FR11
Cavity and waveguide quantum electrodynamics
One photon shows how an atom exchanges and releases energy. A second photon exposes saturation and correlations. Follow both into output ports, then ask which temporal mode a distant receiver can collect.
Start with one excitation; keep following what leaves
Chapters 1–3 build amplitudes, open ports and environmental memory. Chapter 4 adds a second photon. Chapters 5–6 turn the output into a detector or receiver question. Chapters 7–8 read a fixed experiment and build reproducible benchmarks. Each chapter introduces its mathematical tools, develops a worked example and includes exercises with explanations.
Begin directly with Chapter 1. For a broader preparation in photon temporal modes, use FR10 as needed; it is a prerequisite route, not a required completed course. FR10 · Common textbook plan
An excitation oscillates between atom and cavity
- Atom
- Cavity
L1 · 1
How an excitation moves from an atom into light
Build probability amplitudes from atom–cavity exchange, then see why a travelling photon needs a spatial wavepacket.
L2 · 2
How to keep track of light after it leaves
Derive an environmental memory kernel, identify the Markov approximation and connect cavity amplitude to output photon flux.
L2 · 3
When an environment sends light back
Separate finite bandwidth, giant-atom propagation and boundary reflections, then explain a localized photon cloud near a band edge.
L3 · 4
Why two photons cannot always be scattered separately
Build a two-excitation wavefunction and compare atomic saturation with a linear reference from the same one-photon dynamics.
L3 · 5
From a travelling field to a detector record
Separate port amplitudes, photon flux and detector response, and determine when a spatial pair map can become an arrival-time distribution.
L3 · 6
Receiving a photon also means receiving its mode
Calculate collection probability, conditional mode fidelity and unconditional target weight from a saved complex output envelope.
L4 · 7
Connect a temporal mode to a published experiment
Read a fixed Kurpiers photon-interface paper, reproduce its chosen ideal envelope and distinguish squared mean field from photon flux.
L4 · 8
Turn a scattering picture into a reproducible study
Use analytic limits, conservation and convergence checks, then independently benchmark weak-drive fluorescence and detector response.
Three new experiments and four earlier starting points
- Let two photons meet an atom and compare a linear reference
- Follow a finite-band bath into its collected output ports
- Match an emitted photon to a receiver’s temporal mode
The single-excitation route reuses experiments with explicit models: cavity exchange · giant-atom return · band-gap cloud · photon blockade.
The new pair map is an equal-time finite-waveguide state. The port experiment keeps finite-band propagation and open losses. The interface experiment evaluates a controlled source and fixed receiver mode. A separate Markov fluorescence benchmark provides a two-time output-correlation check. Their assumptions are stated where each result is used.
Sources and calculation scope
- Jaynes and Cummings, Comparison of quantum and semiclassical radiation theories, Proc. IEEE 51, 89–109 (1963)
Section II.B, pp. 93–95, Eqs. (35)–(36): single-mode exchange with detuning, checked in the scanned author archive at bayes.wustl.edu. Chapter 1 independently derives its two-amplitude rotating-wave, single-excitation limit.
- Gardiner and Collett, Input and output in damped quantum systems, Phys. Rev. A 31, 3761 (1985)
Section II specifies rotating-wave coupling to a flat bath and derives input–output boundary relations. The course states its own port phase convention and treats the finite-band chain separately from a white-noise port.
- Sheremet et al., Waveguide quantum electrodynamics, Rev. Mod. Phys. 95, 015002 (2023)
The theory overview and Appendix A place single-excitation propagation and input–output relations in their model context. Our two-amplitude examples and schematic figures are original teaching calculations.
- Shen and Fan, Strongly correlated two-photon transport, Phys. Rev. Lett. 98, 153003 (2007)
Fixed author version v2, 13 March 2007. Used for the asymptotic two-photon scattering distinction and correlated component. The finite tight-binding wavepacket model has its own bandwidth and boundaries; it is not the paper’s infinite linear-dispersion S matrix.
- Nysteen et al., Scattering of two photons on a quantum emitter, New J. Phys. 17, 023030 (2015)
Section 2 and the symmetric two-excitation wavefunction establish normalization and photon-density conventions. Author preprint arXiv:1409.1256v1 was also read. Published article is CC BY 3.0; no figure or dataset is copied here.
- Kurpiers et al., Deterministic quantum state transfer and remote entanglement, Nature 558, 264–267 (2018)
Frozen preprint v1, 22 December 2017, Figure 2c,f and Appendix C. We recalculate the ideal sech envelope and the vacuum–one-photon mean-field mapping at the declared 10.4 MHz scale. No experimental data or source artwork is redistributed; transfer efficiency and process tomography are outside the reproduced observable.
- Kimble, Dagenais and Mandel, Photon antibunching in resonance fluorescence, Phys. Rev. Lett. 39, 691 (1977)
Published 12 September 1977, Eq. (5) relates fluorescence correlations to conditional ground-state evolution. The complementary Markov benchmark uses that observable relation; it does not fit the historical counts or experimental apparatus.
- Sandbox Physics, single-excitation finite-band waveguide model and bound-state references
Nearest-neighbour chain dispersion, infinite-chain bound-state reference and finite-window definitions. These are model calculations with declared units, not measured photonic-crystal data.
- Sandbox Physics, existing giant-atom propagation model
The existing model uses 401 sites, maximum time 64 and explicit propagation between two connections to the same emitter. Default separation is 32 and the compact-state preset uses 30. Boundary monitoring and analytic references are retained.
- Sandbox Physics FR11, finite two-excitation scattering model
State basis, ordered pair-map normalization, harmonic comparison, convergence and independent single-mode checks. Exported spatial data remain separate from continuous detector records.
- Sandbox Physics FR11, finite-band ports and collected-mode model
The finite bath keeps its field amplitudes and output losses. Its detector response is a declared synthetic filter. The separate controlled source retains complex output samples for receiver-mode projection.
- Sandbox Physics FR11, reproducible ideal temporal-mode benchmark
Recalculates ideal sech normalization, finite-window survival, overlap and the quarter-versus-half mean-field distinction. Parameters and calculated reference values are saved with the source; no measured points enter the benchmark.
- Sandbox Physics FR11, independent side-fluorescence regression benchmark
Ground-reset optical-Bloch integration versus a finite-drive closed form, weak-drive limit and normalized Gaussian delay response. Deterministic samples and errors are retained in docs/frontier/fr11/fluorescence-benchmark.json.