pith. sign in

arxiv: 2606.31108 · v1 · pith:K7XV7DVFnew · submitted 2026-06-30 · 🪐 quant-ph

Floquet Quasienergy-Resolved Dissipation, Dynamics, and Spectroscopy in Ultrastrong Cavity-QED

Kamran Akbari , Franco Nori , Stephen Hughes This is my paper

Pith reviewed 2026-07-01 05:45 UTC · model grok-4.3

classification 🪐 quant-ph
keywords ultrastrong cavity QEDFloquet theoryquasienergydissipationgeneralized master equationquantum Rabi modelstructured reservoirsnonequilibrium states
0
0 comments X

The pith

Periodic driving in ultrastrong cavity-QED makes dissipation intrinsically quasienergy-resolved rather than resonance-based.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a nonsecular Floquet generalized master equation to describe dissipation and dynamics in periodically driven open cavity-QED systems operating in the ultrastrong-coupling regime. Conventional time-independent dressed-state master equations only capture steady-state populations in limited excitation regimes and fail to predict frequency-resolved spectra or handle strong driving correctly, even for spectrally flat baths. The new framework is formulated in the dressed basis of the quantum Rabi model and applies to structured reservoirs without rotating-wave approximations, resolving resonances into hybridized quasienergy channels with associated decay rates. This approach reveals that dissipation pathways become sideband-selective under driving, enabling control over nonequilibrium populations and fluorescence. A reader would care because it supplies a practical method for predicting and engineering driven open quantum systems where static models break down.

Core claim

Strong periodic driving of cavity-QED in the ultrastrong-coupling regime creates nonequilibrium states whose dissipation is governed by Floquet quasienergies rather than undriven dressed resonances. The authors introduce a nonsecular Floquet generalized master equation framework formulated in the dressed basis of the quantum Rabi model, applicable to structured reservoirs without rotating-wave approximations. Systematic comparisons show that static dressed-basis equations reproduce steady-state populations only in restricted regimes, fail for frequency-resolved observables, and break down under Floquet engineering even for flat baths, with discrepancies amplified by structured environments t

What carries the argument

The nonsecular Floquet generalized master equation formulated in the dressed basis of the quantum Rabi model, which resolves observable resonances into hybridized quasienergy channels and associated decay rates.

If this is right

  • Long-time populations, fluorescence spectra, and Floquet-Liouville eigenspectra can be computed by resolving resonances into hybridized quasienergy channels and decay rates.
  • Static time-independent dressed-basis master equations reproduce steady-state populations only in restricted excitation regimes and fail for frequency-resolved observables.
  • Even spectrally flat baths produce incorrect results under Floquet engineering, while structured reservoirs such as Lorentzian-Ohmic baths amplify discrepancies via sideband-selective decay.
  • The theory enables systematic control of decay pathways and engineering of nonequilibrium quantum states and reservoirs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same quasienergy-resolution principle may apply to other periodically driven open quantum systems such as superconducting circuits or trapped ions.
  • Experiments could test the framework by measuring sideband-resolved decay rates under parametric mechanical modulation in circuit QED.
  • Floquet engineering might allow selective suppression of unwanted decay channels that static theories cannot predict.
  • Quasienergy-resolved dissipation could affect nonequilibrium thermodynamics, such as heat currents in driven reservoirs.

Load-bearing premise

The framework assumes that gauge invariance can be ensured for truncated matter-cavity systems under time-dependent driving when formulated in the dressed basis of the quantum Rabi model.

What would settle it

Compare the measured fluorescence spectrum of a strongly optically pumped or parametrically modulated ultrastrongly coupled cavity-QED device against the quasienergy-resolved resonances predicted by the Floquet master equation versus the static dressed-state predictions.

Figures

Figures reproduced from arXiv: 2606.31108 by Franco Nori, Kamran Akbari, Stephen Hughes.

