Historical research guide · 0928 · 2024
Exact Quantum Electrodynamics of Radiative Photonic Environments
Ben Yuen · Angela Demetriadou
In one minute
Ben Yuen and Angela Demetriadou, at the University of Birmingham, rewrite the quantum theory of light inside a shaped object. The usual approach treats everything outside a cavity or a nanoparticle as a featureless reservoir and makes approximations that quietly discard information about it. These two do not. They start from the exact continuum of electromagnetic modes that the wave equation gives for a particular geometry, quantise it, and then transform that whole continuum into a finite, discrete set of what they call pseudomodes, each one tied to a real resonance of the structure. Nothing is thrown away: near field and far field come out of one description, every quantum correlation is kept, and the emitter’s apparent decay is revealed as energy spreading across a continuum that itself never decays. They demonstrate it on a one-micrometre silicon sphere, solving 613 pseudomodes at once and recovering Rabi oscillations, the Lamb shift, and the expanding light cone of radiated intensity from the same calculation.
Connection
Chapter 2’s central claim is that the vacuum is a structured medium whose structure you can set by geometry — that is what a Casimir plate, a resonator, or a vacuum-energy device is doing. This paper supplies the exact bookkeeping for that claim: given a shape, here is precisely what the quantised field around it does, with no reservoir standing in for the part you did not want to compute.
From the source
The continuum of photonic eigenmodes around a radiating structure can be transformed, with one-to-one correspondence, into a discrete set of complex-frequency pseudomodes that give a complete and exact description of a quantum emitter coupled to that environment — with no reservoir, no Lorentzian model of the local density of states, and no Markov approximation.Abstract; Equations 5 to 9
The pseudomodes are not imposed but emerge from the equations of motion: evaluating the wavenumber integral in the emitter’s amplitude equation exactly, instead of applying the first Markov approximation, turns a continuous integral into a discrete set of coupled pseudomode equations whose complex frequencies are the resonances of the structure.Equations 6, 7 and 8
The propagation delay from source to observation point enters as a step function and a decaying exponential in retarded time, which keeps the physical field regular even though the pseudomodes themselves diverge at large distance — solving the mode-divergence problem that has obstructed canonical quantisation of non-Hermitian, radiating photonic systems.Equation 10 and the paragraph that follows it
The emitter never decays to the ground state at all. Its energy is dispersed over the continuous spectrum of eigenmodes, which has no inherent decay; the apparent decay of a pseudomode amplitude is the tail of the photon wave packet as it propagates, read at the retarded time.The paragraph beginning ‘By transforming the continuum’
Applied to a one-micrometre silicon sphere of refractive index 3.446, 613 pseudomodes solved together reproduce the full dynamics: Rabi oscillations with the strongly coupled resonance, a Lamb shift from all the off-resonant modes, Markovian behaviour for strongly radiating pseudomodes and non-Markovian behaviour for high-quality ones, and an expanding light cone in the radiated intensity.Figures 2 to 5; Equations 11, 12, 17 and 18
The authors state the next step themselves: the method extends to arbitrary photonic geometries through analytic continuation of the local density of states, and can reveal non-Markovian behaviour in nanoscale systems that are already experimentally realizable.Conclusion, final sentence
The way in
https://doi.org/10.1103/physrevlett.133.203604How to cite it
Ben Yuen, Angela Demetriadou (2024) Exact Quantum Electrodynamics of Radiative Photonic Environments doi:10.1103/physrevlett.133.203604