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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Cooperative Spontaneous Emission and Scattering of Light by Ensembles of Atoms

Roy J. Glauber

Published Jan 1, 2007• 0 citations
Publisher

Abstract

The spontaneous emission of light by groupings of identical atoms is a collective process that takes place only in certain favored radiation modes. These have in general a variety of different lifetimes that obey an interesting sum rule and correspondingly different spectral widths and frequency shifts. The light that these atoms scatter resonantly also reflects this complex structure. Article not available.

DOI
10.1364/cqo.2007.ctuc1

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The spontaneous emission of light by groupings of identical atoms is a collective process that takes place only in certain favored radiation modes. These have in general a variety of different lifetimes that obey an interesting sum rule and correspondingly different spectral widths and frequency shifts. The light that these atoms scatter resonantly also reflects this complex structure. Article not available.
A quantum emitted by any of a collection of identical atoms may be absorbed and re-emitted by other atoms many times before it eventually emerges. The radiation process is thus best described as collective or cooperative in nature. The atomic excitations are shown to attenuate as linear combinations of certain characteristic decay modes that lend a complex structure to the spectrum radiated. Instead of a single line, it becomes a closely-spaced multiplet of lines, the elements of which have a variety of lifetimes, line-shifts and line-widths. We calculate these quantities, first with an abstract two-state model for the atoms and then with an isotropic four-state model that accommodates the full polarization dependence of the radiation.
We present a numerical study of the spatial coherence of light that is radiated from a dilute ensemble of atoms. The spatial coherence is established as a result of the collective (cooperative) coupling of the atoms to the light and is qualitatively different from the coherence of a laser. Specifically, the coherence in collective spontaneous emission does not rely on population inversion and stimulated emission, is governed by antiphasing of the dipoles (subradiance), and the key figure of merit for the observed coherence is $\ensuremath{\approx}N/(L/\ensuremath{\lambda})$. Here, NNN is the number of atoms in the ensemble, LLL is the size of the sample, and $\ensuremath{\lambda}$ is the wavelength of the emitted light.
The absorbed/emitted radiation will be treated classically, as a monochromatic plane wave, whereas the atomic system that can absorb/emit such radiation will be described quantum-mechanically. However, no incident radiation beam is needed, and the atom “falls down” after a certain time interval to the ground state without any external reason. In the spontaneous emission processes the emitting atom can be thought of as a classical oscillating dipole, whose amplitude decreases due to the energy loss through the radiation. If an ensemble of identical atoms is considered and if, for simplicity, each atom emits radiation with the same spectral shape and full width at half maximum, it is impossible to ascribe a definite spectral component with intensity to a definite atom. In this case, such a broadening is identical for all atoms in the ensemble. On the microscopic scale, absorption of radiation is reduced to the transitions between pairs of energy levels of a discrete atomic spectrum.
When a quantum system is put into an excited state, it will decay back to the ground state through a process termed spontaneous emission.It is generally assumed that spontaneous emissions between different individual emitters will not be coherent with each other; to produce coherent light, one would need population inversion and stimulated emission.In this work, we show that an optically thin ensemble of 11 000 radiating atoms spontaneously organizes to produce spatially coherent light.The reason for this coherence is collective coupling of the individual emitters via Dicke superradiance and subradiance (as opposed to amplification through stimulated emission).
We study resonator-induced light forces arising from cooperative atom–light interaction. For such collective processes, the force on the sample can be orders of magnitude larger than the sum of conventional light forces on individual atoms. Since resonator-induced light forces can be dissipative even when the incident light is far detuned from atomic transitions, they may be applicable to target particles with a complex level structure. (Some figures in this article are in colour only in the electronic version)
The spectrum of cooperative light emission from ensembles of multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The effects of counter-rotating terms are included using a unitary transformation method. The spectra are analyzed and interpreted in terms of the radiative eigenmodes of the atom ensemble. We further show how the qualitative features arise from the structure of the underlying two-particle dipole-dipole interaction induced by the the vacuum field. We predict that for a suitable modification of the ensemble properties, the sign of the cooperative Lamb shift can be reversed, while still maintaining strong superradiant emission. Finally, we discuss the effects of finite detection resolution and of averaging over many realizations of the random distribution of atoms for given ensemble parameters.