Temporal dynamics in the Bragg reflection of light by cold atoms: flash effect and superradiant decay

Abstract

We study the temporal dynamics of light interacting with a one-dimensional lattice of cold atoms. In such a system, a photonic band gap opens up, yielding an efficient Bragg reflection for an incident field incoming with the right angle and detuning. Here, we report two new effects appearing in the Bragg reflection. First, for some detunings, there is a ``flash'', i.e., a transient increase of the reflected intensity when the incident field is switched off. Second, the subsequent extinction of the reflected field is clearly superradiant, with decay rates up to height times the natural decay rate of the atomic excited state. Numerical simulations are in qualitative agreement with the observations, which can be explained by a classical photonic model. Our results are a step towards exploiting this photonic band gap in atomic systems for quantum-optical applications.

Figures (8)

• Figure 1: (a) Simplified scheme of the setup. Cold atoms from a MOT are trapped in a retroreflected dipole trap forming a 1D lattice, and probed with a weak beam at a small angle $\theta$ from the lattice axis. The transmission $T$ and reflection $R$ are measured with avalanche photodiodes (APDs). (b) Bragg reflection spectra taken for different lattice wavelength $\lambda_\mathrm{lat}$. (c) Corresponding simulations. There is no free parameter except for the atom number (see main text). We also take into account the absorption near resonance due to the residual atoms from the MOT, which is not negligible for the short holding time in the lattice (here 30 ms) used to maximize the reflection.
• Figure 2: (a) Measured reflection coefficient as a function of time at the switch-off of the incident field, for different detunings (indicated in the color bar). (b) Same data but normalized to the steady-state reflectivity $R_\mathrm{ss}$, to better see the switch-off dynamics. The black dashed line shows the natural decay, exp$(-t/\tau_\mathrm{at})$, for comparison. (c, d) Corresponding numerical simulations.
• Figure 3: (a) Superradiant decay rate of the Bragg reflection as a function of the probe detuning. The error bars are the $\pm 2\sigma$ statistical uncertainties of the fit. On the right axis the steady-state reflection coefficient is reported (measured from the same temporal traces). (b) Simulation with the corresponding parameters. The disagreement for $\delta<3\Gamma_0$ is probably due to the absorption by the remaining atoms from the initial MOT.
• Figure 4: Simplified numerical simulations of the decay rate $\Gamma_\mathrm{R}$ of the Bragg reflection as a function of the detuning $\delta$ for different average densities $n_0$. The corresponding steady-state reflection spectra are plotted on the right. The solid horizontal lines have an horizontal extension that represents the full width at half maximum of the spectra, and their height is adjusted by hand to the data. It gives a ratio $F\!W\!H\!M/\Gamma_\mathrm{R} = [2.5, 2.8, 3.1]$, for densities $n_0 = [0.2, 0.5, 1]\times 10^{12}$ cm$^{-3}$, respectively. This approximately constant ratio shows that the decay rate is governed by the width of the spectrum. For the largest density, the decay rate is limited by the extinction rate of the incident laser.
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