pith. sign in

arxiv: 2605.17025 · v2 · pith:5ZEMZMA4new · submitted 2026-05-16 · 🪐 quant-ph · physics.optics

Quantum Optical Soliton Dynamics Beyond Linearization: An Open-System Approach

Chris Gustin , Ryotatsu Yanagimoto , Edwin Ng , Hideo Mabuchi This is my paper

Pith reviewed 2026-05-25 06:01 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords quantum solitonsopen quantum systemsmaster equationLanczos supermodenon-Gaussian dynamicschi(3) nonlinearityphoton losshigher-order dispersion
0
0 comments X

The pith

Two open-system methods model quantum soliton dynamics without restricting to linear approximations.

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

The paper develops two techniques for quantum dynamics of chi(3) optical solitons by splitting the full field into a soliton system and a residual reservoir. One reduces the reservoir to a discrete Lanczos supermode basis that keeps dynamics in a handful of modes; the other traces out a non-local environment to obtain a Markovian master equation. Both reproduce quantum phase shifts and photon loss in simulations while remaining valid outside the linearized regime. They therefore supply computational routes to non-Gaussian soliton behavior that standard linear or fully perturbative treatments cannot reach. The work also shows that both classical and master-equation pictures underestimate dissipation once higher-order dispersion broadens the soliton.

Core claim

Projecting the quantum field into a soliton system plus reservoir, then treating the reservoir either by a discrete Lanczos supermode expansion or by deriving a Markovian master equation, captures quantum-induced phase shifts in a minimal basis and reveals photon loss arising from non-Markovian dispersive couplings; the same master equation predicts radiation consistent with classical theory yet both classical and master-equation results dramatically underestimate actual dissipation because of soliton broadening induced by dispersive coupling.

What carries the argument

Open-system projection of the quantum field into soliton system and reservoir components, with the reservoir handled either by discrete Lanczos supermode expansion or by Markovian tracing.

If this is right

  • The methods remain valid for non-Gaussian regimes where linearized treatments break down.
  • The Lanczos-supermode approach captures photon loss that arises from non-Markovian dispersive couplings.
  • The master-equation approach reproduces quantum phase shifts using only a single mode.
  • Both methods identify a hierarchy of perturbations and the stability structure of the soliton.
  • In the presence of higher-order dispersion the master equation matches classical radiation predictions but underestimates total dissipation.

Where Pith is reading between the lines

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

  • The same projection strategy could be tested on multi-soliton collisions or on solitons in other nonlinear media.
  • Direct comparison of the predicted photon-loss rates against time-resolved measurements on ultrashort pulses would quantify the broadening effect.
  • The few-mode reduction may enable real-time simulation of soliton-based quantum gates that current full-field codes cannot handle.

Load-bearing premise

Splitting the quantum field into a distinct soliton system and a reservoir that can be treated by Lanczos supermodes or Markovian elimination is sufficient to capture the essential dynamics.

What would settle it

A full quantum-field simulation or an ultrashort-pulse experiment in the non-linearized regime that produces phase shifts or photon-loss rates differing substantially from the predictions of the Lanczos-supermode or master-equation calculations.

Figures

Figures reproduced from arXiv: 2605.17025 by Chris Gustin, Edwin Ng, Hideo Mabuchi, Ryotatsu Yanagimoto.

Figure 1
Figure 1. Figure 1: Schematic of quantum soliton (a) continuum model [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: LSM coupling matrices for (a) GVD-induced linear [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Real (red) and imaginary (blue) components of the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of LSM interactions. Dominant GVD [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: (b) shows the photon number histograms of the change in relative Fock state probability Pn(t) − Pn(0), where Pn = ⟨n| ρˆ r 0 |n⟩, with ˆρ r 0 = Trm≥1(ˆρS), revealing photon loss away from the center quasi-stable point with n ≈ n¯ photons, suggestive of soliton formation. 2 3 4 [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Wigner function of the fundamental soliton super [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Simulations of solitons with the nonlinear Gaussian approximation. (a,b) soliton amplitude [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Fractional photon loss from the soliton supermode [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: (a) dispersive wave photon loss ∆n3 from a ¯n = 5000 soliton as a function of TOD parameter β3 for GSSF, ME, and LSM models, with window width πδk/n¯ = 1 and at time t = 2T0. For the ME model we approximate ∆n3 ≈ n¯ − ⟨aˆ † 0aˆ0⟩. The approximate form given in the text with only the rates of Eq. (17a) is plotted as solid orange, and the full [44] ME is given by dashed orange lines. (b,c) reservoir photon n… view at source ↗
read the original abstract

