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Laser Physics

Size dependence of single-photon superradiance of cold and dilute atomic ensembles

A. S. Kuraptsev, Igor M. Sokolov

Published Oct 12, 2017• 4 citations
Publisher

Abstract

Abstract We report a theoretical investigation of angular distribution of a single-photon superradiance from cold and dilute atomic clouds. In the present work we focus our attention on the dependence of superradiance on the size and shape of the cloud. We analyze the dynamics of the afterglow of atomic ensemble excited by pulse radiation. Two theoretical approaches are used. The first is the quantum microscopic approach based on a coupled-dipole model. The second approach is random walk approximation. We show that the results obtained in both approaches coincide with a good accuracy for incoherent fluorescence excited by short resonant pulses. We also show that the superradiance decay rate changes with size differently for radiation emitted into different directions.

DOI
10.1088/1555-6611/aa761c

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Abstract We report a theoretical investigation of angular distribution of a single-photon superradiance from cold and dilute atomic clouds. In the present work we focus our attention on the dependence of superradiance on the size and shape of the cloud. We analyze the dynamics of the afterglow of atomic ensemble excited by pulse radiation. Two theoretical approaches are used. The first is the quantum microscopic approach based on a coupled-dipole model. The second approach is random walk approximation. We show that the results obtained in both approaches coincide with a good accuracy for incoherent fluorescence excited by short resonant pulses. We also show that the superradiance decay rate changes with size differently for radiation emitted into different directions.
On the basis of a quantum microscopic approach we study the dynamics of the afterglow of a dilute Gaussian atomic ensemble excited by pulsed radiation. Taking into account the vector nature of the electromagnetic field we analyze in detail the angular and polarization distribution of single-photon superradiance of such an ensemble. The dependence of the angular distribution of superradiance on the length of the pulse and its carrier frequency as well as on the size and the shape of the atomic clouds is studied. We show that there is substantial dependence of the superradiant emission on the polarization and the direction of fluorescence. We observe essential peculiarities of superradiance in the region of the forward diffraction zone and in the area of the coherent backscattering cone. We demonstrate that there are directions for which the rate of fluorescence is several times more than the decay rate of the timed-Dicke state. We show also that single-photon superradiance can be excited by incoherent excitation when atomic polarization in the ensemble is absent. Besides a quantum microscopic approach, we analyze single-photon superradiance on the basis of the theory of incoherent multiple scattering in optically thick media (random walk theory). In the case of very short resonant and long nonresonant pulses we derive simple analytical expressions for the decay rate of single-photon superradiance for incoherent fluorescence in an arbitrary direction.
Abstract The fluorescence dynamics of optically dense but dilute atomic ensembles cooled to sub-Doppler temperatures and excited by resonant pulsed radiation is studied. Apart from total radiation intensity, the temporal variations of the spectral composition of fluorescence and its polarization, as well as the variation of the spatial distribution of excitation in the atomic ensemble, are analyzed. Based on this analysis, it is shown that the role of radiation trapping becomes smaller with time, and subradiance quantum states formed as a result of the resonant dipole–dipole interatomic interaction become the main factor determining the slow atomic excitation decay. The dependence of the subradiance form on the ensemble size is analyzed.
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.
The dynamics of the fluorescence of dilute atomic ensembles excited by resonant pulsed radiation has been analyzed. It has been found that the motion of atoms in ensembles cooled to sub-Doppler temperatures in certain time intervals noticeably enhances subradiance rather than suppressing it. It has also been shown that the time dependence of the spontaneous decay rate can be nonmonotonic. The revealed features occur because the character of the slow decay of the atomic excitation is determined after a certain time mainly by the dynamics of subradiant two-atom quantum states, which are due to the resonant dipole–dipole interaction between atoms.
The dynamics of the fluorescence of dilute atomic ensembles excited by resonant pulsed radiation has been analyzed. It has been found that the motion of atoms in ensembles cooled to sub-Doppler temperatures in certain time intervals noticeably enhances subradiance rather than suppressing it. It has also been shown that the time dependence of the spontaneous decay rate can be nonmonotonic. The revealed features occur because the character of the slow decay of the atomic excitation is determined after a certain time mainly by the dynamics of subradiant two-atom quantum states, which are due to the resonant dipole–dipole interaction between atoms.
In this work we present a numerical and experimental investigation of the collective early-time decay rates of a strongly driven and optically dense cold atomic cloud. We prepare the atomic ensemble by driving the system to its steady state with varying Rabi frequencies ΩΩΩ that go from the weak Ω≪ΓΩ\ll ΓΩ≪Γ to the strong driving regime Ω≫ΓΩ\gg ΓΩ≫Γ, where ΓΓΓ is the single-atom decay rate. We investigate the early-time dynamics in the transition between the strong and weak driving regimes using: i) angular-dependent observables such as the light emitted by the cloud, and ii) global observables, i.e., the excited state population. When driving the cloud on-resonance, we find that as a function of the driving frequency, the behavior of the collected light at certain angles transitions from the single-photon subradiant regime to a superradiant regime while the behavior of the excited state population does not show superradiance. The experiment shows good agreement with numerical predictions in the regime of parameters under study.