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arXiv:1504.05077 · Physical Review Letters

Cooperative Emission of a Pulse Train in an Optically Thick Scattering Medium

Chang Chi Kwong, Tao Yang, Dominique Delande, Romain Pierrat, David Wilkowski

Published Nov 24, 2015• 55 citations
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Abstract

An optically thick cold atomic cloud emits a coherent flash of light in the forward direction when the phase of an incident probe field is abruptly changed. Because of cooperativity, the duration of this phenomena can be much shorter than the excited lifetime of a single atom. Repeating periodically the abrupt phase jump, we generate a train of pulses with short repetition time, high intensity contrast, and high efficiency. In this regime, the emission is fully governed by cooperativity even if the cloud is dilute.

DOI
10.1103/physrevlett.115.223601

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An optically thick cold atomic cloud emits a coherent flash of light in the forward direction when the phase of an incident probe field is abruptly changed. Because of cooperativity, the duration of this phenomena can be much shorter than the excited lifetime of a single atom. Repeating periodically the abrupt phase jump, we generate a train of pulses with short repetition time, high intensity contrast, and high efficiency. In this regime, the emission is fully governed by cooperativity even if the cloud is dilute.
We study the coherent transmission of light through cold strontium atomic clouds, using the narrow intercombination line. In the first part of the thesis, the cooperative emission in the coherent transmission is studied experimentally. By applying fast changes to the incident probe field, flashes of light are observed in the forward direction. The peak intensity of the flashes can be much larger than the incident intensity. These flashes are called superflashes. Due to cooperative effect, the time scale of the flashes are shortened with respect to the single scatterer lifetime. By packing these flashes, we generate a pulse train with short repetition time, where the dynamics can almost be fully governed by cooperative effect. The effect of atomic density on the coherent transmission of light is also studied theoretically and numerically. The effective refractive index of the cloud is calculated up to the second order in atomic density. It is eventually validated with a numerical simulation of the coherent light transmission. The second part of the thesis focuses on the effect of magnetic field on the coherent transmission of light. The strontium intercombination line has a sensitivity in the milligauss regime, which is the typical value of stray magnetic field in the lab. An active magnetic field control system is implemented to cancel the low frequency and AC 50~Hz stray magnetic field. Using this control system, we study the nonlinear magneto-optical rotation (NMOR) effect due to a high intensity light field transmitting through a dilute and thin cloud of strontium atom. Interestingly, at sufficiently high cloud temperature, the NMOR effect can have a higher sensitivity to the magnetic field, compared to its linear counterpart at the same cloud temperature.
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.
Scully and coworkers [M. O. Scully, E. S. Fry, C. H. R. Oii, and K. W\'odkiewicz, Phys. Rev. Lett. 96, 010501 (2006)] demonstrated that there is directional, phase-matched emission following the excitation of an ensemble of atoms by a single-photon pulse. While the phase-matched emission intensity is proportional to the the number of atoms, for optically thin samples the total energy emitted in the phase-matched direction is much less than that radiated in other directions. Moreover, even for optically thin samples, it is necessary to take into account effects related to cooperative decay if energy is to be conserved in the overall emission process. An analytic calculation is presented to show explicitly how cooperative decay reduces the incoherent emission and restores energy conservation in this low-density limit.
Cooperative scattering in cold atoms has gained renewed interest, in particular in the context of single-photon superradiance, with the recent experimental observation of super- and subradiance in dilute atomic clouds. Numerical simulations to support experimental signatures of cooperative scattering are often limited by the number of dipoles which can be treated, well below the number of atoms in the experiments. In this paper, we provide systematic numerical studies aimed at matching the regime of dilute atomic clouds. We use a scalar coupled-dipole model in the low excitation limit and an exclusion volume to avoid density-related effects. Scaling laws for super- and subradiance are obtained and the limits of numerical studies are pointed out. We also illustrate the cooperative nature of light scattering by considering an incident laser field, where half of the beam has a π phase shift. The enhanced subradiance obtained under such condition provides an additional signature of the role of coherence in the detected signal.