We introduce two approaches to modeling the quantum dynamics of optical $\chi^{(3)}$ solitons. Taking an open-system viewpoint, we project the underlying quantum field into system (soliton) and residual reservoir components. The reservoir is treated as either (i) a discrete ``Lanczos supermode'' (LSM) expansion which localizes dynamics to a few-supermode basis, or (ii) a non-local environment which can be traced out by deriving a Markovian master equation (ME). Using these methods, we analyze and identify the quantum structure of both the soliton's stability and its hierarchy of perturbations. Through numerical simulations, we confirm both methods effectively capture quantum-induced soliton phase shifts in a concise few-mode (single-mode for ME) basis, and the LSM approach also captures photon loss which arises from non-Markovian dispersive couplings. As neither method is limited to the linearized regime, our approaches provide powerful computational tools to analyze complex non-Gaussian quantum dynamics of solitons where other commonly-used methods fail, providing insight into such non-perturbative regimes. We also investigate radiation that occurs in the presence of higher-order dispersion with ultrashort pulses, deriving a ME that predicts photon loss consistent with classical theory, but find that both classical and ME theory dramatically underestimate the actual amount of dissipation, which we explain in terms of dispersive coupling-induced soliton broadening.

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 two open-system methods for quantum χ(3) soliton dynamics: (i) a discrete Lanczos supermode (LSM) expansion of the reservoir and (ii) a Markovian master equation (ME) obtained by tracing out a non-local environment. Both rely on projecting the quantum field into a soliton 'system' and residual 'reservoir'. Numerical simulations are reported to confirm that these capture soliton phase shifts (in few-mode or single-mode bases) and, for LSM, photon loss from non-Markovian couplings. The work also derives an ME for radiation under higher-order dispersion and finds that both classical and ME theories underestimate dissipation, attributed to dispersive coupling-induced broadening. The central claim is that these approaches enable analysis of non-Gaussian dynamics beyond linearization where standard methods fail.

Significance. If the system-reservoir projection holds in non-Gaussian regimes, the methods would provide useful computational tools for soliton quantum dynamics beyond linearized treatments. The explicit demonstration that dissipation is underestimated due to broadening supplies a concrete, testable observation. The dual-method (LSM vs. ME) comparison is a strength for internal consistency, though the paper reports no machine-checked proofs or fully open reproducible code.

major comments (1)
  1. [Abstract] Abstract: The assertion that the approaches 'provide powerful computational tools to analyze complex non-Gaussian quantum dynamics of solitons where other commonly-used methods fail' rests on numerical simulations whose support is internal to the projected models. No comparison is presented to an independent unprojected reference (e.g., exact diagonalization on a discretized field or quantum-trajectory evolution of the full Hamiltonian). This directly affects the load-bearing claim that the soliton-reservoir split plus LSM/ME truncation remains accurate once fluctuations are non-Gaussian and non-perturbative.
minor comments (2)
  1. [Abstract] Abstract: The numerical confirmation of phase shifts and photon loss provides no details on error analysis, convergence with respect to basis size, or the specific parameters and system sizes employed.
  2. The manuscript would benefit from a quantitative side-by-side comparison of LSM and ME predictions on identical observables (phase shift magnitude, loss rate) to clarify the regime where the Markovian approximation holds.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive feedback on the manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: The assertion that the approaches 'provide powerful computational tools to analyze complex non-Gaussian quantum dynamics of solitons where other commonly-used methods fail' rests on numerical simulations whose support is internal to the projected models. No comparison is presented to an independent unprojected reference (e.g., exact diagonalization on a discretized field or quantum-trajectory evolution of the full Hamiltonian). This directly affects the load-bearing claim that the soliton-reservoir split plus LSM/ME truncation remains accurate once fluctuations are non-Gaussian and non-perturbative.

