Collective light-matter coupling

Update as of Sep 9, 2026:

I am considering adapting the upcoming collective quantum minicourse to the age of AI. Maybe every one of my lectures, or at least every second lecture could suggest one mostly unsolved former PhD-level theory problem. The goal of the lecture would be to provide a general introduction to each problem, to explain why it is interesting, and to give some reading material and guidance. Then students with access to AI might be able to do something original, and in a week we will review who did what.

We could learn together in a safe space how to apply new tools to unsolved problems and see the limits of these tools, with no impact on ongoing MSc/PhD projects. Everyone who actively participates will earn credit points, mostly for free , without having to solve any of the hard problems (maybe there will be a couple of regular, easier solved problems with solutions provided by TAs).

Collective minicourse is coming back strong in the fall 2026 and it will cover quantum collective light-matter interactions

Lecture 1: Jaynes-Cummings, Tavis-Cummings models

Lecture 2: Master equation, derivation

Lecture 3: Quantum optics of emitters in a medium

Lecture 4: Antibunching and its suppression. 2-photon physics

Lecture 5: Superradiant burst

Lecture 6: Subradiance (optional)

Lecture 7: Dicke phase transition (Dr. Efi Shahmoon)

Lecture 8: Dicke phase transition-2? (Dr. Efi Shahmoon)

Tutorial 1: Superradiant burst (Gadi Horovitz)

Tutorial 2: Dicke phase transition (Nikita Leppenen)

Approximate plan of the minicourse in the fall 2025:

Light scattering on one resonant emitter and on array of emitters. The concept of a Non-Hermitian Hamiltonian.
Superradiant and subradiant modes in an array of emitters. Collective Rabi splitting.
Non-Hermitian Hamiltonians. Unconjugated orthogonality between the eigenmodes. Purcell effect. Strong and weak coupling. Friedrich-Wintgen condition.
Bound states in continuum.
Basic non-Markovian effects. Breakdown of the superradiant regime for the array of emitters.
Beyond the atoms: plasmonic and Mie resonances in optics, nuclear resonances for gamma rays

Potential problems to solve to get the credits for the 2025 course : ProblemsLMI2025Oct4.pdf

very raw book draft (updated on May 16, 2025; extended and to be published hopefully in the early 2027).

Interaction of arrays of emitters with photons is now a subject of active research. This is driven by a recent emergence of highly coherent artificial emitter platforms, such as those based on cold atoms, superconducting qubits, and semiconductor quantum dots. While the basic physical effects in these systems, for example, Dicke superradiance, have been known for decades, I am not aware of any systematic modern considerations, especially suitable for teaching purposes. I believe that one of the best ways to learn theoretical physics is to solve problems. So, I am compiling a set of problems and solutions describing various cooperative effects in the scattering of light from the resonant structures, mostly focusing on 1D arrays.

These problems elucidate the formation of collective superradiant and subradiant modes, formation of collective polaritonic states, Bragg scattering, and so on. Most of the problems at the moment are focused on the classical optics regime. Almost no previous knowledge of quantum mechanics is required. Classical electrodynamics at the undergraduate level should be mostly sufficient.

I would be very grateful for any ideas for more problems and for finding misprints. For each of the problems posted below there are prepared solutions available on demand by email.

List of problems

Collective modes and Green functions

Resonant light scattering an emitter coupled to the waveguide link to pdf

Interference in light scattering from two emitters link to pdf

Coupled dipole equations for light scattering on an array link to pdf

Dispersion law of polaritons in an array of emitters link to pdf

Dispersion law of polaritons in an array of emitters, chirally coupled to the waveguide link to pdf

Destructive interference for two coupled emitters link to pdf

Collective eigenmodes in Bragg-spaced array of emitters link to pdf

Collective eigenmodes in an array of emitters depending on the period link to pdf

Decay rate of collective subradiant states link to pdf

Decay rate of most subradiant states by Fermi Golden Rule link to pdf

Reciprocity for the transmission coefficients link to pdf

Polariton reflection coefficient from the edge of the array link to pdf

Nonconjugated orthogonality for non-Hermitian Hamiltonian link to pdf

transfer matrices

Transfer matrix via reflection and transmission coefficients link to pdf

Transfer matrix via the reflection and transmission coefficients link to pdf

Reflection and transmission coefficients via the transfer matrix link to pdf

Dispersion law in transfer matrix method link to pdf

Polariton dispersion law in the transfer matrix method link to pdf

Polariton dispersion law in the Bragg structure (numerical) link to pdf

Polariton dispersion law in the Bragg structure (analytical) link to pdf

Polariton dispersion law in an effective medium approximation link to pdf

Reflection from multilayered structure (numerical) link to pdf

Reflection from multilayered structure vs period (numerical) link to pdf

Reflection from multilayered Bragg-spaced structure vs number of emitters (numerical) link to pdf

Reflection from multilayered structure vs number of emitters (numerical+analytical) link to pdf

Emitters in a cavity

Green function for an emitter near a mirror link to pdf

Green function for an emitter in a cavity link to pdf

Reflection from a cavity link to pdf

Reflection from an emitter in cavity link to pdf

Rabi splitting and Purcell effect for an emitter in cavity link to pdf

collective Rabi splitting for N emitters in cavity link to pdf

Some literature

semiconductor quantum wells

E. L. Ivchenko, A. I. Nesvizhskii, and S. Jorda, Bragg Reflection of Light from Quantum-Well Structures, Phys. Solid State 36, 1156 (1994) pdf

E. L. Ivchenko, Chapter 3 in Optical Spectroscopy of Semiconductor Nanostructures (Alpha Science International, Harrow, UK (2005) pdf

superconducting qubits

A. F. van Loo, A. Fedorov, K. Lalumiere, B. C. Sanders, A. Blais, and A. Wallraff, Photon-Mediated Interactions between Distant Artificial Atoms, Science 342, 1494 (2013) web

atoms

Y.-X. Zhang and K. Mølmer, Theory of Subradiant States of a One-Dimensional Two-Level Atom Chain, Phys. Rev. Lett. 122, 203605 (2019) web

review

A.S. Sheremet, M.I. Petrov, I.V. Iorsh, A.V. Poshakinskiy, and A.N. Poddubny, Waveguide quantum electrodynamics: Collective radiance and photon-photon correlations Rev. Mod. Phys. 95, 015002 (2023) web pdf

Classical Electrodynamics and Photonics

These are lecture notes (in Russian) on the course of classical electrodynamics and corresponding problems. The course was designed and read by ANP in Russian in St. Petersburg Academic University in 2016–2021 (teaching assistants: Grigory Budkin, Dmitry Smirnov and Nikita Leppenen).

link to pdf

Videos for part of lectures from 2020/2021 semester (in Russian) YouTube link

We also have a set of 70+ original problems with solutions covering various aspects of modern classical electrodynamics, photonics and metamaterials physics, available upon request.

Optomechanics

These are partial lecture notes (in English) on the course on optomechanics. The course was designed and read by ANP together with Mikhail Petrov in ITMO University, St. Petersburg 2020–2021.