Figure 1
Figure 1. Figure 1: Time-dependent cavity-QED models. (a) Schematic of an optically pumped and dissipative cavity-QED system via the cavity or the TLS operator. An external laser Ωd(t) of strength Ωd = ηdωc (the Rabi frequency) and frequency ωd can be used to possibly pump either the cavity or the TLS. (b) An example schematic of a Floquet-engineered dissipative cavity-QED system; here, the Floquet engineering of the QRM is a… view at source ↗
Figure 2
Figure 2. Figure 2: Historical/conceptual positioning of the presented work. (a) Historical development leading to the presented theoretical framework. The left branch summarizes the evolution of Floquet theory from closed periodically driven quantum systems [17, 19] to open systems [20–27], and then to open strongly interacting systems [28]. The right branch summarizes the development of USC cavity-QED [29–32], including the… view at source ↗
Figure 3
Figure 3. Figure 3: Energy basis states for an optically driven cavity-QED system. (a) Eigenenergies of the QRM for the first eight states, with the Hamiltonian in Eq. (4), plotted versus the (normalized) cavity-TLS coupling rate η with their labels and parities (blue: even; red: odd). The vertical black dot-dashed line in panel (a) marks η = 0.5, where it is used to calculate the quasienergies in panels (b), and also for fut… view at source ↗
Figure 4
Figure 4. Figure 4: Optically driven open cavity-QED in USC: Average number of cavity excitations versus the optical drive frequency ωd. The other relevant parameters are: η = 0.5, ηd = 0.3 (drive amplitude), ωa = ωc, and γ = 0.01ωa. Temporal average of the number of cavity excitations are compared among three different approaches: (i) phenomenological Floquet theory (thin solid gray curves), from Eq. (69); (ii) TI-GME (blue … view at source ↗
Figure 5
Figure 5. Figure 5: Optically driven cavity-QED in USC: Incoherent cavity spectra. Cavity emitted spectra, obtained from the TI-GME (dashed blue) and the F-GME (solid orange) approaches. For clarity, a reference spectra with weak incoherent pumping (Pinc = 0.01ηdωc) is also plotted with the thin gray curves in each panel. Panels (a) and (c) show the spectra for the flat bath, and the right panels (b) and (d) show the spectra … view at source ↗
Figure 6
Figure 6. Figure 6: Mechanically driven cavity-QED: Energy basis. (a) Eigenenergies of the QRM plotted versus the cavity-TLS static coupling rate η0 with their labels and parities (blue: even; red: odd). When the mechanical drive (here, vibration of the TLS) is switched on with ωd = 0.65ωc, the energy basis of the QRM, are initially renormalized [dashed curved in (a) vs. η0 (with ηM = 0.3) and (b) vs. ηM (with η0 = 0.5) due t… view at source ↗
Figure 7
Figure 7. Figure 7: Mechanically driven open cavity-QED in USC: Floquet-engineered QRM steady-state cavity popu￾lations. Temporal average of the steady-state number of cavity excitations are compared among three different approaches: (i) phenomenological Floquet theory (thin gray curves), (ii) TI-GME (blue curves) and (iii) F-GME (orange curves). Panel (a) shows the results for the flat baths [Eq. (29)], whereas the right pan… view at source ↗
Figure 8
Figure 8. Figure 8: Mechanically driven open cavity-QED in USC (Floquet-engineering the dissipative QRM in USC): Cavity spectra. (Incoherent) spectra for the cavity excitations, obtained from the TI-GME (dashed blue curves) and the F-GME (thick solid orange curves) approaches. Left panel (a) shows the spectra for the flat bath, and the right panel (b) show the spectra for the Lorentzian bath with the central frequency of ω0 =… view at source ↗
Figure 9
Figure 9. Figure 9: Optically driven cavity-QED: gauge￾consistency check. We show the Floquet quasienergy curves of the DQRM as a function of the optical coherent pump drive, using two different values of the cavity-TLS cou￾pling η = 0.05 (a) and η = 0.5 (b). The comparison is made for different gauges of the DQRM, i.e., solid blue: ‘C’ (correct Coulomb), dashed gold: ‘D’ (correct dipole), dotted magenta: ’NC’, and dot-dashed… view at source ↗
Figure 10
Figure 10. Figure 10: Optically driven cavity-QED examples: Eigenenergies, transition probabilities and populations as a function of ωd. (a) Shifted eigenenergies to show the initial crossings/anticrossings of the energy states that seed the quasienergy anticrossings. (b) Floquet quasienergies in the primary BZ; circles mark anticrossings associated with dominant drive-assisted excitation transitions. (c) Floquet transition pr… view at source ↗
Figure 11
Figure 11. Figure 11: Optically driven open cavity-QED in USC: cavity Bright modes. Shown in panels (a) and (c) are the spectral modal linewidth and peak prominence of [PITH_FULL_IMAGE:figures/full_fig_p054_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Optically driven open cavity-QED in USC: TLS average number of excitations versus the optical drive frequency ωd. Same as [PITH_FULL_IMAGE:figures/full_fig_p054_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Optically driven cavity-QED in USC: TLS (incoherent) spectra. Same as [PITH_FULL_IMAGE:figures/full_fig_p056_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Optically driven open cavity-QED in USC: TLS Bright modes. Shown in panels (a) and (c) are the spectral modal linewidth and peak prominence of [PITH_FULL_IMAGE:figures/full_fig_p057_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Mechanically driven cavity-QED: Eigenenergies, transition probabilities and populations as a function of the drive frequency ωM. Same as [PITH_FULL_IMAGE:figures/full_fig_p058_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Mechanically driven open cavity-QED in USC: cavity bright modes. Shown in panels (a) and (c) are the spectral modal linewidth and peak prominence of [PITH_FULL_IMAGE:figures/full_fig_p062_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Mechanically driven open cavity-QED in USC (Floquet-engineering the dissipative QRM in USC): TLS average number of excitations vs. mechanical drive’s frequency ωM. Same as [PITH_FULL_IMAGE:figures/full_fig_p063_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Mechanically driven open cavity-QED in USC (Floquet-engineering the dissipative QRM in USC): TLS (incoherent) spectra. Same as [PITH_FULL_IMAGE:figures/full_fig_p064_18.png] view at source ↗
Figure 19
Figure 19. Figure 19 [PITH_FULL_IMAGE:figures/full_fig_p064_19.png] view at source ↗
read the original abstract