    Authors: We agree that external validation against an unprojected reference would strengthen the central claim. The soliton-reservoir decomposition is a unitary change of basis for the field operators and is therefore exact prior to any truncation of the reservoir. The LSM and ME approaches then introduce controlled truncations whose accuracy is assessed through mutual consistency between the two methods and through reproduction of known results (phase shifts, photon loss) that lie outside the linearized regime. Direct benchmarks via exact diagonalization or full quantum trajectories are computationally prohibitive for the continuous-mode model in the non-Gaussian regime of interest; this is precisely why reduced open-system descriptions are developed. We will revise the abstract to qualify the claim, replacing the assertion of 'powerful computational tools ... where other commonly-used methods fail' with a more precise statement that the methods 'enable analysis of non-Gaussian soliton dynamics beyond the reach of linearized treatments'. revision: yes

Circularity Check

0 steps flagged

No circularity: standard open-system methods applied to solitons

full rationale

The paper's derivation chain applies conventional system-reservoir projection and standard techniques (Lanczos supermode expansion, Markovian master equation) from open quantum systems to the soliton problem. No load-bearing step reduces by the paper's own equations to a self-defined input, fitted parameter renamed as prediction, or self-citation chain. Numerical simulations are presented as external validation of the projected dynamics rather than tautological outputs. The central claim of utility beyond linearization rests on the independent applicability of these established methods, making the derivation self-contained against external benchmarks in quantum optics.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the validity of the system-reservoir projection and the effectiveness of LSM discretization or Markovian approximation for non-Gaussian dynamics; no free parameters or invented entities are explicitly named in the abstract.

axioms (1)
  • domain assumption The quantum field can be projected into system (soliton) and residual reservoir components with the reservoir treatable via LSM or Markovian tracing.
    Invoked at the start of the method descriptions in the abstract.

pith-pipeline@v0.9.0 · 5782 in / 1196 out tokens · 47488 ms · 2026-05-25T06:01:39.296515+00:00 · methodology

Review history (2 revisions) →

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

87 extracted references · 87 canonical work pages · 1 internal anchor

  1. [1]

    We use the LSM method with various finite truncations of number of supermodes, as well as the full ME given by the dissipator in Eq

    Low-photon number regime We first investigate the low-photon number regime, where we perform full quantum simulations with a stan- dard numerical package [73]. We use the LSM method with various finite truncations of number of supermodes, as well as the full ME given by the dissipator in Eq. (8), and these results are compared to a numerically-exact simul...

    work page

  2. [2]

    simultons

    High-photon number regime Next, we move to a regime with larger ¯n, where the soliton becomes asymptotically closer to its stable clas- sical solution, and we can employ a nonlinear Gaussian approximation to solve for the quantum mean-field and covariances [44]. For these large ¯nsimulations, we use the effective Hamiltonian form of the ME given by ˆHeff ...

    work page

  3. [3]

    Hirota and J

    R. Hirota and J. Satsuma,N-Soliton Solutions of Model Equations for Shallow Water Waves, J. Phys. Soc. Jpn. 40, 611 (1976)

    work page 1976

  4. [4]

    Khaykovich, F

    L. Khaykovich, F. Schreck, G. Ferrari, T. Bourdel, J. Cu- bizolles, L. D. Carr, Y. Castin, and C. Salomon, Forma- tion of a Matter-Wave Bright Soliton, Science296, 1290 (2002)

    work page 2002

  5. [5]

    K. E. Lonngren, Soliton experiments in plasmas, Plasma Phys.25, 943 (1983)

    work page 1983

  6. [6]

    Belinski and E

    V. Belinski and E. Verdaguer,Gravitational Solitons (Cambridge University Press, 2001)

    work page 2001

  7. [7]

    Y. S. Kivshar and G. P. Agrawal,Optical Solitons(Aca- demic Press, 2003)

    work page 2003

  8. [8]

    McDonald, C

    G. McDonald, C. Kuhn, K. Hardman, S. Bennetts, P. Everitt, P. Altin, J. Debs, J. Close, and N. Robins, Bright Solitonic Matter-Wave Interferometer, Phys. Rev. Lett.113, 013002 (2014)

    work page 2014

  9. [9]

    D. V. Tsarev, S. M. Arakelian, Y.-L. Chuang, R.-K. Lee, and A. P. Alodjants, Quantum metrology beyond Heisen- berg limitwith entangled matter wave solitons, Opt. Ex- press26, 19583 (2018)

    work page 2018

  10. [10]

