Collective early-time spontaneous decay of a strongly driven cold atomic ensemble

TL;DR

The paper addresses early-time collective decay in a strongly driven, optically dense cold atomic ensemble by combining a nonlinear coupled-dipoles mean-field model with experiments on a $^{174}$Yb cloud. It drives the system to steady state at varying strengths $\Omega$ (covering $\Omega \ll \Gamma$ to $\Omega \gg \Gamma$) and then analyzes the decay of both angularly resolved elastically scattered light and the excited-state population after switch-off. A key finding is that on resonance, off-axis scattering transitions from subradiant to superradiant with increasing driving intensity, while $N_e(t)$ tends toward the single-atom decay in the strong-driving limit, with quantitative agreement for $\Omega/\Gamma>1$. The results illustrate observable-dependent signatures of collective dynamics in open quantum systems and provide a benchmark for beyond-mean-field effects and future explorations of coherence in strongly driven atomic ensembles.

Abstract

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 $Ω$ that go from the weak $Ω\ll Γ$ to the strong driving regime $Ω\gg Γ$, where $Γ$ 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.

Figures (3)

• Figure 1: Early-time dynamics from different initial conditions. (a) Illustration of time dynamics of different global quantities normalized to their steady-state values: excited-state population, and total elastic/inelastic emitted power by the cloud. The dynamics is computed using the mean-field model described in the text after driving the system to a steady state with different Rabi frequencies $\Omega/\Gamma = \{0.05,2\}$. The black dashed line shows the single-atom decay for reference. The total elastically emitted power is defined as $P_{el} = \int\int_S I_{el} (\theta,\phi) dS$ where $S$ is the unit sphere. The insets show the time evolution of the ratio between the inelastic and elastic total emitted power in each situation. (b) Extracted early-time decay rate of the elastically scattered light $\Gamma_N^{\theta}$ (blue points) and $\Gamma_N^{N_e}$ (solid green line) as a function of the detection angle, focusing on the forward and backward directions. The dashed, black line marks the single atom decay rate. In this case, the time interval used for the fitting is $T_{fit} \Gamma = 0.1$. We can see that both in the SP and SD regimes there is a rich angular dependence for the scattered light, which is specially evident in the forward and backward directions, where the influence of the phase induced by the driving field is stronger. Simulations were done with $N = 10^3$ and an optical depth of $b_0 = 8$.
• Figure 2: Numerical results on early-time collective decay as a function of on-resonance driving frequency for a cloud with peak optical depth $b_0 = 12$. The black, dashed line marks the single atom behavior. Blue circles (red triangles) are the extracted decay of the light emitted at an angle $\theta = \pi/2rad$ ($\theta = 2\pi~rad$). Green squares are the results from the decay of the excited state population. Yellow crosses correspond to treat the atomic coherences $\Lambda$ as an observable. The dashed line joining them is just a guide for the eye. (a) Off-resonance driving scenario with $\Delta = -10 \Gamma$. (b) On-resonance driving scenario. For all the simulations we used $N = 5\times10^3$ atoms, and a time $T_{fit} \Gamma = 0.75$ was used to extract the decay rates. We checked that the results do not change in a significant way considering shorter times up to $T_{fit} \Gamma = 0.1$.
• Figure 3: Experimental results. (a) Energy level scheme of $^{174}$Yb atoms and schematic representation of the experimental setup described in the main text. (b) Measured early-time decay rates together with numerical predictions for the elastically scattered light at $\theta = \pi/3$ (blue points) and excited state population (green squares). Small full markers correspond to numerical simulations. For these simulations, we used $b_0 = 15$ and $N = 8\times 10^3$. The confidence bands on the numerical results correspond to the standard deviation of 5 different random atomic configurations. Big empty markers corresponds to experimental results. The error bars on the experimental points represent the uncertainty in the fitting procedure to extract the exponential decay constant. For both the theoretical and the experimental data we used a fitting time $T_{fit}\Gamma \approx 1$. The inset shows an example of a time trace of the decay dynamics of the system as recorded using the intensity (blue trace) and population (green squares) methods for the same driving conditions. Both signals are normalized to their steady-state values. The dot-dashed line corresponds to the single atom decay dynamics.