Strong periodic driving of cavity-quantum electrodynamics (QED) in the ultrastrong-coupling regime creates nonequilibrium states whose dissipation is governed by Floquet quasienergies rather than undriven dressed resonances. However, modeling such a regime is a significant theoretical challenge, including a number of subtle problems such as the need to ensure gauge invariance for truncated matter-cavity systems with time-dependent driving. To fill this theoretical gap, we introduce a nonsecular Floquet generalized master equation framework for strongly driven open cavity-QED systems, formulated in the dressed basis of the quantum Rabi model and applicable to structured reservoirs without rotating-wave approximations. Our theory can thus model Floquet-driven dynamics in open ultrastrong-coupling cavity-QED, and demonstrates a wide range of quantum state control. Using strong optical pumping and parametric mechanical modulation, we compute long-time populations, fluorescence spectra, and the Floquet-Liouville eigenspectra, resolving observable resonances into hybridized quasienergy channels and decay rates. By systematically comparing with conventional time-independent dressed-basis generalized master equations, we show that static approaches only reproduce steady-state populations in restricted excitation regimes, and fail for frequency-resolved observables and break down under appropriate Floquet engineering, surprisingly, even for spectrally flat baths. Structured environments, such as Lorentzian-Ohmic reservoirs, further amplify these discrepancies through sideband-selective decay. Our results demonstrate that dissipation in driven ultrastrong cavity-QED is intrinsically quasienergy resolved and we establish Floquet-dissipative theory as an accurate and powerful framework for predicting spectra, controlling decay pathways, and engineering nonequilibrium quantum states and reservoirs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces a nonsecular Floquet generalized master equation framework formulated in the dressed basis of the quantum Rabi model for strongly driven open ultrastrong-coupling cavity-QED systems. It addresses gauge invariance in truncated systems under time-dependent driving and applies the theory to compute long-time populations, fluorescence spectra, and Floquet-Liouville eigenspectra under optical pumping and parametric modulation. Systematic comparisons demonstrate that conventional time-independent dressed-basis GMEs reproduce steady-state populations only in restricted regimes and fail for frequency-resolved observables, even for flat baths, with larger discrepancies in structured (Lorentzian-Ohmic) reservoirs; the work concludes that dissipation is intrinsically quasienergy-resolved.

