Observation of Vacuum-Induced Collective Quantum Beats

We demonstrate collectively enhanced vacuum-induced quantum beat dynamics from a three-level V-type atomic system. Exciting a dilute atomic gas of magneto-optically trapped ${}^{85}\mathrm{Rb}$ atoms with a weak drive resonant on one of the transitions, we observe the forward-scattered field after a sudden shut-off of the laser. The subsequent radiative dynamics, measured for various optical depths of the atomic cloud, exhibits superradiant decay rates, as well as collectively enhanced quantum beats. Our work is also the first experimental illustration of quantum beats arising from atoms initially prepared in a single excited level as a result of the vacuum-induced coupling between excited levels.

Figure 1

(a) Experimental setup. Linearly polarized excitation beam containing train of pulses illuminates cold ${}^{85}\mathrm{Rb}$ atomic cloud produced by MOT. Photons scattered by cloud in forward direction coupled into single-mode fiber, counted by avalanche photodiode, and histogrammed to obtain atomic radiative decay profile. (b) Relevant energy levels of ${}^{85}\mathrm{Rb}$ atom. Excitation beam (780 nm) resonantly drives $|1⟩\leftrightarrow |2⟩$ transition. ${\mathrm{\Gamma }}_{22}$ and ${\mathrm{\Gamma }}_{33}$ are decay rates of excited levels $|2⟩$ and $|3⟩$, respectively, to ground level $|1⟩$.

Figure 2

(a) Examples of the histogrammed photon counts for various optical depths, representing forward-mode intensity, and normalized to that of excitation pulse. As excitation pulse is abruptly (within $\approx 3.5\mathrm{ns}$) turned off, flash of photon emission occurs with peak intensity close to $I_0$. (b) Zoomed-in view of decay profiles after flash peak for analysis. Intensity of each curve further normalized to exponential decay amplitude $I_0$ [$\approx$ flash peak size shown in Fig. 2]. Error bars represent shot-noise limit of photon counts. Overlaid solid lines fit data using Eq. (1), whose results are displayed in Fig. 3 for entire OD range of experiment. Black dashed line represents single-atom decay curve $I(t)=e^{-{\mathrm{\Gamma }}_{22}t}$ (${\mathrm{\Gamma }}_{22}=2\pi ·6.1\mathrm{MHz}$) without considering collective effects. In inset, absolute values of fast-Fourier transforms of beat signals for $\mathrm{OD}=0.9$ (solid blue), 2.1 (dashed red), and 4.2 (dash-dotted green line) show peaks at splitting between two excited levels (see Supplemental Material for detail [17]).

Figure 3

(a) Beat contrast $I_{\mathrm{b}}$ plotted as function of ${\mathrm{\Gamma }}_{22}^{(N)}/{\mathrm{\Gamma }}_{22}$ for various ODs. Plotted error bars represent one-sigma confidence interval of fitting to modulated decay curves. Shaded region displays one-sigma confidence band of linear fit to data. Red solid line is theory curve plotting Eq. (2). Inset shows linear dependence of ${\mathrm{\Gamma }}_{22}^{(N)}/{\mathrm{\Gamma }}_{22}$ on OD. (b) Beat phase $\varphi$ subtracted by common offset ${\varphi }_0$ presented. Shaded region represents one-sigma confidence band of fitting of Eq. (4) to data.