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Laser Physics

Correlated spontaneous emission on the Volga

Marlan O. Scully

Published May 1, 2007• 84 citations
Publisher

Abstract

In a recent paper [1], the emission of radiation from an ensemble of N atoms excited by a single photon was studied. That paper stimulated spirited discussions and debate. For example, it was argued at the 2006 Volga River conference on quantum control that the important conclusion that follows from the nuclear physics γ-ray studies of this problem was the prediction of the suppression of the resonance level width. In this connection, the results of [1] were argued to be incorrect since no line narrowing was reported. In the present paper, it is shown that there is no radiative suppression associated with the Dicke state given in [1]. However, the interplay between quantum optics (Dicke super and subradiant states) and nuclear physics (forward scattering of γ radiation) provides interesting problems and insights. The present paper is derived from the authors’ lectures and discussions on the subject and is intended to be pedagogical.

DOI
10.1134/s1054660x07050064

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In a recent paper [1], the emission of radiation from an ensemble of N atoms excited by a single photon was studied. That paper stimulated spirited discussions and debate. For example, it was argued at the 2006 Volga River conference on quantum control that the important conclusion that follows from the nuclear physics γ-ray studies of this problem was the prediction of the suppression of the resonance level width. In this connection, the results of [1] were argued to be incorrect since no line narrowing was reported. In the present paper, it is shown that there is no radiative suppression associated with the Dicke state given in [1]. However, the interplay between quantum optics (Dicke super and subradiant states) and nuclear physics (forward scattering of γ radiation) provides interesting problems and insights. The present paper is derived from the authors’ lectures and discussions on the subject and is intended to be pedagogical.
Coherence and interference play crucial roles in emission and absorption of photons to and from large systems with many atoms. Confusion has arisen because nuclear X-ray physicists and atomic quantum-optics physicists do not understand one another's individual descriptions of related phenomena. Basic physics same for all wave lengths from optical to nuclear gamma ray photons. But different languages are used to describe this physics in different domains. Crucial parameters vary over many orders of magnitude and what is intuitive or counterintuitive varies widely. Differences in parameters arising from differences between coherent emission effects in different domains produce very different results. Unified general treatment of the entire photon spectrum makes basic physics intelligible to all. In the optical region the mean distance between the scattering atoms is much longer than the photon wave length, Dicke superradiant scattering is isotropic and multiple scattering, Fano couplings are important and the lifetimes of intermediate stats are sufficiently short to be negligible. In X-ray scattering the mean distance between atoms is comparable to the photon wave length, Dicke superradiance is concentrated in a forward peak, multiple scattering and Fano effects are negligible, lifetimes are measurably long, speedup shortening the lifetime is important and most of the radiation is not elastically scattered but lost to absorption. Explicit calculations for a one-dimensional array shows the great difference between the case where the photon wave length is much shorter or comparable to the distance between nearest neighbors. A full investigation of the angular distribution and speedup of the intensity for two and three-dimensional scatterers give very different results for the two cases.
This report results from a contract tasking Moscow State University as follows: Exploration of methods to control the radiative gamma- processes in nuclei is currently one of the most promising investigation directions of the modern Quantum Nucleonics - a new realm of contemporary Physics which spreads the basic conceptual ideas and methods of optical Quantum Electronics of atoms and molecules to the gamma-ray range and atomic nuclei and even anti-particles. One of the most important problems in this field is the generation of coherent gamma-radiation by a Gamma-ray Lasing (GRL) process which makes use of excited nuclei as an amplifying medium. The most likely medium for gamma-ray lasers is an ensemble of metastable nuclear isomers, Direct excitation of these isomeric states by electrons or X-ray photons will also create a deeper understanding of nuclear structure and properties.
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.
Recent work has shown that collective single photon emission from an ensemble of resonate two-level atoms, i.e., single photon superradiance, is a rich field of study. The present Letter addresses the flip side of superradiance, i.e., subradiance. Single photon subradiant states are potentially stable against collective spontaneous emission and can have ultrafast readout. In particular it is shown how many atom collective effects provide a new way to control spontaneous emission by preparing and switching between subradiant and superradiant states.
Superradiance, i.e., spontaneous emission of coherent radiation by an ensemble of two-level atoms in collective states introduced by Dicke in 1954, is one of the enigmatic problems of quantum optics. The startling gist is that even though the atoms have no dipole moment they radiate with increased intensity in particular directions. Following the advances in our understanding of superradiant emission by atoms in entangled W-states we examine the quantum statistical properties of superradiance. Such investigations require the system to have at least two excitations in order to explore the photon-photon correlations of the radiation emitted by such states. We present specifically results for the spatially resolved photon-photon correlations of systems prepared in doubly excited W-states and give conditions when the atomic system emits nonclassial light. Equally, we derive the conditions for the occurrence of bunching and even of superbunching, a rare phenomenon otherwise known only from nonclassical states of light like the squeezed vacuum. We finally investigate the photon-photon cross correlations of the spontaneously scattered light and highlight the nonclassicalty of such correlations. The theoretical findings can be implemented with current technology, e.g., using ions in a linear rf-trap, atoms in an optical lattice or quantum dots in a cavity.
The problem of the interaction of N atoms with a laser beam and vacuum modes can give rise to many interesting phenomena concerning the spontaneous emission of light and its propagation in the medium. The cooperative effects, for example, such as superadiance and subradiance, are effects related to the coherence created between the atoms when a photon is emitted spontaneously by a single excited atom. Superradiance can be defined as the enhancement of the spontaneous emission due to constructive interference of the scattered light. Its counterpart, subradiance, is the trapping of some remaining light due to destructive interference. In cold atoms, some previous theoretical works predict and characterize these two cooperative effects in a large and diluted atomic cloud, in the regime of low intensities and large detunings of the incident laser. The theoretical model is a coupled-dipole model for two-level atoms driven by a low-intensity field and in the scalar approach. The experiment consists in measuring the super- and subradiant decay rates from the temporal emitted intensity after the switch off of the incident laser in the steady state. Our experimental setup consists in a magneto-optical trap of rubidium 87 atoms at large resonant optical thicknesses. A probe beam excites the atoms close to the D2 line. The intensity emitted is detected by a single photon detector with no afterpulsing and a calibration procedure allows us to determine the resonant optical thickness of the cloud and its temperature. In this work, we report the experimental observation of super- and subradiance in a large cloud of cold atoms. For subradiance, the main result is the linear evolution of the characteristic time with the resonant optical thickness of the cloud and its independence of the detuning. For superradiance, we observe superradiance out of the forward direction. We verify the validity of our interpretations with the predictions of the coupled-dipole model. Finally, we discuss the interplay of subradiance and radiation trapping, as well as theoretical predictions for: a setup of a phased cloud, to control the subradiant amplitude emission; and temperature effects, where subradiance is shown to be robust in a large range of temperatures.