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arXiv:1603.02522 · Physical Review A

Decoherence by spontaneous emission: A single-atom analog of superradiance

Reinaldo de Melo e Souza, François Impens, Paulo A. Maia Neto

Published Dec 16, 2016• 4 citations
arXivHTMLPDF

Abstract

We show that the decoherence of the atomic center-of-mass induced by spontaneous emission involves interferences corresponding to a single-atom analog of superradiance. We use a decomposition of the stationary decoherence rate as a sum of local and nonlocal contributions obtained to second order in the interaction by the influence functional method. These terms are respectively related to the strength of the coupling between system and environment, and to the quality of the information about the system leaking into the environment. While the local contribution always yields a positive decoherence rate, the nonlocal one may lead to recoherence when only partial information about the system is obtained from the disturbed environment. The nonlocal contribution contains interferences between different quantum amplitudes leading to oscillations of the decoherence rate reminiscent of superradiance. These concepts, illustrated here in the framework of atom interferometry within a trap, may be applied to a variety of quantum systems.

DOI
10.1103/physreva.94.062114

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We show that the decoherence of the atomic center-of-mass induced by spontaneous emission involves interferences corresponding to a single-atom analog of superradiance. We use a decomposition of the stationary decoherence rate as a sum of local and nonlocal contributions obtained to second order in the interaction by the influence functional method. These terms are respectively related to the strength of the coupling between system and environment, and to the quality of the information about the system leaking into the environment. While the local contribution always yields a positive decoherence rate, the nonlocal one may lead to recoherence when only partial information about the system is obtained from the disturbed environment. The nonlocal contribution contains interferences between different quantum amplitudes leading to oscillations of the decoherence rate reminiscent of superradiance. These concepts, illustrated here in the framework of atom interferometry within a trap, may be applied to a variety of quantum systems.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.
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The transversely confined propagating modes of an optical fiber mediate virtually infinite range energy exchanges among atoms placed within their field, which adds to the inherent free space dipole–dipole coupling. Typically, the single atom free space decay rate largely surpasses the emission rate into the guided fiber modes. However, scaling up the atom number as well as the system size amounts to entering a collective emission regime, where fiber-induced superradiant spontaneous emission dominates over free space decay. We numerically study this super- and subradiant decay of highly excited atomic states for one or several transverse fiber modes as present in hollow core fibers. As particular excitation scenarios we compare the decay of a totally inverted state to the case of π /2 pulses applied transversely or along the fiber axis as in standard Ramsey or Rabi interferometry. While a mean field approach fails to correctly describe the initiation of superradiance, a second-order approximation accounting for pairwise atom–atom quantum correlations generally proves sufficient to reliably describe superradiance of ensembles from two to a few hundred particles. In contrast, a full account of subradiance requires the inclusion of all higher order quantum correlations. Considering multiple guided modes introduces a natural effective cut-off for the interaction range emerging from the dephasing of different fiber contributions.
Atom coherence in the cooperative interaction between the atoms and a single photon creates ultrafast spontaneous emission and ultrastrong intensity peaks, namely single-photon superradiance, which has attracted considerable research interest in the recent years. As the investigation for such a single-photon superradiance usually involves only quantum emitters, in this paper we present the cooperative atom-photon interaction in a system including whispering gallery mode resonators, which are one of the most essential components in nanophotonic devices. Here we both analytically and computationally show that the separated atoms on a resonator can obtain cooperative interaction, manifesting superradiant coupling strength, which results in the ultrafast spontaneous emission and ultrastrong intensity peaks. The conditions of such single-photon superradiance are called whispering gallery mode superradiance conditions. Furthermore, the atoms are proved to have cooperative interaction on a cascade of resonators by a renormalization approach.
Spontaneous emission of an excited two-level nonrelativistic atom is examined in the Schr\"odinger picture by treating the atom's external and internal degrees of freedom on the same quantum footing. After all atomic transitions that lead to the evolution of this atom-vacuum system are analyzed, it is found that the atom's spontaneous emission rate is reduced by its center-of-mass motion. It is also found that, as a result of the entanglement between atomic and photonic states, the spontaneous emission process cannot be explained as a process that takes place in one coordinate system moving with the atom but is observed in another stationary system.
Second-order interference effects in the spontaneous emission by two identical two-level atoms, separated a distance apart and both initially excited, are considered. On the basis of the analysis in our previous paper published in 2004, within fourth-order perturbation, detailed analysis of the second-order quantum interference in the emitted field is made. The interference arises both from single-photon states and two-photon states owing to interferences between different decaying sequences. By detailed analysis we have found some cancellations between single-photon and two-photon interference terms, and an interpretation of this is given. The contributions from the single- and the two-photon states as well as the total interference are analysed numerically for various interatomic distances and times. The contribution from a two-photon state is mostly larger than that from a single-photon state except when the atomic electric dipole is large, in which case the two contributions can be comparable. It is shown that the emission patterns from the two interacting atoms provide more information on atom–atom correlations than the decay time evolution of the atomic states population does. The number of interference fringes and the distance between them depend on the interatomic distance in a similar fashion to Young's interference fringes.