    Marin-Palomo, J

    P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H. P. Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger, K. Vijayan, W. Freude, T. J. Kippenberg, and C. Koos, Microresonator-based solitons for massively parallel coherent optical communi- cations, Nature546, 274 (2017)

    work page 2017

  11. [11]

    E. R. Andresen, P. Berto, and H. Rigneault, Stimulated Raman scattering microscopy by spectral focusing and fiber-generated soliton as Stokes pulse, Opt. Lett.36, 2387 (2011)

    work page 2011

  12. [12]

    B. Shen, L. Chang, J. Liu, H. Wang, Q.-F. Yang, C. Xi- ang, R. N. Wang, J. He, T. Liu, W. Xie, J. Guo, D. Kinghorn, L. Wu, Q.-X. Ji, T. J. Kippenberg, K. Va- hala, and J. E. Bowers, Integrated turnkey soliton micro- combs, Nature582, 365 (2020)

    work page 2020

  13. [13]

    E. J. Weinberg,Classical Solutions in Quantum Field Theory(Cambridge University Press, 2012)

    work page 2012

  14. [14]

    Jackiw, Quantum meaning of classical field theory, Rev

    R. Jackiw, Quantum meaning of classical field theory, Rev. Mod. Phys.49, 681 (1977)

    work page 1977

  15. [15]

    J. N. Maki and T. Kodama, Phenomenological Quantiza- tion Scheme in a Nonlinear Schr¨ odinger Equation, Phys. Rev. Lett.57, 2097 (1986)

    work page 2097

  16. [16]

    P. D. Drummond, R. M. Shelby, S. R. Friberg, and Y. Ya- mamoto, Quantum solitons in optical fibres, Nature365, 307 (1993)

    work page 1993

  17. [17]

    J. P. Gordon and H. A. Haus, Random walk of coherently amplified solitons in optical fiber transmission, Opt. Lett. 11, 665 (1986)

    work page 1986

  18. [18]

    S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Squeezing of quantum solitons, Phys. Rev. Lett. 58, 1841 (1987)

    work page 1987

  19. [19]

    Rosenbluh and R

    M. Rosenbluh and R. M. Shelby, Squeezed Optical Soli- tons, Phys. Rev. Lett.66, 153 (1990)

    work page 1990

  20. [20]

    Di Mauro Villari, D

    L. Di Mauro Villari, D. Faccio, F. Biancalana, and C. Conti, Quantum soliton evaporation, Phys. Rev. A 98, 043859 (2018)

    work page 2018

  21. [21]

    Korolkova, R

    N. Korolkova, R. Loudon, G. Gardavsky, M. W. Hamil- ton, and G. Leuchs, Time evolution of a quantum soliton in a Kerr medium, J. Mod. Opt.48, 1339 (2001)

    work page 2001

  22. [22]

    Yanagimoto, T

    R. Yanagimoto, T. Onodera, E. Ng, L. G. Wright, P. L. McMahon, and H. Mabuchi, Engineering a Kerr-Based Deterministic Cubic Phase Gate via Gaussian Opera- tions, Phys. Rev. Lett.124, 240503 (2020)

    work page 2020

  23. [23]

    Yanagimoto, E

    R. Yanagimoto, E. Ng, L. G. Wright, L. G. Wright, T. Onodera, T. Onodera, and H. Mabuchi, Efficient sim- ulation of ultrafast quantum nonlinear optics with matrix product states, Optica8, 1306 (2021)

    work page 2021

  24. [24]

    Tsang, Quantum Temporal Correlations and Entan- glement via Adiabatic Control of Vector Solitons, Phys

    M. Tsang, Quantum Temporal Correlations and Entan- glement via Adiabatic Control of Vector Solitons, Phys. Rev. Lett.97, 023902 (2006)

    work page 2006

  25. [25]

    Bao, M.-G

    C. Bao, M.-G. Suh, B. Shen, K. S ¸afak, A. Dai, H. Wang, L. Wu, Z. Yuan, Q.-F. Yang, A. B. Matsko, F. X. K¨ art- ner, and K. J. Vahala, Quantum diffusion of microcavity solitons, Nat. Phys.17, 462 (2021)

    work page 2021

  26. [26]

    Jeong, D

    D. Jeong, D. Kwon, I. Jeon, I. Hwan Do, J. Kim, and H. Lee, Ultralow jitter silica microcomb, Optica7, 1108 (2020)

    work page 2020

  27. [27]

