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arXiv:1104.2989 · Physical Review A

Quantum-interference-initiated superradiant and subradiant emission from entangled atoms

Ralph Wiegner, Joachim von Zanthier, G. S. Agarwal

Published Aug 5, 2011• 80 citations
arXivHTMLPDF

Abstract

We calculate the radiative characteristics of emission from a system of entangled atoms which can have a relative distance larger than the emission wavelength. We develop a quantum multipath interference approach which explains both super- and subradiance though the entangled states have zero dipole moment. We derive a formula for the radiated intensity in terms of different interfering pathways. We further show how the interferences lead to directional emission from atoms prepared in symmetric $W$ states. As a byproduct of our work we show how Dicke's classic result can be understood in terms of interfering pathways. In contrast to the previous works on ensembles of atoms, we focus on finite numbers of atoms prepared in well characterized states.

DOI
10.1103/physreva.84.023805

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We calculate the radiative characteristics of emission from a system of entangled atoms which can have a relative distance larger than the emission wavelength. We develop a quantum multipath interference approach which explains both super- and subradiance though the entangled states have zero dipole moment. We derive a formula for the radiated intensity in terms of different interfering pathways. We further show how the interferences lead to directional emission from atoms prepared in symmetric WWW states. As a byproduct of our work we show how Dicke's classic result can be understood in terms of interfering pathways. In contrast to the previous works on ensembles of atoms, we focus on finite numbers of atoms prepared in well characterized states.
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with a nonvanishing dipole moment. We find that the two configurations produce similar far-field intensity patterns, although they stem from fundamentally distinct types of coherence: while in the second case the atoms display coherence among the individual particles, leading to Young-type interference like that known from classical dipoles, atoms in Dicke states possess collective quantum coherence stemming from entanglement and quantum correlations of the state, leading to an interference pattern resulting from enhanced spontaneous emission. This demonstrates that the radiation generated by synchronized dipoles and Dicke superradiance---even if they do produce the same interference pattern---are fundamentally distinct phenomena and have to be interpreted in different ways.
We investigate Dicke subradiance of N≥2 distant quantum sources in free space, i.e., the spatial emission patterns of spontaneously radiating noninteracting multilevel atoms or multiphoton sources, prepared in totally antisymmetric states. We find that the radiated intensity is marked by a full suppression of spontaneous emission in particular directions. In resemblance to the analogous, yet inverted, superradiant emission profiles of N distant two-level atoms prepared in symmetric Dicke states, we call the corresponding emission patterns directional Dicke subradiance. We further derive that higher-order intensity correlations of the light emitted by statistically independent thermal light sources display the same directional Dicke subradiant behavior and show that it stems from the same interference phenomenon as in the case of quantum sources. We finally present measurements of directional Dicke subradiance for N=2,…,5 distant thermal light sources corroborating the theoretical findings.
Superradiance typically requires preparation of atoms in highly entangled multiparticle states, the so-called Dicke states. In this paper we discuss an alternative route where we prepare such states from initially uncorrelated atoms by a measurement process. By measuring higher-order intensity-intensity correlations we demonstrate that we can simulate the emission characteristics of Dicke superradiance by starting with atoms in the fully excited state. We describe the essence of the scheme by first investigating two excited atoms. Here we demonstrate how via Hanbury Brown and Twiss type of measurements we can produce Dicke superradiance and subradiance displayed commonly with two atoms in the single excited symmetric and antisymmetric Dicke states, respectively. We thereafter generalize the scheme to arbitrary numbers of atoms and detectors, and explain in detail the mechanism which leads to this result. The approach shows that the Hanbury Brown and Twiss type of intensity interference and the phenomenon of Dicke superradiance can be regarded as two sides of the same coin. We also present a compact result for the characteristic functional which generates all order intensity-intensity correlations.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
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.
Fully excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954 [Phys. Rev. 93, 99 (1954)]. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\ensuremath{\lambda}$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of distant noninteracting atoms with mutual separations much larger than $\ensuremath{\lambda}$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.