pith. sign in

arxiv: 2510.16634 · v2 · submitted 2025-10-18 · 🪐 quant-ph

Cavity QED beyond the Jaynes-Cummings model

Abeer Al Ghamdi , Gin Jose , Almut Beige This is my paper

Pith reviewed 2026-05-18 05:36 UTC · model grok-4.3

classification 🪐 quant-ph
keywords cavity QEDmulti-mode fielddecay rateJaynes-Cummingsstrong couplingmetallic mirrorssubwavelength cavity
0
0 comments X

The pith

A multi-mode dynamical model of the cavity field shows the emitter decay rate equals its free-space value in most cases.

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

The paper replaces the usual single-mode Jaynes-Cummings description with a full dynamical multi-mode treatment of the electromagnetic field inside the resonator. This reveals that an emitter in a subwavelength cavity with metallic mirrors can experience a much larger decay rate than in free space because of constructive interference among the emitted light. Across general cavity geometries, however, the calculated decay rate remains very close to the free-space rate. The result offers a possible reason why experiments using planar mirrors have not reached the strong-coupling regime.

Core claim

By modeling the electromagnetic field inside the resonator with a full dynamical multi-mode description rather than a single mode, the decay rate of an emitter inside a subwavelength cavity with metallic mirrors can greatly exceed its free-space value due to constructive interference, yet equals the free-space rate to a very good approximation for most configurations.

What carries the argument

Full dynamical multi-mode description of the electromagnetic field, which tracks the emitted light across many modes instead of reducing the resonator field to one mode.

If this is right

  • In subwavelength cavities with metallic mirrors the decay rate can increase substantially through constructive interference.
  • For typical planar-mirror cavities the decay rate stays close to the free-space value.
  • The near-equality of rates supplies one reason atom-cavity experiments with planar mirrors have not entered the strong-coupling regime.

Where Pith is reading between the lines

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

  • The same multi-mode approach could be applied to other mirror materials or cavity shapes to predict when interference enhancements appear.
  • Designs that deliberately exploit the subwavelength metallic geometry might achieve larger effective decay rates without requiring single-mode perfection.
  • Time-resolved measurements of emitted light in such cavities could directly map the interference effects that the model predicts.

Load-bearing premise

The electromagnetic field inside the resonator must be treated with a full dynamical multi-mode description rather than being reduced to a single mode, and the mirrors must be metallic with the cavity subwavelength in size.

What would settle it

Direct measurement of an emitter's decay rate inside a subwavelength metallic-mirror cavity that finds the rate equal to the free-space rate rather than much larger would test the constructive-interference enhancement; a rate that deviates strongly from free space in non-subwavelength planar cavities would test the general-equality claim.

Figures

Figures reproduced from arXiv: 2510.16634 by Abeer Al Ghamdi, Almut Beige, Gin Jose.

Figure 1
Figure 1. Figure 1: FIG. 1. [Colour online] Standard view of atom-cavity systems [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. [Colour online] Schematic view of an atom at a position [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The spontaneous decay rate Γ [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. [Colour online] Schematic view of an atom placed at the centre of of a cavity which consists of two partially transparent [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. [Colour online] The spontaneous decay rate Γ [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. [Colour online] The spontaneous decay rate Γ [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
read the original abstract

As atom-cavity systems are becoming more sophisticated, the limitations of the Jaynes-Cummings model are becoming more apparent. In this paper, we therefore take a more dynamical approach to the modelling of atom-cavity systems and do not reduce the electromagnetic field inside the resonator to a single mode. Our approach shows that the decay rate Gamma_cav of an emitter inside a subwavelength cavity with metallic mirrors can be much larger than its free space decay rate Gamma_free due to constructive interference effects of the emitted light. In general, however, we find that Gamma_cav = Gamma_free to a very good approximation which might explain why atom-cavity experiments with planar mirrors have not been able to operate in the so-called strong coupling regime.

