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Journal of Modern Optics

Properties of far-field fluorescence from an ensemble of interacting Sr atoms

Deshui Yu

Published Aug 20, 2015• 9 citations
Publisher

Abstract

We systematically investigate the far-zone fluorescence from a number of laser-driven two-level atoms with the cooperative effects stemming from the virtual exchange of photons between identical atoms. Due to the large interaction-induced energy level shifts, i.e. the collective Lamb shifts, both atomic excitation and photon emission do not maximize at the resonant light-atom coupling. In addition, the long-range dissipative interactions among atoms lead to the disproportion between the atomic excitation and the photon emission. Moreover, we discuss the temporal properties of the far-field fluorescence light from the atomic ensemble. The first-order correlation function indicates a damped light-atom dynamics combined with a strong background of the elastic photon scattering. The second-order correlation function illustrates that in the weak-excitation limit the scattered light exhibits the nonclassical photon antibunching behavior, while the bunched photons arrive at the photodetector in the saturated-excitation limit.

DOI
10.1080/09500340.2015.1078505

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We systematically investigate the far-zone fluorescence from a number of laser-driven two-level atoms with the cooperative effects stemming from the virtual exchange of photons between identical atoms. Due to the large interaction-induced energy level shifts, i.e. the collective Lamb shifts, both atomic excitation and photon emission do not maximize at the resonant light-atom coupling. In addition, the long-range dissipative interactions among atoms lead to the disproportion between the atomic excitation and the photon emission. Moreover, we discuss the temporal properties of the far-field fluorescence light from the atomic ensemble. The first-order correlation function indicates a damped light-atom dynamics combined with a strong background of the elastic photon scattering. The second-order correlation function illustrates that in the weak-excitation limit the scattered light exhibits the nonclassical photon antibunching behavior, while the bunched photons arrive at the photodetector in the saturated-excitation limit.
We analyze the temporal response of the fluorescence light that is emitted from a dense gas of cold atoms driven by a laser. When the average interatomic distance is comparable to the wavelength of the photons scattered by the atoms, the system exhibits strong dipolar interactions and collective dissipation. We solve the exact dynamics of small systems with different geometries and show how these collective features are manifest in the scattered light properties such as the photon emission rate, the power spectrum and the second-order correlation function. By calculating these quantities beyond the weak (linear) driving limit, we make progress in understanding the signatures of collective behavior in these many-body systems. Furthermore, we shed light on the role of disorder and averaging on the resonance fluorescence, of direct relevance for recent experimental efforts that aim at the exploration of many-body effects in dipole–dipole interacting gases of atoms.
Cooperative scattering has been the subject of intense research in the last years. In this article, we discuss the concept of cooperative scattering from a broad perspective. We briefly review the various collective effects that occur when light interacts with an ensemble of atoms. We show that some effects that have been recently discussed in the context of ‘single-photon superradiance’, or cooperative scattering in the linear-optics regime, can also be explained by ‘standard optics’, i.e. using macroscopic quantities such as the susceptibility or the diffusion coefficient. We explain why some collective effects depend on the atomic density, and others on the optical depth. In particular, we show that, for a large and dilute atomic sample driven by a far-detuned laser, the decay of the fluorescence, which exhibits superradiant and subradiant dynamics, depends only on the on-resonance optical depth. We also discuss the link between concepts that are independently studied in the quantum-optics community and in the mesoscopic-physics community. We show that the coupled-dipole model predicts a departure from Ohm’s law for the diffuse light, that incoherent multiple scattering can induce a saturation of fluorescence and we also show the similarity between the weak-localization correction to the diffusion coefficient and the inaccuracy of Lorentz local field correction to the susceptibility.
Finding a comprehensive and general description of the collective Lamb shift and cooperative broadening in a radiatively interacting system is a long-standing open question. Both energy levels and linewidth of individual atoms are modified by the exchange of real and virtual photons making up the dipole-dipole interaction. We introduce a method to theoretically study weakly-driven, low-excited ensembles of two-level atoms, and obtain an analytic description of the collective Lamb shift and linewidth via a self-consistent formalism including infinite order of correlations which stem from only two-body interactions. We predict the dependency of these quantities, as measurables, on system parameters: the number density of the ensemble, the detuning of an external probe field, and the geometry of the sample.
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Atomic ensembles strongly interacting with light constitute rich quantum-optical many-body systems, with the potential for observing cooperative effects and dissipative nonequilibrium phase transitions. We theoretically analyze the conditions under which a driven atomic ensemble in free space, characterized by strong dipole-dipole interactions and large spatial extent, can undergo a superradiant phase transition, also known as cooperative resonance fluorescence. In an atomic array, stationary states that conserve the collective pseudospin exhibit completely cooperative decay and undergo a second-order phase transition in the large atom number limit. In contrast, decay mechanisms on longer timescales that fail to conserve pseudospin can lead to discontinuous first-order phase transition at a critical finite atom number, disrupting cooperation despite sharing many similar observable characteristics. A hallmark of the superradiant phase transition is an abrupt shift from total light reflection off the atoms to rapidly increasing transmission, accompanied by significant quantum fluctuations, as a function of light intensity.