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Physical Review A

Superradiant pulses and directed angular momentum states

Roy J. Glauber, Fritz Haake

Published Jan 1, 1976• 112 citations
Publisher

Abstract

We investigate the statistical properties of superradiant pulses emitted by a system of many atoms. By using a representation of the atomic density operator in terms of directed angular-momentum states (which are also known as atomic coherent states), we find that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise. The emitted light pulses are then found to exhibit very large quantum fluctuations for atomic initial states corresponding to complete or nearly complete excitation. For all other atomic initial states the superradiant pulses show classical behavior.

DOI
10.1103/physreva.13.357

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We investigate the statistical properties of superradiant pulses emitted by a system of many atoms. By using a representation of the atomic density operator in terms of directed angular-momentum states (which are also known as atomic coherent states), we find that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise. The emitted light pulses are then found to exhibit very large quantum fluctuations for atomic initial states corresponding to complete or nearly complete excitation. For all other atomic initial states the superradiant pulses show classical behavior.
We investigate the statistical aspects of the cooperative emission of radiation by a system of many atoms. By solving the equation of motion for a suitably defined quasiprobability distribution which represents the density operator of the atoms, we find explicit expressions for the expectation values of products of atomic observables. The system is found to exhibit large quantum fluctuations for the most highly excited initial states of the atoms. For all others it exhibits nearly classical behavior. Previous numerical evaluations of the radiated intensity and its variance are found to be in good agreement with the present results.
We investigate the statistical aspects of the cooperative emission of radiation by a system of many atoms. By solving the equation of motion for a suitably defined quasiprobability distribution which represents the density operator of the atoms, we find explicit expressions for the expectation values of products of atomic observables. The system is found to exhibit large quantum fluctuations for the most highly excited initial states of the atoms. For all others it exhibits nearly classical behavior. Previous numerical evaluations of the radiated intensity and its variance are found to be in good agreement with the present results.
We discuss the solution of the "superradiance master equation" derived in a preceding paper. During the first few photon transient times the cooperative atomic decay goes through a non-adiabatic oscillatory regime. For later times the decay takes place monotonically in time with the electromagnetic field following it adiabatically. The emitted light pulse has different statistical properties for an incoherently and a coherently prepared "superradiant" atomic initial state. The former case is characterized by large quantum fluctuations and strong atom-atom and atom-field correlations. In the latter case quantum fluctuations are small and the system behaves essentially classically. By also solving for a class of coherently prepared intermediate initial states we show that large quantum fluctuations occur only if the initial total occupancy of the excited state differs from the total number of atoms at most by a number of order unity.
A system of many #we-level atoms or molecules in a collective Dieke state (1) interacting with a single resonant mode of the quantized radiation field has often been adopted as a quantum-mechanical model for a point laser (2). In a previous paper (3) we reported exact dosed-form solutions and photon statistics of coherent spontaneous emission for the model atom-field state in the l imit of infinitely large co-operation number. The purpose of this paper is to report more general results based on this modeI. We give the exact closed-form solutions and photon statistics of coherent emission in the presence of an applied field for the model atom-field state in the same limit. For an initial atomic Dicke state interacting with an applied field in a coherent (Glauber) state (a), the emitted pulse can be desoribed in terms of Glauber states only when the levels of excitation of the initial Dicke states are (~ superradiant ~ (~). For an initially highly inverted system or low excited system, the photon distributions undergo large fluctuations. The model interaction Hamil tonian is given by
Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.
We investigate the stimulated emission of superradiant atoms coupled to a waveguide induced by a coherent-state photon pulse. We provide an analytical result when a short π pulse is incident, which shows that the atoms emit photons coherently into the output pulse, which remains a coherent state in the short pulse limit. An incident pulse is amplified in a phase-preserving manner, where noise is added almost entirely in the phase direction in phase space. This property improves the ratio of the intensity signal to noise after the amplification for sufficiently short pulses. This is a unique feature different from general phase-preserving linear amplifiers, where the signal-to-noise ratio deteriorates in the amplification process. We also discuss the dependence of the photon-emission probability on pulse parameters, such as the pulse area and the duration.