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 / 1 minor

Summary. The manuscript develops a multi-mode dynamical treatment of an emitter coupled to the electromagnetic field inside a subwavelength cavity bounded by metallic mirrors, without reducing the field to a single mode as in the Jaynes-Cummings model. It reports that the cavity-modified decay rate Gamma_cav can substantially exceed the free-space rate Gamma_free in special cases due to constructive interference, but finds Gamma_cav = Gamma_free to a good approximation in general; this is offered as a possible explanation for the absence of strong-coupling regimes in planar-mirror atom-cavity experiments.

Significance. If the multi-mode calculation is robust, the work supplies a concrete dynamical reason why strong coupling remains elusive in subwavelength planar cavities and illustrates the quantitative importance of retaining the full mode continuum. The absence of parameter fitting and the direct comparison of Gamma_cav to Gamma_free are positive features; however, the lack of explicit derivation details, convergence tests, or error bounds in the abstract limits the immediate assessment of how general the reported equality is.

major comments (1)
  1. [Abstract and main text] Abstract and main text: the central claim that Gamma_cav approximates Gamma_free 'to a very good approximation' in general requires that the sum over all allowed modes (including evanescent components near the metallic walls) exactly recovers the free-space local density of states at the emitter position. The subwavelength geometry together with perfect-metal boundary conditions can modify both mode density and local field strength; without reported truncation criteria, convergence checks, or an explicit free-space benchmark calculation, the equality could be an artifact of the chosen mode basis rather than a general result.
minor comments (1)
  1. [Abstract] The abstract would be clearer if it briefly indicated whether the multi-mode dynamics are solved numerically or analytically and what boundary conditions are imposed on the metallic mirrors.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for highlighting both the potential significance of the multi-mode treatment and the need for greater transparency in the supporting numerical details. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract and main text] Abstract and main text: the central claim that Gamma_cav approximates Gamma_free 'to a very good approximation' in general requires that the sum over all allowed modes (including evanescent components near the metallic walls) exactly recovers the free-space local density of states at the emitter position. The subwavelength geometry together with perfect-metal boundary conditions can modify both mode density and local field strength; without reported truncation criteria, convergence checks, or an explicit free-space benchmark calculation, the equality could be an artifact of the chosen mode basis rather than a general result.

    Authors: We agree that explicit documentation of the mode summation is required to establish that the reported near-equality is not an artifact. Our dynamical calculation is based on the complete set of electromagnetic modes satisfying the perfect-metal boundary conditions of the planar cavity; this set necessarily incorporates both propagating and evanescent components. At generic emitter locations the modifications to the local density of states and to the local field strength largely cancel, yielding Γ_cav ≈ Γ_free, while at special positions constructive interference produces the enhancements already shown in the manuscript. In the revised version we will add an appendix that (i) states the truncation criteria (maximum transverse wave-vector and total number of retained modes), (ii) presents convergence plots of Γ_cav versus mode cutoff, and (iii) provides a direct numerical benchmark in which the cavity-mode sum is evaluated at the emitter position and compared with the known free-space local density of states. These additions will make the generality of the result verifiable and will clarify that the observed behavior follows from the completeness of the mode basis rather than from an incomplete truncation. revision: yes

Circularity Check

0 steps flagged

Multi-mode dynamical treatment yields Gamma_cav ≈ Gamma_free as computed outcome, not by construction

full rationale

The paper derives its central result—that the cavity-modified decay rate Gamma_cav equals the free-space rate Gamma_free to a good approximation in general, while allowing larger values from constructive interference—directly from an explicit multi-mode dynamical model of the electromagnetic field inside a subwavelength metallic-mirror cavity. No parameter is fitted to the target equality, no quantity is defined in terms of itself, and no load-bearing step reduces to a self-citation or ansatz smuggled from prior work by the same authors. The equality emerges as the net outcome of summing over the allowed modes under the stated boundary conditions rather than being presupposed or forced by the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that a full dynamical treatment of the multi-mode field is both feasible and necessary, together with standard quantum-optics boundary conditions for metallic mirrors.