Significance. If the central results hold, the framework establishes Floquet-dissipative theory as necessary for accurate prediction of spectra, decay pathways, and nonequilibrium state engineering in driven USC cavity-QED, with explicit demonstrations of sideband-selective effects and breakdown of static approaches. The systematic comparisons across excitation regimes and reservoir types provide concrete evidence of the framework's advantages.

major comments (1)
  1. [Abstract and §1] Abstract and §1 (gauge-invariance discussion): The load-bearing assumption is that gauge invariance can be ensured for truncated matter-cavity systems under periodic driving when working in the dressed Rabi basis. The manuscript correctly identifies this as a subtle problem, yet provides no explicit verification such as cross-comparison of length- versus velocity-gauge observables or other gauge-invariant quantities to confirm that the computed quasienergy channels, decay rates, and sideband spectra remain physical after truncation. This directly affects the validity of all quasienergy-resolved claims.
minor comments (2)
  1. Figure captions and axis labels should explicitly state the driving amplitude and modulation parameters used for each panel to facilitate direct comparison with the text.
  2. The manuscript would benefit from a short table summarizing the regimes (e.g., driving strength, bath spectral density) where static GMEs agree or disagree with the Floquet results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and for identifying a key point on gauge invariance. We address the comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and §1] Abstract and §1 (gauge-invariance discussion): The load-bearing assumption is that gauge invariance can be ensured for truncated matter-cavity systems under periodic driving when working in the dressed Rabi basis. The manuscript correctly identifies this as a subtle problem, yet provides no explicit verification such as cross-comparison of length- versus velocity-gauge observables or other gauge-invariant quantities to confirm that the computed quasienergy channels, decay rates, and sideband spectra remain physical after truncation. This directly affects the validity of all quasienergy-resolved claims.

    Authors: We agree that explicit verification strengthens the claims. The manuscript identifies the gauge issue and adopts the dressed Rabi basis to mitigate truncation artifacts under driving, but does not include direct numerical checks such as length- versus velocity-gauge comparisons for the quasienergy-resolved quantities. In the revised manuscript we will add such a cross-comparison (for steady-state populations, fluorescence spectra, and selected decay rates) in §1 or a dedicated appendix, confirming that the reported quasienergy channels and sideband features remain consistent across gauges within the truncation employed. revision: yes

Circularity Check

0 steps flagged

No circularity; framework extends standard techniques without reduction to inputs

full rationale

The derivation introduces a nonsecular Floquet generalized master equation in the dressed quantum Rabi basis for driven open cavity-QED systems and compares its predictions (populations, spectra, Liouville eigenspectra) against conventional time-independent dressed-basis GMEs. No quoted equations or steps reduce by construction to fitted inputs, self-definitions, or unverified self-citation chains; the gauge-invariance handling is presented as a careful formulation choice rather than a tautology. The central claim that dissipation is quasienergy-resolved follows from the Floquet structure applied to structured reservoirs, with explicit numerical contrasts to static approaches serving as independent content. This is a standard extension of established methods and remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. Standard open-quantum-system assumptions are implied but not detailed.

axioms (2)
  • standard math Markovian and Born approximations underlying generalized master equations
    Standard for deriving master equations in open quantum systems
  • domain assumption Validity of the quantum Rabi model dressed basis for ultrastrong coupling
    The framework is formulated in this basis as stated in the abstract

pith-pipeline@v0.9.1-grok · 5833 in / 1385 out tokens · 33598 ms · 2026-07-01T05:45:51.658370+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

166 extracted references · 4 canonical work pages · 1 internal anchor

  1. [1]

    6(a) is the same as that of the optical drive case, as the static QRM eigenenergiesremainthesame

    Periodic mechanical drive For the (periodic) mechanical drive case, the energy state labels based on their orders from Fig. 6(a) is the same as that of the optical drive case, as the static QRM eigenenergiesremainthesame. However, thequasienergy state labels from their orders in the range[−ωd/2, ωd/2) from Fig. 6(b), from bottom to top atηM =0.3(verti- ca...

  2. [2]

    S.HarocheandJ.-M.Raimond,Exploring the Quantum: Atoms, Cavities, and Photons(OxfordUniversityPress, 2006)

    2006

  3. [3]

    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, Nature436, 87 (2005)

    2005

  4. [4]

    M. B. et al., Quantum Rabi oscillation: A direct test of field quantization in a cavity, Phys. Rev. Lett.76, 1800 (1996)

    1996

  5. [5]

    Niemczyk, F

    T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nature Physics6, 772 (2010)

    2010

  6. [6]

    Forn-Díaz, J

    P. Forn-Díaz, J. Lisenfeld, D. Marcos, J. J. Garcia- 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, 237001 (2010)

    2010

  7. [7]

    Tomonaga, R

    A. Tomonaga, R. Stassi, H. Mukai, F. Nori, F. Yoshi- hara, and J. S. Tsai, Spectral properties of two super- conducting artificial atoms coupled to a resonator in the ultrastrong coupling regime, Nat Commun16, 5294 (2025)

