu.be/T7Xa8qlvbIo/
    Publications on this topic are available online here: https://dml.riken.jp/pub/

MP4 presentations on “Virtual photons in ultra-strongly coupled systems or Quantum Nonlinear Optics without Photons”:

  • Long Version (~37 minutes) [MP4]
  • Short Version (~27 minutes) [MP4]

PDF files of two brief talks on: virtual photons and the ultrastrong coupling between light and matter.

  • Electroluminescence + Radiation pressure [PDF]
  • Nonlinear quantum optics using real and/or virtual photons [PDF]