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arXiv:1707.05237

Superradiance and subradiance in extended media

Jonathan Schonfeld

Published Jun 20, 2017• 0 citations
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Abstract

In super- or subradiance, a quantum superposition of excited atoms collectively emits a photon much more or much less rapidly than an isolated atom. Superradiant and subradiant lifetimes have been derived for finite spheres of uniform media, either by simulating random samples or by expanding in spherical harmonics and analyzing Bessel functions. We introduce a simple regulator that applies to unbounded media, enabling trivial derivation and analysis of lifetimes via elementary Fourier techniques. The regulator can be interpreted as a correlation length for atomic positions; the regularized system describes localized regions of enhanced radiative activity in otherwise quiescent surroundings.

DOI
10.48550/arxiv.1707.05237

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In super- or subradiance, a quantum superposition of excited atoms collectively emits a photon much more or much less rapidly than an isolated atom. Superradiant and subradiant lifetimes have been derived for finite spheres of uniform media, either by simulating random samples or by expanding in spherical harmonics and analyzing Bessel functions. We introduce a simple regulator that applies to unbounded media, enabling trivial derivation and analysis of lifetimes via elementary Fourier techniques. The regulator can be interpreted as a correlation length for atomic positions; the regularized system describes localized regions of enhanced radiative activity in otherwise quiescent surroundings.
Superradiance and subradiance are collective effects that emerge from coherent interactions between quantum emitters. Due to their many-body nature, theoretical studies of extended samples with length larger than the atomic transition wavelength are usually restricted to their early-time behavior or to the few-excitation limit. We use herein a mean-field approach to reduce the complex many-body system to an effective two-atom master equation that includes all correlations up to second order and that can be numerically propagated in time. We find that three-dimensional and two-dimensional inverted atomic arrays sustain superradiance below a critical lattice spacing and quantify the scaling of the superradiant peak for both dimensionalities. Finally, we study the late-time dynamics of the system and demonstrate that a subradiant phase appears before the system finally relaxes.
We have developed a novel method to describe superradiance and related cooperative and collective effects in a closed form. Using the method we derive a two-atom master equation in which any complexity of atomic levels, semiclassical coupling fields and quantum fluctuations in the fields can be included, at least in principle. As an example, we consider the dynamics of an initially inverted two-level system and show how even such in a simple system phenomena such as the initial radiation burst or broadening due to dipole-dipole interactions occur, but it is also possible to estimate the population of the subradiant state during the radiative decay. Finally, we find that correlation only, not entanglement is responsible for superradiance.
Abstract Single photon emission from a collection of resonantly excited two-level atoms is an expanding field. Recent work has shown single photon superradiance from an extended ensemble yields enhanced directional spontaneous emission. This paper presents an operator which commutes with the observables and breaks their degeneracy for the single photon states. Its eigenvectors are a unimodular basis for the single photon states. A simple scheme is given for writing out these states directly without iterative construction and without requiring recourse to Gram–Schmidt orthogonalization. A relatively simple scheme is proposed for experimental realization. In the final part of the paper the mathematical method is extended to generate cooperative states with smaller cooperativity number R .
We consider the problem of two-photon cooperative emission in systems of two-level atoms. Two physically distinct regimes are analyzed. First, we investigate the case of a small number of atoms. We study the evolution of two-photon super- and sub-radiant states and associated two-photon spectra. Second, we investigate the problem of a constant density of atoms confined to a spherical volume. We analyze separately the cases in which the radius is small or large in comparison to the resonant wavelength.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.
Dipole-dipole interactions are at the origin of long-lived collective atomic states, often called subradiant, which are explored for their potential use in novel photonic devices or in quantum protocols. Here, we study subradiance beyond the single-excitation regime and experimentally demonstrate a 200-fold increase in the population of these modes, as the saturation parameter of the driving field is increased. We attribute this enhancement to a mechanism similar to optical pumping through the well-coupled superradiant states. The lifetimes are unaffected by the pump strength, as the system is ultimately driven toward the single-excitation sector. Our study is a new step in the exploration of the many-body dynamics of large open systems.