    2025

  8. [8]

    S.-P. Wang, A. Mercurio, A. Ridolfo, Y. Wang, M. Chen, W. Wang, Y. Liu, H. Sun, T. Li, F. Nori, S. Savasta, and J. Q. You, Strong coupling between a single-photon and a two-photon Fock state, Nat Com- mun16, 8730 (2025)

    2025

  9. [9]

    Frisk Kockum, A

    A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and matter, Nature Reviews Physics1, 19 (2019)

    2019

  10. [10]

    Forn-Díaz, L

    P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, Ultrastrong coupling regimes of light-matter interaction, Rev. Mod. Phys.91, 025005 (2019)

    2019

  11. [11]

    De Liberato, Virtual photons in the ground state of a dissipative system, Nat Commun8, 1465 (2017)

    S. De Liberato, Virtual photons in the ground state of a dissipative system, Nat Commun8, 1465 (2017)

    2017

  12. [12]

    Sinova, S

    J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin Hall effects, Rev. Mod. Phys. 87, 1213 (2015)

    2015

  13. [13]

    Etxezarreta Martinez, P

    J. Etxezarreta Martinez, P. Fuentes, P. Crespo, and J. Garcia-Frias, Time-varying quantum channel mod- els for superconducting qubits, npj Quantum Inf7, 1 (2021)

    2021

  14. [14]

    Hamazaki, Exceptional dynamical quantum phase transitions in periodically driven systems, Nat Commun 12, 5108 (2021)

    R. Hamazaki, Exceptional dynamical quantum phase transitions in periodically driven systems, Nat Commun 12, 5108 (2021)

    2021

  15. [15]

    BÃękkegaard, L

    T. BÃękkegaard, L. B. Kristensen, N. J. S. Loft, C. K. Andersen, D. Petrosyan, and N. T. Zinner, Realization ofefficientquantumgateswithasuperconductingqubit- qutrit circuit, Sci Rep9, 13389 (2019)

    2019

  16. [16]

    Y.-H. Chen, A. Kalev, and I. Hen, Quantum algorithm for time-dependent Hamiltonian simulation by permu- tation expansion, PRX Quantum2, 030342 (2021)

    2021

  17. [17]

    Floquet, Sur les équations différentielles linéaires à coefficients périodiques, Annales Scientifiques de l’École Normale Supérieure 2,12, 47 (1883)

    G. Floquet, Sur les équations différentielles linéaires à coefficients périodiques, Annales Scientifiques de l’École Normale Supérieure 2,12, 47 (1883)

  18. [18]

    J. H. Shirley, Solution of the Schrödinger equation with a Hamiltonian periodic in time, Phys. Rev.138, B979 (1965)

    1965

  19. [19]

    Deng, J.-L

    C. Deng, J.-L. Orgiazzi, F. Shen, S. Ashhab, and A. Lu- pascu,ObservationofFloquetstatesinastronglydriven artificial atom, Phys. Rev. Lett.115, 133601 (2015)

    2015

  20. [20]

    Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, Phys

    H. Sambe, Steady states and quasienergies of a quantum-mechanical system in an oscillating field, Phys. Rev. A7, 2203 (1973)

    1973

  21. [21]

    Grifoni and P

    M. Grifoni and P. Hänggi, Driven quantum tunneling, Physics Reports304, 229 (1998)

    1998

  22. [22]

    Kohler, T

    S. Kohler, T. Dittrich, and P. Hänggi, Floquet- Markovian description of the parametrically driven, dis- sipative harmonic quantum oscillator, Phys. Rev. E55, 300 (1997)

    1997

  23. [23]

    Kohler, J

    S. Kohler, J. Lehmann, and P. HÃďnggi, Driven quan- tum transport on the nanoscale, Physics Reports406, 379 (2005)

    2005

  24. [24]

    Hausinger and M

    J. Hausinger and M. Grifoni, Dissipative two-level sys- tem under strong ac driving: A combination of Floquet and Van Vleck perturbation theory, Phys. Rev. A81, 022117 (2010)

    2010

  25. [25]

    Hausinger,Dissipative dynamics of a qubit-oscillator system in the ultrastrong coupling and driving regimes, Ph.D

    J. Hausinger,Dissipative dynamics of a qubit-oscillator system in the ultrastrong coupling and driving regimes, Ph.D. thesis (2010)

    2010

  26. [26]