axioms (1)
  • domain assumption The electromagnetic field inside the resonator can be modeled dynamically without reduction to a single mode.
    Explicitly stated as the core methodological departure in the abstract.

pith-pipeline@v0.9.0 · 5651 in / 1229 out tokens · 41209 ms · 2026-05-18T05:36:04.555489+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Our approach shows that the decay rate Γ_cav of an emitter inside a subwavelength cavity with metallic mirrors can be much larger than its free space decay rate Γ_free due to constructive interference effects... In general, however, we find that Γ_cav = Γ_free to a very good approximation

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages

  1. [1]

    3)22"3+cos (22

    in the 1970s, by Amos and barnes in the 90-ies [54], and by Eschner et al. [55] in the 1990’s. As we shall see below, the dependence of our predicted spontaneous decay rates on the atom-mirror distance is in agreement with these experiments for certain mirror reflection rates. Afterwards, we use the same methodology to obtain an expression for Γcav in Eq....

    work page 1990

  2. [2]

    Usually, the mirrors are shaped such that they refocus the light back onto the emit- ter to encourage re-absorption by the source

    Here we only consider cavities with planar mirrors which is normally not the case in atom-cavity ex- periments [30]. Usually, the mirrors are shaped such that they refocus the light back onto the emit- ter to encourage re-absorption by the source. In our paper, the possible re-absorption of light has been neglected

    work page

  3. [3]

    Here we neglected the re-absorption of light due to the relatively small size of an atom compared to the wavelengthλ 0 of the emitted light (cf. Eq. (46)). Increasing the size of the emitter might alter inter- ference effects and might increase re-absorption

    work page

  4. [4]

    Another assumption made in this paper is that the atom is placed exactly at the centre of the resonator (cf. Fig. 5). Moving the emitter to a different posi- tion is likely to impact the interference of the light coming from the emitter. More detailed calcula- tions are needed to study the dependence of Γ cav on the atomic position

    work page

  5. [5]

    Breaking this symmetry is also likely to change the amount of interference inside the res- onator

    Our calculations also assume that the reflection ratesr a andr b on the insides of the resonator mirrors are both real and both same, i.e.r a = rb =r mir. Breaking this symmetry is also likely to change the amount of interference inside the res- onator. However, our discussion in Section III B suggests that changing the balance betweenr a andr b is unlike...

    work page

  6. [6]

    Instead, we assumed thatr mir is always the same

    Finally, let us point out that our calculations do not take into account that the reflection rate of a mirror surface depends on the angle of the incom- ing light. Instead, we assumed thatr mir is always the same. However, we do not expect that this sim- plification has a big impact on our results, since we only consider dipole moment vectorsD 01 which ar...

    work page

  7. [7]

    Jaynes and F

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

    work page 1963

  8. [8]

    B. W. Shore and P. L. Knight,The Jaynes-Cummings Model, J. Mod. Opt.40, 1195 (1993)

    work page 1993

  9. [9]

    Larson, T

    J. Larson, T. Mavrogordatos, S. Parkins and A. Vidiella- Barranco,The Jaynes–Cummings model: 60 years and still counting, JOSA B41, JCM1 (2024)

    work page 2024

  10. [10]

    Haroche and J.M

    S. Haroche and J.M. Raimond,Radiative properties of Rydberg states in resonant cavities, Adv. At. Mol. Phys. 20, 350 (1985)

    work page 1985

  11. [11]

    Rempe, H

    G. Rempe, H. Walther and N. Klein,Observation of quantum collapse and revival in a one-atom maser, Phys. Rev. Lett.58, 353 (1987)

    work page 1987

  12. [12]

    Meschede,Radiating atoms in confined space: From spontaneous emission to micromasers, Phys

    D. Meschede,Radiating atoms in confined space: From spontaneous emission to micromasers, Phys. Rep.211, 201 (1992)

    work page 1992

  13. [13]