    K. Jia, X. Wang, D. Kwon, J. Wang, E. Tsao, H. Liu, X. Ni, J. Guo, M. Yang, X. Jiang, J. Kim, S. Zhu, Z. Xie, and S.-W. Huang, Photonic Flywheel in a Monolithic Fiber Resonator, Phys. Rev. Lett.125, 143902 (2020)

    work page 2020

  28. [28]

    Erkintalo, Got the quantum jitters, Nat

    M. Erkintalo, Got the quantum jitters, Nat. Phys.17, 432 (2021)

    work page 2021

  29. [29]

    E. W. Wright, Quantum theory of soliton propagation in an optical fiber using the Hartree approximation, Phys. Rev. A43, 3836 (1991)

    work page 1991

  30. [30]

    Yao, Quantum fluctuations of optical solitons in fibers, Phys

    D. Yao, Quantum fluctuations of optical solitons in fibers, Phys. Rev. A52, 4871 (1995)

    work page 1995

  31. [31]

    F. X. K¨ artner and H. A. Haus, Quantum-mechanical sta- bility of solitons and the correspondence principle, Phys. Rev. A48, 2361 (1993)

    work page 1993

  32. [32]

    S. Ward, R. Allahverdi, and A. Mafi, Quantum decay of an optical soliton, Phys. Rev. A107, 053513 (2023)

    work page 2023

  33. [33]

    L. D. M. Villari, D. Faccio, F. Biancalana, and C. Conti, Quantum soliton evaporation, Phys. Rev. A98, 043859 (2018)

    work page 2018

  34. [34]

    Baak and F

    S.-S. Baak and F. K¨ onig, Quantum backreaction effect in optical solitons, New J. Phys.27, 015001 (2025)

    work page 2025

  35. [35]

    L. G. Helt and N. Quesada, Degenerate squeezing in waveguides: a unified theoretical approach, J. Phys. Pho- ton.2, 035001 (2020)

    work page 2020

  36. [36]

    H. A. Haus and Y. Lai, Quantum theory of soliton squeez- ing: a linearized approach, J. Opt. Soc. Am. B7, 386 (1990)

    work page 1990

  37. [37]

    A. B. Matsko and L. Maleki, On timing jitter of mode locked Kerrfrequency combs, Opt. Express21, 28862 (2013). 13

    work page 2013

  38. [38]

    Olivares, Quantum optics in the phase space: A tu- torial on Gaussian states, Eur

    S. Olivares, Quantum optics in the phase space: A tu- torial on Gaussian states, Eur. Phys. J. Special Topics 203, 3 (2012)

    work page 2012

  39. [39]

    S. L. Braunstein and P. van Loock, Quantum informa- tion with continuous variables, Rev. Mod. Phys.77, 513 (2005)

    work page 2005

  40. [40]

    Yoon and J

    B. Yoon and J. W. Negele, Time-dependent Hartree ap- proximation for a one-dimensional system of bosons with attractiveδ-function interactions, Phys. Rev. A16, 1451 (1977)

    work page 1977

  41. [41]

    Calogero and A

    F. Calogero and A. Degasperis, Comparison between the exact and Hartree solutions of a one-dimensional many- body problem, Phys. Rev. A11, 265 (1975)

    work page 1975

  42. [42]

    Haus and Y

    A. Haus and Y. Lai, Quantum theory of solitons in optical fibers. I. Time-dependent Hartree approximation, Phys. Rev. A40, 844 (1989)

    work page 1989

  43. [43]

    Levit, J

    S. Levit, J. W. Negele, and Z. Paltiel, Time-dependent mean-field theory and quantized bound states, Phys. Rev. C21, 1603 (1980)

    work page 1980

  44. [44]

    Singer, M

    F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, Femtosecond solitons in nonlinear optical fibers: Classi- cal and quantum effects, Phys. Rev. A46, 4192 (1992)

    work page 1992

  45. [45]

    J. R. Schrieffer and P. A. Wolff, Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Phys. Rev.130, 1605 (1963)

    work page 1963

  46. [46]

    (See Supplemental Material at [URL will be inserted by publisher] for more detailed information.)

    work page

  47. [47]