    Hausinger and M

    J. Hausinger and M. Grifoni, Qubit-oscillator system: An analytical treatment of the ultrastrong coupling regime, Phys. Rev. A82, 062320 (2010)

    2010

  27. [27]

    Restrepo,Driven Open Quantum Systems: Aspects of Non-Markovianity and Strong Coupling, Ph.D

    S. Restrepo,Driven Open Quantum Systems: Aspects of Non-Markovianity and Strong Coupling, Ph.D. thesis (2019)

    2019

  28. [28]

    Restrepo, J

    S. Restrepo, J. Cerrillo, P. Strasberg, and G. Schaller, From quantum heat engines to laser cooling: Flo- quet theory beyond the BornâĂŞMarkov approxima- tion, New Journal of Physics20, 053063 (2018)

    2018

  29. [29]

    Akbari and S

    K. Akbari and S. Hughes, Double dressing in strongly driven, strongly interacting open quantum systems: Floquet generalized master equation and Floquet- Liouville spectroscopy (2026), arXiv:To be submitted [quant-ph]

    2026

  30. [30]

    I. I. Rabi, On the Process of Space Quantization, Phys- ical Review49, 324 (1936)

    1936

  31. [31]

    I. I. Rabi, Space quantization in a gyrating magnetic field, Physical Review51, 652 (1937)

    1937

  32. [32]

    Nataf and C

    P. Nataf and C. Ciuti, Vacuum degeneracy of a circuit qed system in the ultrastrong coupling regime, Physical Review Letters104, 023601 (2010)

    2010

  33. [33]

    Ashhab, J

    S. Ashhab, J. R. Johansson, A. M. Zagoskin, and 67 F. Nori, Two-level systems driven by large-amplitude fields, Phys. Rev. A75, 063414 (2007)

    2007

  34. [34]

    De Bernardis, P

    D. De Bernardis, P. Pilar, T. Jaako, S. De Liberato, and P. Rabl, Breakdown of gauge invariance in ultrastrong- coupling cavity QED, Phys. Rev. A98, 053819 (2018)

    2018

  35. [35]

    Di Stefano, A

    O. Di Stefano, A. Settineri, V. MacrÃň, L. Garziano, R. Stassi, S. Savasta, and F. Nori, Resolution of gauge ambiguities in ultrastrong-coupling cavity quan- tum electrodynamics, Nat. Phys.15, 803 (2019)

    2019

  36. [36]

    Settineri, O

    A. Settineri, O. Di Stefano, D. Zueco, S. Hughes, S. Savasta, and F. Nori, Gauge freedom, quantum mea- surements, and time-dependent interactions in cavity QED, Phys. Rev. Res.3, 023079 (2021)

    2021

  37. [37]

    Salmon, C

    W. Salmon, C. Gustin, A. Settineri, O. D. Stefano, D. Zueco, S. Savasta, F. Nori, and S. Hughes, Gauge- independent emission spectra and quantum correla- tions in the ultrastrong coupling regime of open system cavity-QED, Nanophotonics11, 1573 (2022)

    2022

  38. [38]

    Gustin, S

    C. Gustin, S. Franke, and S. Hughes, Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media, Phys. Rev. A107, 013722 (2023)

    2023

  39. [39]

    Gustin, J

    C. Gustin, J. Ren, S. Franke, and S. Hughes, Dis- sipation in the broadband and ultrastrong coupling regimes of cavity quantum electrodynamics: An ab initio quantized quasinormal mode approach (2025), arXiv:2507.21408 [Light: Science & Applications, in press]

    work page arXiv 2025

  40. [40]

    Beaudoin, J

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

    2011

  41. [41]

    Ridolfo, M

    A. Ridolfo, M. Leib, S. Savasta, and M. J. Hartmann, Photon blockade in the ultrastrong coupling regime, Physical Review Letters109, 193602 (2012)

    2012

  42. [42]

    Ridolfo, O

    A. Ridolfo, O. Di Stefano, N. Fina, R. Saija, and S. Savasta, Quantum regression theorem in the ultra- strong coupling regime, Physical Review Letters109, 193602 (2012)

    2012

  43. [43]

    Settineri, V

    A. Settineri, V. Macrí, A. Ridolfo, O. Di Stefano, A. F. Kockum, F. Nori, and S. Savasta, Dissipation and ther- mal noise in hybrid quantum systems in the ultrastrong- coupling regime, Phys. Rev. A98, 053834 (2018)

    2018

  44. [44]