    McKeever, A

    J. McKeever, A. Boca, A. D. Boozer, J. R. Buck and H. J. Kimble,A One-Atom Laser in a Regime of Strong Coupling, Nature425, 268 (2003)

    work page 2003

  14. [14]

    Walther, B

    H. Walther, B. T. H. Varcoe, B. G. Englert and T. Becker,Cavity quantum electrodynamics, Rep. Prog. Phys.69, 1325, (2006)

    work page 2006

  15. [15]

    Stokes, P

    A. Stokes, P. Deb and A. Beige,Using thermodynamics to identify quantum subsystems, J. Mod. Opt.64, S7 (2017)

    work page 2017

  16. [16]

    G. S. Agarwal,Quantum Optics, Springer Tracts of Mod- ern Physics70(Springer-Verlag, Berlin 1974)

    work page 1974

  17. [17]

    H. P. Breuer and F. Petruccione,The theory of open quantum systems(Oxford University Press, 2002)

    work page 2002

  18. [18]

    G. C. Hegerfeldt,How to reset an atom after a photon de- tection: Applications to photon-counting processes, Phys. Rev. A47, 449 (1993)

    work page 1993

  19. [19]

    Stokes, A

    A. Stokes, A. Kurcz, T. P. Spiller and A. Beige,Extending the validity range of quantum optical master equations, Phys. Rev. A85, 053805 (2012)

    work page 2012

  20. [20]

    D. F. Walls and G. J. Milburn,Quantum Optics(Springer Berlin, Heidelberg, 1995)

    work page 1995

  21. [21]

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

    work page 1997

  22. [22]

    G. C. Gerry and P. L. Knight,Introductory Quantum Optics(Cambridge University Press (2005)

    work page 2005

  23. [23]

    Vogel and D.-G

    W. Vogel and D.-G. Welsch,Quantum Optics(Wiley- VCH. Berlin, 2006)

    work page 2006

  24. [24]

    M. A. Jørgensen, D. Pandey, E. Amooghorban, S. Xiao, N. Stenger, and M. Wubs,Collective single-photon emis- sion and energy transfer in thin-layer dielectric and plas- monic systems, Nanophotonics14, 2015 (2025)

    work page 2015

  25. [25]

    Benson, C

    O. Benson, C. Santori, M. Pelton and Y. Yamamoto, Regulated and Entangled Photons from a Single Quantum Dot, Phys. Rev. Lett.84, 2513 (2000)

    work page 2000

  26. [26]

    Pelton,Modified spontaneous emission in nanopho- tonic structures, Nat

    M. Pelton,Modified spontaneous emission in nanopho- tonic structures, Nat. Photon.7, 427 (2015)

    work page 2015

  27. [27]

    X. Li, J. Li, J. Moon, R. Wilmington, D. Lin, K. G¨ undo˘ gdu, and Q. Gu,Experimental observation of Purcell-enhanced spontaneous emission in a single-mode plasmonic nanocavity, ACS Photonics11, 3375 (2024)

    work page 2024

  28. [28]

    Chikkaraddy, B

    R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess and J. J. Baumberg,Single-molecule strong coupling at room temperature in plasmonic nanocavities, Nature535, 127 (2016)

    work page 2016

  29. [29]

    Russell, T

    K. Russell, T. Liu, S. Cui, and E. Hu,Large Spontaneous Emission Enhancement in Plasmonic Nanocavities,Nat. Photon.6, 459 (2012)

    work page 2012

  30. [30]

    O. S. Ojambati, K. B. Arnardottir, B. W. Lovett, J. Keeling and J. J. Baumberg,Few-emitter lasing in sin- gle ultra-small nanocavities, J. Nanophotonics13, 2679 (2024)

    work page 2024

  31. [31]

    Yablonovitch,Inhibited Spontaneous Emission in Solid-State Physics and Electronics, Phys

    E. Yablonovitch,Inhibited Spontaneous Emission in Solid-State Physics and Electronics, Phys. Rev. Lett.58, 2059 (1987)

    work page 2059

  32. [33]