    Lai and H

    Y. Lai and H. A. Haus, Quantum theory of solitons in optical fibers. ii. exact solution, Phys. Rev. A40, 854 (1989)

    work page 1989

  48. [48]

    Yao, Quantum coherence of optical solitons in fibers, Phys

    D. Yao, Quantum coherence of optical solitons in fibers, Phys. Rev. A52, 1574 (1995)

    work page 1995

  49. [49]

    F. X. K¨ artner and L. Boivin, Quantum noise of the fun- damental soliton, Phys. Rev. A53, 454 (1996)

    work page 1996

  50. [50]

    Yanagimoto, E

    R. Yanagimoto, E. Ng, M. Jankowski, R. Nehra, T. P. McKenna, T. Onodera, L. G. Wright, R. Hamerly, A. Marandi, M. M. Fejer, and H. Mabuchi, Mesoscopic ultrafast nonlinear optics—the emergence of multimode quantum non-Gaussian physics, Optica11, 896 (2024)

    work page 2024

  51. [51]

    Jankowski, R

    M. Jankowski, R. Yanagimoto, E. Ng, R. Hamerly, T. P. McKenna, H. Mabuchi, and M. M. Fejer, Ultrafast second-order nonlinear photonics—from classical physics to non-gaussian quantum dynamics: a tutorial, Adv. Opt. Photon.16, 347 (2024)

    work page 2024

  52. [52]

    Gustin, R

    C. Gustin, R. Yanagimoto, E. Ng, T. Onodera, and H. Mabuchi, Effective field theories in broadband quan- tum optics: modeling phase modulation and two-photon loss from cascaded quadratic nonlinearities, Quantum Sci. Technol.10, 025035 (2025)

    work page 2025

  53. [53]

    Brecht, D

    B. Brecht, D. V. Reddy, C. Silberhorn, and M. G. Raymer, Photon Temporal Modes: A Complete Frame- work for Quantum Information Science, Phys. Rev. X5, 041017 (2015)

    work page 2015

  54. [54]

    Onodera, E

    T. Onodera, E. Ng, C. Gustin, N. L¨ orch, A. Yama- mura, R. Hamerly, P. L. McMahon, A. Marandi, and H. Mabuchi, Nonlinear quantum behavior of ultrashort- pulse optical parametric oscillators, Phys. Rev. A105, 033508 (2022)

    work page 2022

  55. [55]

    Patera, N

    G. Patera, N. Treps, C. Fabre, and G. J. de Valc´ arcel, Quantum theory of synchronously pumped type I optical parametric oscillators: characterization of the squeezed supermodes, Eur. Phys. J. D56, 123 (2010)

    work page 2010

  56. [56]

    Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral op- erators, J

    C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral op- erators, J. Res. Natl. Bur. Stand.45, 255 (1950)

    work page 1950

  57. [57]

    Gustin, J

    C. Gustin, J. Ren, S. Franke, and S. Hughes, Dissipation in the Broadband and Ultrastrong Coupling Regimes of Cavity Quantum Electrodynamics: AnAb InitioQuan- tized Quasinormal Mode Approach, arXiv:2507.21408 (2025), arXiv:2507.21408 [quant-ph]

    work page arXiv 2025

  58. [58]

    R. M. Fuchs, J. Ren, S. Franke, S. Hughes, and M. Richter, Quantum dynamics of coupled quasinormal modes and quantum emitters interacting via finite-delay propagating photons (2026), arXiv:2604.12605 [cond- mat.mes-hall]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  59. [59]

    Franke, S

    S. Franke, S. Hughes, M. K. Dezfouli, P. T. Kristensen, K. Busch, A. Knorr, and M. Richter, Quantization of Quasinormal Modes for Open Cavities and Plasmonic Cavity Quantum Electrodynamics, Phys. Rev. Lett.122, 213901 (2019)

    work page 2019

  60. [60]

    A. Garg, J. N. Onuchic, and V. Ambegaokar, Effect of friction on electron transfer in biomolecules, J. Chem. Phys.83, 4491 (1985)

    work page 1985

  61. [61]

    Shubrook, J

    M. Shubrook, J. Iles-Smith, and A. Nazir, Non- Markovian quantum heat statistics with the reaction co- ordinate mapping, Quantum Sci. Technol.10, 025063 (2025)

    work page 2025

  62. [62]

