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Physical Review A

Hidden equivalence in the collective emission from a dilute atomic cloud

Anwei Zhang, Xianfeng Chen, Luqi Yuan

Published Feb 22, 2019• 0 citations
Publisher

Abstract

We investigate the collective spontaneous emission from an ensemble of two-level atoms evenly distributed inside a sphere with a low density. An initial symmetric single-excitation state is considered and polarizations for all atoms are assumed to be aligned in the same direction. We find that the superradiant decay rate of the ensemble exhibits oscillatory features dependent on the radius of the sphere and the atomic radiation wavelength, indicating that the collective emission rate can be less than the single-atom decay rate for certain parameters. Moreover, the system exhibits a hidden equivalence where the collective emission from the ensemble gives the same radiation rate as the case of a two-atom model where one atom is at the center of the sphere and the other effective large atom, composed of all other atoms, is localized at the edge of the sphere along the polarization direction. Our result hence provides a potential method towards exploring complex many-body physics by simplifying the model into a two-body problem.

DOI
10.1103/physreva.99.023842

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We investigate the collective spontaneous emission from an ensemble of two-level atoms evenly distributed inside a sphere with a low density. An initial symmetric single-excitation state is considered and polarizations for all atoms are assumed to be aligned in the same direction. We find that the superradiant decay rate of the ensemble exhibits oscillatory features dependent on the radius of the sphere and the atomic radiation wavelength, indicating that the collective emission rate can be less than the single-atom decay rate for certain parameters. Moreover, the system exhibits a hidden equivalence where the collective emission from the ensemble gives the same radiation rate as the case of a two-atom model where one atom is at the center of the sphere and the other effective large atom, composed of all other atoms, is localized at the edge of the sphere along the polarization direction. Our result hence provides a potential method towards exploring complex many-body physics by simplifying the model into a two-body problem.
We consider collective emission of a single photon from a cloud of NNN two-level atoms (one excited, $N\ensuremath{-}1$ ground state). For a dense cloud the problem is reduced to finding eigenfunctions and eigenvalues of an integral equation. We discuss an exact analytical solution of this many-atom problem for a spherically symmetric atomic cloud. Some eigenstates decay much faster then the single atom decay rate, while the others undergo very slow decay. We show that virtual processes yield a small effect on the evolution of rapidly decaying states. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important yielding additional decay channels which results in a slow decay of the otherwise trapped states. We also show that quantum mechanical treatment of spontaneous emission of weakly excited atomic ensemble is analogous to emission of NNN classical harmonic oscillators.
We study emission of a single photon from a spherically symmetric cloud of NNN atoms (one atom is excited; $N\ensuremath{-}1$ are in the ground state) and present an exact analytical expression for eigenvalues and eigenstates of this many-body problem. We found that some states decay much faster than the single-atom decay rate, while other states are trapped and undergo very slow decay. When the size of the atomic cloud is small compared with the radiation wavelength, we found that the radiation frequency undergoes a large shift.
Recent works have shown that collective single photon spontaneous emission from an ensemble of N resonant two-level atoms is a rich field of study. Superradiance describes emission from a completely symmetric state of N atoms, with a single excited atom prepared with a given phase, for instance imprinted by an external laser. Instead, subradiance is associated with the emission from the remaining N−1 asymmetric states, with a collective decay rate less than the single-atom value. Here, we discuss the properties of the orthonormal basis of symmetric and asymmetric states and the entanglement properties of superradiant and subradiant states.
We study the collective radiation properties of cold, trapped ensembles of atoms. We consider the high-density regime with the mean interatomic distance being comparable to, or smaller than, the wavelength of the resonant optical radiation emitted by the atoms. We find that the emission rate of a photon from an excited atomic ensemble is strongly enhanced for an elongated cloud. We analyze collective single-excitation eigenstates of the atomic ensemble and find that the absorption-emission spectrum is broadened and shifted to lower frequencies as compared to the noninteracting (low-density) or single-atom spectrum. We also analyze the spatial and temporal profile of the emitted radiation. Finally, we explore how to efficiently excite the collective superradiant states of the atomic ensemble from a long-lived storage state in order to implement matter-light interfaces for quantum computation and communication applications.
The collective scattering of light by a large number of coupled scatterers yields a rich many-body physics, yet treating such a problem in the quantum regime is a challenge.In this thesis, we consider a large atomic cloud in free space and driven by a monochromatic light, where the vacuum modes induce long-range dipole-dipole interactions.In order to study clouds of hundreds of particles, higher order correlation terms are neglected, keeping only quantum correlations between pair of atoms: this allows to reduce the number of degrees of freedom from 2 2N in the full quantum model to N 2 .Most of the works in the literature on dipole-dipole interactions have been performed in the linear optics limit, and our techniques allow to compare classical to beyond-semi-classical results.In particular, superradiance and subradiance have been reported in the decay dynamics of the cloud.Differently, by considering a system in the ground state and switching on the pump, we show that superradiance is also present in the Rabi oscillations at a rate obtained from using a single-dipole model for the radiated intensity.A frequency shift in the Rabi oscillations is also reported, which can be interpreted, in a linear dispersion theory, as a signature of a collective multimode vacuum Rabi splitting.While the classical dipoles model captures correctly the dynamics in the low-intensity regime, it fails for higher saturation, where semi-classical methods can be applied successfully.In particular, we observe a quantum subradiant decay in the intensity of the radiated field in the saturated regime.Furthermore, considering the decay dynamics starting from an initially strongly driven cloud, we observed that the states with n < N/2 excited atoms decays much slower than the ones with n > N/2: in other words, the upper part of the Dicke ladder is characterized by a superradiant emission, and the lower part by a subradiant one.Finally, investigating the fluorescence spectrum, we obtained quantum cooperative effects that modify the steady-state spectrum: additional sidebands at twice the Rabi frequency for the system driven at resonance and, out of resonance, an asymmetry in the peaks at the generalized Rabi frequency, and for all detection angles.We also present preliminary results of a sensor model that can capture the time evolution of the spectrum in the decay dynamics, a situation that the quantum regression theorem fails to describe.Several of these results were discussed in parallel with experimental data obtained by an experimental group of collaborators, and others aim to guide future experiments.
We introduce a straightforward quantum-electrodynamic approach to the problem of superradiant spontaneous emission from a system of two-level atoms, and also discuss two classical superradiant systems. The same physical concepts underlie our treatment of both the quantum and classical cases. Explicit expressions are found which describe the time evolution and directional character of the radiated power. Our approach applies to an arbitrary number of atoms which are confined to a region with linear dimensions which may be large compared with the mean wavelength of the emitted radiation. The radiative decay half-life of a large many-atom system is found to be much shorter than the natural lifetime of a single atom, but not as short as the half-life of a small atomic system with the same number of atoms. The far-field radiation pattern appropriate to the case of a circular cylinder of emitters which have been excited by a plane-wave pulse is considered in detail. Polar plots are presented of the radiation patterns produced when the atoms are excited by a plane-wave pulse. Exciting pulses traveling in directions both parallel and at an angle of 10\ifmmode^\circ\else\textdegree\fi{} to the axis of the cylinder are considered. A discussion and generalization of Dicke's "coherence-brightening" criterion is given.