Download Stopped-light quantum electrodynamics (QED)

Stopped-light quantum electrodynamics (QED)
Supervisor: Prof. Ortwin Hess
Co-supervisors: Prof. Myungshik Kim, Dr. Tommaso Tufarelli (University of Nottingham)
Background
For the past three decades, quantised light-matter interactions have been intensively studied within
the cavity QED paradigm, where photons are spatially confined by a high-finesse cavity (e.g. a pair
of mirrors). An atom inside the cavity could then interact with the same photon multiple times, as
the latter bounces back and forth between cavity walls before eventually escaping into free space.
This mechanism is at the basis of the strong coupling regime, whose rich phenomenology greatly
advanced our understanding of quantised radiation (1).
Nowadays, new exotic possibilities for strong light-matter interaction are emerging beyond the
cavity QED scenario. Following recent advances in the design of stopped-light structures, it is now
possible to devise media in which the group velocity of light is negligible for a wide range of
wavevectors (2). Such media allow for nontrivial interactions between photons and atoms: if
emitted photons cannot propagate away from their source atom fast enough, they can have a
significant chance of being re-absorbed and re-emitted multiple times before escaping. Such
dynamics would be reminiscent of the strong coupling regime of cavity QED, despite the absence
of a cavity! Yet, the two types of dynamics also present important qualitative differences upon
closer analysis. What is more, at present very little theory has been developed for stopped light
QED, and going beyond even the simplest toy models presents a significant, yet exciting,
theoretical challenge.
MSc Project
Initially you will familiarise yourself with the basics of stopped light, as well as the standard
techniques of quantum optics and the theory of open quantum systems (e.g. the master equation
formalism). You will be exposed to the simplest toy models of stopped light-QED, initially
developed in the context of photonic bandgap materials, featuring a two-level emitter embedded in
a medium with quadratic dispersion relation (3). You will quickly realise that such model embodies
a complicated open quantum system, not immediately amenable to treatment with the standard
framework of master equations in Lindblad form (4). Yet, exact solutions may be available in the
(rather restrictive) special case where the dynamics involves at most one photon at a time.
PhD Project
Your will seek to advance the modelling of quantum emitters embedded in stopped-light media,
uncovering the physics of a novel regime of strong light-matter interaction that does not rely on the
geometrical confinement of photons. One of the most significant hurdles you will encounter will be
the modelling of multi-photon processes. So far, such challenge has only been partly overcome in
very specific models by employing variational methods (5), or in some cases by brute-force
numerics (6). You will review existing results and explore a variety of open quantum systems
techniques to advance the field beyond its current boundaries. Depending on your inclinations you
may try to exploit further the use of variational techniques, consider a variety of non-Lindblad
master equations, or even borrow techniques and ideas from many-body physics.
In short, the goals of the project may be summarised by the following broad questions
 Is it possible to devise a tractable quantum optical model of stopped light QED, which
includes multi-photon physics?
 What are the deepest qualitative and quantitative analogies / differences between cavity
QED and stopped light QED?
 Can stopped light QED teach us something new about the quantised interaction between
light and matter?
REFERENCES
(1) Serge Haroche, Jean-Michel Raimond, Exploring the Quantum, Oxford University Press
(2006).
(2) T. Pickering et al., Cavity-free plasmonic nanolasing enabled by dispersionless stopped
light, Nat. Comm. 5, 4972 (2014).
(3) S. John and T. Quang, Spontaneous emission near the edge of a photonic band gap, Phys.
Rev. A 50, 1764 (1994).
(4) H.-P. Breuer and F. Petruccione, The theory of open quantum systems, Oxford University
Press (2002).
(5) G. Calajo' et al., Atom-field dressed states in slow-light waveguide QED, Phys. Rev. A 93,
033833 (2016).
(6) P. Lambropoulos et al., Fundamental quantum optics in structured reservoirs, Rep. Prog.
Phys. 63, 455 (2000).