    Akbari, F

    K. Akbari, F. Nori, and S. Hughes, Floquet engineering the quantum Rabi model in the ultrastrong coupling regime, Phys. Rev. Lett.134, 063602 (2025)

    2025

  45. [45]

    Hughes and H

    S. Hughes and H. J. Carmichael, Phonon-mediated pop- ulation inversion in a semiconductor quantum-dot cav- ity system, New Journal of Physics15, 053039 (2013)

    2013

  46. [46]

    Q. Wang, Z. Gong, C. Duan, Z. Tang, and J. Wu, Dy- namical scaling in the Ohmic spin-boson model studied by extended hierarchical equations of motion, The Jour- nal of Chemical Physics150, 084114 (2019)

    2019

  47. [47]

    Kaldewey, S

    T. Kaldewey, S. Lüker, A. V. Kuhlmann, S. R. Valentin, J.-M. Chauveau, A. Ludwig, A. D. Wieck, D. E. Reiter, T. Kuhn, and R. J. Warburton, Demonstrating the de- coupling regime of the electron-phonon interaction in a quantum dot using chirped optical excitation, Phys. Rev. B95, 241306 (2017)

    2017

  48. [48]

    C.GustinandS.Hughes,Efficientpulse-excitationtech- niques for single photon sources from quantum dots in optical cavities, Advanced Quantum Technologies3, 1900073 (2020)

    2020

  49. [49]

    Zhou, Y.-A

    Z.-Y. Zhou, Y.-A. Yan, S. Hughes, J. Q. You, and F. Nori, Accessing the bath information in open quan- tum systems with the stochasticc-number Langevin equation method, Phys. Rev. A100, 042112 (2019)

    2019

  50. [50]

    R.-C. Ge, C. Van Vlack, P. Yao, J. F. Young, and S. Hughes, Accessing quantum nanoplasmonics in a hy- brid quantum dot–metal nanosystem: Mollow triplet of a quantum dot near a metal nanoparticle, Phys. Rev. B 87, 205425 (2013)

    2013

  51. [51]

    Vannucci and N

    L. Vannucci and N. Gregersen, Highly efficient and indistinguishable single-photon sources via phonon- decoupled two-color excitation, Phys. Rev. B107, 195306 (2023)

    2023

  52. [52]

    Schnell, C

    A. Schnell, C. Weitenberg, and A. Eckardt, Dissipative preparation of a Floquet topological insulator in an op- tical lattice via bath engineering, SciPost Phys.17, 052 (2024)

    2024

  53. [53]

    Jaynes and F

    E. Jaynes and F. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proceedings of the IEEE51, 89 (1963)

    1963

  54. [54]

    F. W. Cummings, Reminiscing about thesis work with E T Jaynes at Stanford in the 1950s, J. Phys. B: At. Mol. Opt. Phys.46, 220202 (2013)

    2013

  55. [55]

    Larson and T

    J. Larson and T. Mavrogordatos,The JaynesâĂŞCum- mings Model and its Descendants (Second Edition), 2053-2563 (IOP Publishing, 2024)

    2053

  56. [56]

    M. V. Rybin, S. F. Mingaleev, M. F. Limonov, and Y. S. Kivshar, Purcell effect and Lamb shift as interference phenomena, Sci Rep6, 20599 (2016)

    2016

  57. [57]

    Kiraz, P

    A. Kiraz, P. Michler, C. Becher, B. Gayral, A. Imamoħlu, L. Zhang, E. Hu, W. V. Schoenfeld, and P. M. Petroff, Cavity-quantum electrodynamics us- ing a single InAs quantum dot in a microdisk structure, Applied Physics Letters78, 3932 (2001)

    2001

  58. [58]

    G. S. Agarwal, Control of the Purcell effect via unex- cited atoms and exceptional points, Phys. Rev. Res.6, L012050 (2024)

    2024

  59. [59]

    Yamamoto and H

    Y. Yamamoto and H. A. Haus, Preparation, mea- surement and information capacity of optical quantum states, Rev. Mod. Phys.58, 1001 (1986)

    1986

  60. [60]

    R. J. Thompson, G. Rempe, and H. J. Kimble, Observa- tion of normal-mode splitting for an atom in an optical cavity, Phys. Rev. Lett.68, 1132 (1992)

    1992

  61. [61]

    R. H. Dicke, Coherence in Spontaneous Radiation Pro- cesses, Phys. Rev.93, 99 (1954)

    1954

  62. [62]

