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Physical Review A

Nonlocal effects in single-photon superradiance

Anatoly A. Svidzinsky

Published Jan 17, 2012• 31 citations
Publisher

Abstract

We consider influence of nonlocal (retardation) effects caused by the finite value of the speed of light on collective emission of a single photon by atomic ensembles. Using a fully quantum mechanical description of light and atoms we obtain an evolution equation for the atomic system that takes into account retardation. We found an exact analytical solution of this equation for the atomic slab geometry that yields insight on how the crossover between local and nonlocal dynamics occurs. In particular, it shows that initially nonlocal evolution, accompanied by collective oscillations of atomic population, becomes local at large time. In addition, atomic excitation in some parts of the sample rises above its initial value. We propose an experiment in which the transition between local and nonlocal regimes can be observed by increasing the size of the atomic sample or atomic density.

DOI
10.1103/physreva.85.013821

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Journal of Physics B Atomic and Molecular Physics•Mar 14, 1987•17 citations
We consider influence of nonlocal (retardation) effects caused by the finite value of the speed of light on collective emission of a single photon by atomic ensembles. Using a fully quantum mechanical description of light and atoms we obtain an evolution equation for the atomic system that takes into account retardation. We found an exact analytical solution of this equation for the atomic slab geometry that yields insight on how the crossover between local and nonlocal dynamics occurs. In particular, it shows that initially nonlocal evolution, accompanied by collective oscillations of atomic population, becomes local at large time. In addition, atomic excitation in some parts of the sample rises above its initial value. We propose an experiment in which the transition between local and nonlocal regimes can be observed by increasing the size of the atomic sample or atomic density.
To build up a collective emission, the atoms in an ensemble must coordinate their behavior by exchanging virtual photons. We study this non-Markovian process in a subwavelength atom chain coupled to a one-dimensional (1D) waveguide and find that retardation is not the only cause of non-Markovianity. The other factor is the memory of the photonic environment, for which a single excited atom needs a finite time, the Zeno regime, to transition from quadratic decay to exponential decay. In the waveguide setup, this crossover has a time scale longer than the retardation, thus impacting the development of collective behavior. By comparing a full quantum treatment with an approach incorporating only the retardation effect, we find that the field memory effect, characterized by the population of atomic excitation, is much more pronounced in collective emissions than that in the decay of a single atom. Our results maybe useful for the dissipation engineering of quantum information processings based on compact atom arrays.
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.
As shown by Hegerfeldt, positivity of energy in quantum mechanics leads to nonlocal effects, where a state that is initially localized immediately develops infinite tails. In a previous paper we have described the mechanism of such effects for relativistic free fields. In this paper we discuss the nonlocal effects for a more complex system that consists of a two-level atom interacting with a radiation field. We study the dressing process of the bare ground state in terms of the photon density. In this process there appears a nonlocal cloud that remains around the atom and ``Zeno'' photons that move away from the atom with the speed of light. Nonlocality is seen to be to due to a ``curtain'' effect where the cloud is initially covered by the Zeno photons, and immediately afterwards is uncovered as the photons move away from the atom. No superluminal speeds are involved. We also consider nonlocal effects associated with a partially dressed state where the atom is excited starting from the true ground state. The excitation of the atom produces a nonlocal rearrangement of the photon cloud, which leads to precursors to the usual retarded field.
The collective nature of light emission by atomic ensembles yields fascinating effects such as superradiance and radiation trapping even at the single-photon level. Light emission is influenced by virtual transitions and the collective Lamb shift which yields peculiar features in temporal evolution of the atomic system. We study how two-dimensional atomic structures collectively emit a single photon. Namely, we consider spherical, cylindrical, and spheroidal shells with two-level atoms continuously distributed on the shell surface and find exact analytical solutions for eigenstates of such systems and their collective decay rates and frequency shifts. We identify states which undergo superradiant decay and states which are trapped and investigate how size and shape of the shell affects collective light emission. Our findings could be useful for quantum information storage and the design of optical switches.
The collective nature of light emission by atomic ensembles yields fascinating effects such as superradiance and radiation trapping even at the single-photon level.Light emission is influenced by virtual transitions and the collective Lamb shift which yields peculiar features in temporal evolution of the atomic system.We study how two-dimensional atomic structures collectively emit a single photon.Namely, we consider spherical, cylindrical, and spheroidal shells with two-level atoms continuously distributed on the shell surface and find exact analytical solutions for eigenstates of such systems and their collective decay rates and frequency shifts.We identify states which undergo superradiant decay and states which are trapped and investigate how size and shape of the shell affects collective light emission.Our findings could be useful for quantum information storage and the design of optical switches.
For pt.II see ibid., vol.19, p.2109 (1986). This paper is the third in a theoretical study of subradiance, i.e. the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. The paper is devoted to the problem of the cooperative spontaneous emission of atomic samples with linear dimensions much smaller than the wavelength of the emitted light. The treatment, which is based on a fully quantum mechanical description of the problem, corroborates the results obtained in a semiclassical treatment by Friedberg and Hartmann (1974). Starting from a master equation describing both the cooperative spontaneous emission and the dipole-dipole interaction, a statistical treatment of the latter is introduced and the corresponding symmetry relaxation is studied. The evolution of the atoms is described in three typical cases that correspond to different sample geometries and/or atomic distributions. In one of these cases, in particular, the symmetry is first conserved and the atoms follow Dicke's predictions for a time. A 'retarded' symmetry breaking then occurs suddenly, near the zero value of the collective energy, as in Friedberg and Hartmann's calculations for a small sphere. With regard to the further evolution of the atoms in this case, which cannot be studied in a semiclassical model, it is shown that the decay rate quickly becomes much smaller than the incoherent decay rate. An unquestionable subradiance phenomenon is thus predicted in this case.