    Englund, D

    D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto and J. Vuck- ovic,Controlling the Spontaneous Emission Rate of Sin- gle Quantum Dots in a Two-Dimensional Photonic Crys- tal, Phys. Rev. Lett.95, 013904 (2005)

    work page 2005

  33. [34]

    H. N. S. Krishnamoorthy, J. H. Song, I. Kretzschmar, and V. M. Menon,Photoluminescence modification in self- assembled fluorescent 3D photonic crystals,Proc. IEEE Long Island Systems, Applications and Technology Con- ference(2010), pp. 1–6

    work page 2010

  34. [35]

    C. So, T. Doherty, M. I. Jspeert, J. O. Ernst and A. Kuhn,Fabrication, Characterisation and Prospects of a High-Finesse Microcavity Created From Tapered Fused Silica Substrates, in Quantum 2.0 Conference and Exhibi- tion, Technical Digest Series (Optica Publishing Group, 2024), paper QW3A.46

    work page 2024

  35. [36]

    Hunger, T

    D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. H¨ ansch and J. Reichel,A fiber Fabry–Perot cavity with high finesse, New J. Phys.12, 065038 (2010)

    work page 2010

  36. [37]

    A. M. Shaltout, J. Kim, A. Boltasseva, V. M. Shalaev and A. V. Kildishev,Ultrathin and multicolour optical cavities with embedded metasurfaces, Nat. Comm.9, 2673 (2018)

    work page 2018

  37. [38]

    A. I. Barreda, M. Zapata-Herrera, I. Palstra, L. Mercad´ e, J. Aizpurua, A. F. Koenderink, and A. Mart´ ınez,Hybrid photonic–plasmonic cavities based on the nanoparticle- on-a-mirror configuration, Photon. Res.9, 2398 (2021)

    work page 2021

  38. [39]

    Y. Liu, Z. Yang, T. Wang, J. Yu, T. Jianrong, and Q. Liao,Spontaneous emission mediated by moir´ e hyper- bolic metasurfaces, Nanomaterials15, 228 (2025)

    work page 2025

  39. [40]

    Saharyan , J.-R

    A. Saharyan , J.-R. Alvarez, T. H. Doherty, A. Kuhn and S. Guerin,Light-matter interaction in open cavities with dielectric stacks, Appl. Phys. Lett.118, 154002 (2021)

    work page 2021

  40. [41]

    T. M. Barlow, R. Bennett and A. Beige,A master equa- tion for a two-sided optical cavity, J. Mod. Opt.62, S11 (2015)

    work page 2015

  41. [42]

    T. D. Barrett, T. H. Doherty and A. Kuhn,Pushing Purcell enhancement beyond its limits, New J. Phys.22, 063013 (2020)

    work page 2020

  42. [43]

    De Bernardis, A

    D. De Bernardis, A. Mercurio and S. De Liberato,Tuto- rial on nonperturbative cavity quantum electrodynamics: is the Jaynes–Cummings model still relevant?, JOSA B 41, C206 (2024)

    work page 2024

  43. [44]

    Blaha, A

    M. Blaha, A. Rauschenbeutel and J. Volz, Jaynes–Cummings model breaks down when the cavity geometry significantly reduces free-space emission, JOSA B41, C222 (2024)

    work page 2024

  44. [45]

    W. Chen, K. ¨Ozdemir, S. Zhao, J. Wiersig and L. Yang, 15 Exceptional points enhance sensing in an optical micro- cavity, Nature,548, 192 (2017)

    work page 2017

  45. [46]

    H. N. Krishnamoorthy, Z. Jacob, E. Narimanov, I. Kret- zschmar and V. M. Menon,Spontaneous emission in non- local materials, Light Sci. Appl.6, e16273 (2017)

    work page 2017

  46. [47]

    Al Ghamdi, B

    A. Al Ghamdi, B. Dawson, G. Jose and A. Beige,Remote non-invasive Fabry-Perot cavity spectroscopy for label- free sensing, Sensors23, 385 (2023)

    work page 2023

  47. [48]