    R. H. Lehmberg, Radiation from ann-atom system. i. general formalism, Phys. Rev. A2, 883 (1970)

    1970

  63. [63]

    G. S. Agarwal, Master-equation approach to sponta- neous emission, Phys. Rev. A2, 2038 (1970)

    2038

  64. [64]

    C. C. Tannoudji, G. Grynberg, and J. Dupont-Roe, Atom-photon interactions(New York, NY (United States); John Wiley and Sons Inc., 1991)

    1991

  65. [65]

    L.C.Andreani, G.Panzarini,andJ.-M.Gérard,Strong- coupling regime for quantum boxes in pillar microcavi- ties: Theory, Phys. Rev. B60, 13276 (1999)

    1999

  66. [66]

    C. M. Lange, E. Daggett, V. Walther, L. Huang, and J. D. Hood, Superradiant and subradiant states in lifetime-limited organic molecules through laser-induced tuning, Nat. Phys.20, 836 (2024)

    2024

  67. [67]

    M. O. Scully and M. S. Zubairy,Quantum Optics(Cam- bridge University Press, Cambridge, 1997)

    1997

  68. [68]

    G. S. Agarwal,Quantum Optics(Cambridge University Press, 2012)

    2012

  69. [69]

    W. Qin, A. F. Kockum, C. S. MuÃśoz, A. Miranow- icz, and F. Nori, Quantum amplification and simulation of strong and ultrastrong coupling of light and matter, Physics Reports1078, 1 (2024). 68

    2024

  70. [70]

    H. J. Carmichael, Dissipation in Quantum Mechanics: The Master Equation Approach, inStatistical Methods in Quantum Optics 1: Master Equations and Fokker- Planck Equations, Texts and Monographs in Physics, edited by H. J. Carmichael (Springer, Berlin, Heidel- berg, 1999) pp. 1–28

    1999

  71. [71]

    Breuer and F

    H. Breuer and F. Petruccione,The Theory of Open Quantum Systems(Oxford University Press, 2002)

    2002

  72. [72]

    H. J. Carmichael,Statistical Methods in Quantum Op- tics 1: Master Equations and Fokker-Planck Equations (Springer Science & Business Media, 2013)

    2013

  73. [73]

    D. A. Lidar, Lecture notes on the theory of open quan- tum systems (2020), arXiv:1902.00967 [quant-ph]

    work page arXiv 2020

  74. [74]

    Akbari, W

    K. Akbari, W. Salmon, F. Nori, and S. Hughes, General- ized dicke model and gauge-invariant master equations for two atoms in ultrastrongly-coupled cavity quantum electrodynamics, Phys. Rev. Res.5, 033002 (2023)

    2023

  75. [75]

    Jeske, D

    J. Jeske, D. J. Ing, M. B. Plenio, S. F. Huelga, and J. H. Cole, Bloch-Redfield equations for modeling light- harvesting complexes, The Journal of Chemical Physics 142, 064104 (2015)

    2015

  76. [76]

    T. V. Tscherbul and P. Brumer, Partial secular Bloch- Redfield master equation for incoherent excitation of multilevel quantum systems, J. Chem. Phys.142, 104107 (2015)

    2015

  77. [77]

    J. Lim, D. J. Ing, J. Rosskopf, J. Jeske, J. H. Cole, S. F. Huelga, and M. B. Plenio, Signatures of spa- tially correlated noise and non-secular effects in two- dimensional electronic spectroscopy, The Journal of Chemical Physics146, 024109 (2017)

    2017

  78. [78]

    Nafari Qaleh and A

    Z. Nafari Qaleh and A. T. Rezakhani, Enhancing en- ergy transfer in quantum systems via periodic driving: Floquet master equations, Phys. Rev. A105, 012208 (2022)

    2022

  79. [79]

    Mori, Floquet states in open quantum systems, An- nualReviewofCondensedMatterPhysics14,35(2023)

    T. Mori, Floquet states in open quantum systems, An- nualReviewofCondensedMatterPhysics14,35(2023)

    2023

  80. [80]

    Winczewski, A

    M. Winczewski, A. Mandarino, G. Suarez, R. Alicki, andM.Horodecki,Intermediate-timesdilemmaforopen quantum system: Filtered approximation to the refined weak-coupling limit, Phys. Rev. E110, 024110 (2024)

    2024

Showing first 80 references.