    Anto-Sztrikacs and D

    N. Anto-Sztrikacs and D. Segal, Capturing non- Markovian dynamics with the reaction coordinate method, Phys. Rev. A104, 052617 (2021)

    work page 2021

  63. [63]

    K. H. Hughes, C. D. Christ, and I. Burghardt, Effective- mode representation of non-Markovian dynamics: A hi- erarchical approximation of the spectral density. I. Ap- plication to single surface dynamics, J. Chem. Phys.131, 024109 (2009)

    work page 2009

  64. [64]

    Imamo˘ glu, Stochastic wave-function approach to non- Markovian systems, Phys

    A. Imamo˘ glu, Stochastic wave-function approach to non- Markovian systems, Phys. Rev. A50, 3650 (1994)

    work page 1994

  65. [65]

    B. M. Garraway, Nonperturbative decay of an atomic sys- tem in a cavity, Phys. Rev. A55, 2290 (1997)

    work page 1997

  66. [66]

    B. J. Dalton, S. M. Barnett, and B. M. Garraway, Theory of pseudomodes in quantum optical processes, Phys. Rev. A64, 053813 (2001)

    work page 2001

  67. [67]

    Pleasance, B

    G. Pleasance, B. M. Garraway, and F. Petruccione, Gen- eralized theory of pseudomodes for exact descriptions of non-Markovian quantum processes, Phys. Rev. Res.2, 043058 (2020)

    work page 2020

  68. [68]

    Lambert, S

    N. Lambert, S. Ahmed, M. Cirio, and F. Nori, Mod- elling the ultra-strongly coupled spin-boson model with unphysical modes, Nat. Commun.10, 1 (2019)

    work page 2019

  69. [69]

    E. Ng, R. Yanagimoto, M. Jankowski, M. M. Fejer, and H. Mabuchi, Quantum noise dynamics in nonlinear pulse propagation, arXiv:2307.05464 (2023), arXiv:2307.05464 [quant-ph]

    work page arXiv 2023

  70. [70]

    T. J. Park and J. C. Light, Unitary quantum time evolu- tion by iterative Lanczos reduction, J. Chem. Phys.85, 5870 (1986)

    work page 1986

  71. [71]

    Cohen-Tannoudji, J

    C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electro- dynamics(Wiley-VCH, Weinheim, 1997)

    work page 1997

  72. [72]

    Breuer and F

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

    work page 2002

  73. [73]

    Nathan and M

    F. Nathan and M. S. Rudner, Universal Lindblad equa- tion for open quantum systems, Phys. Rev. B102, 115109 (2020)

    work page 2020

  74. [74]

    Lai and H

    Y. Lai and H. A. Haus, Quantum theory of solitons in optical fibers. II. Exact solution, Phys. Rev. A40, 854 (1989). 14

    work page 1989

  75. [75]

    Kr¨ amer, D

    S. Kr¨ amer, D. Plankensteiner, L. Ostermann, and H. Ritsch, QuantumOptics.jl: A Julia framework for sim- ulating open quantum systems, Comput. Phys. Commun 227, 109 (2018)

    work page 2018

  76. [76]

    Akhmediev and M

    N. Akhmediev and M. Karlsson, Cherenkov radiation emitted by solitons in optical fibers, Phys. Rev. A51, 2602 (1995)

    work page 1995

  77. [77]

    V. I. Kruglov and H. Triki, Periodic and solitary waves in an inhomogeneous optical waveguide with third-order dispersion and self-steepening nonlinearity, Phys. Rev. A 103, 013521 (2021)

    work page 2021

  78. [78]

    D. T. H. Tan, K. Ikeda, P. C. Sun, and Y. Fainman, Group velocity dispersion and self phase modulation in silicon nitride waveguides, Applied Physics Letters96, 061101 (2010)

    work page 2010

  79. [79]

    A. V. Buryak, P. D. Trapani, D. V. Skryabin, and S. Trillo, Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications, Physics Re- ports370, 63 (2002)

    work page 2002

  80. [80]

    D. D. Hickstein, D. R. Carlson, H. Mundoor, J. B. Khur- gin, K. Srinivasan, D. Westly, A. Kowligy, I. I. Smalyukh, S. A. Diddams, and S. B. Papp, Self-organized nonlinear gratings for ultrafast nanophotonics, Nat. Photonics13, 494 (2019)

    work page 2019

Showing first 80 references.