    Hecht,Optics(Pearson Harlow, 2017)

    E. Hecht,Optics(Pearson Harlow, 2017)

    work page 2017

  48. [49]

    Southall, D

    J. Southall, D. Hodgson, R. Purdy and A. Beige,Locally- acting mirror Hamiltonians, J. Mod. Opt.68, 647 (2021)

    work page 2021

  49. [50]

    Waite, D

    G. Waite, D. Hodgson, B. Lang, V. Alapatt and A. Beige, A local photon perspective on the momentum of light, Phys. Rev. A111, 023703 (2025)

    work page 2025

  50. [51]

    Furtak-Wells, L

    N. Furtak-Wells, L. A. Clark, R. Purdy and A. Beige, Quantising the electromagnetic field near two-sided semi- transparent mirrors, Phys. Rev. A97, 043827 (2018)

    work page 2018

  51. [52]

    Furtak-Wells, B

    N. Furtak-Wells, B. Dawson, T. Mann, G. Jose and A. Beige,Mirror-mediated ultralong-range dipole-dipole in- teractions, Opt. Quantum Electron.56, 1287 (2024)

    work page 2024

  52. [53]

    E. M. Purcell, H. C. Torrey and R. V. Pound,Reso- nance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev.69, 37 (1946)

    work page 1946

  53. [54]

    K. H. Drexhage,Influence of a dielectric interface on fluorescence decay time, J. Lumin.1, 693 (1970)

    work page 1970

  54. [55]

    R. R. Chance, A. Prock and R. Silbey,Molecular fluo- rescence and energy transfer near interfaces, Adv. Chem. Phys.37, 1 (1978)

    work page 1978

  55. [56]

    Kleppner,Inhibited spontaneous emission, Phys

    D. Kleppner,Inhibited spontaneous emission, Phys. Rev. Lett.47, 233 (1981)

    work page 1981

  56. [57]

    Dorner and P

    U. Dorner and P. Zoller,Laser-driven atoms in half- cavities, Phys. Rev. A66, 023816 (2002)

    work page 2002

  57. [58]

    A. S. Kuraptsev and I. M. Sokolov,Near-field excitation exchange between motionless point atoms located near the conductive surface, SPIE10717, 193 (2018)

    work page 2018

  58. [59]

    K. H. Drexhage,IV Interaction of light with monomolec- ular dye layers, Prog. Opt.12, 163 (1974)

    work page 1974

  59. [60]

    R. M. Amos and W. L. Barnes,Modification of the spon- taneous emission rate of Eu 3+ ions close to a thin metal mirror, Physical Review B55(11), 7249 (1997)

    work page 1997

  60. [61]

    Eschner, C

    J. Eschner, C. Raab, F. Schmidt-Kaler and R. Blatt, Light interference from single atoms and their mirror im- ages, Nature413, 495 (2001)

    work page 2001

  61. [62]

    Fox,Optical properties of solids(Oxford Master Series in Physics, Oxford University Press, Oxford, 2010)

    M. Fox,Optical properties of solids(Oxford Master Series in Physics, Oxford University Press, Oxford, 2010)

    work page 2010

  62. [63]

    Lodahl, A

    P. Lodahl, A. F. van Driel, I. S. Nikolaev, A. Irman, K. Overgaag, D. Vanmaekelbergh, and W. L. Vos,Con- trolling the dynamics of spontaneous emission from quan- tum dots by photonic crystals, Nature430, 654 (2004)

    work page 2004

  63. [64]

    R., Bennett, T. M. Barlow and A. Beige,A physically motivated quantization of the electromagnetic field, Eur. J. Phys.37, 014001 (2015)

    work page 2015

  64. [65]

    J. Metz, M. Trupke, and A. Beige,Robust entanglement through macroscopic quantum jumps, Phys. Rev. Lett. 97, 040503 (2006)

    work page 2006