Experimental observation of subabsorption

TL;DR

This work demonstrates subabsorption, the absorptive analog of subradiance, in a dilute, disordered ensemble of ultracold $^{87}$Rb atoms. By time-resolving the absorption of a weak resonant pulse, the authors show that the rise-time can exceed the single-atom value $2\tau_a$ (with $\tau_a=1/\Gamma_a=26.2$ ns) due to long-range dipole–dipole correlations, and that motional dephasing rapidly suppresses this effect. A Maxwell–Bloch propagation model captures baseline non-interacting behavior, while a collective dipole–dipole simulation with a density-dependent dephasing term $\gamma_{DD}=\beta n$—fitted with $\beta/2\pi=4.9\times10^{-5}$ Hz cm$^3$—reproduces the observed subabsorption peak. These results highlight the fragility of multi-atom correlations to temperature and open avenues for exploring subradiant-like absorptive phenomena in atomic arrays and beyond.

Abstract

We predict and experimentally demonstrate a new type of collective (cooperative) coupling effect where a disordered atomic ensemble absorbs light with a rise-time longer (i. e., at a rate slower) than what is dictated by single-atom physics. This effect, which we name subabsorption, can be viewed as the absorptive analog of subradiance. The experiment is performed using a dilute ensemble of ultracold $^{87}$Rb atoms with a low optical depth, and time-resolving the absorption of a weak (tens of photons per pulse) resonant laser beam. In this dilute regime, the collective interaction relies on establishing dipole-dipole correlations over many atoms; i.e., the interaction is not dominated by the nearest neighbors. As a result, subabsorption is highly susceptible to motional dephasing: even a temperature increase of 60 $μ$K is enough to completely extinguish the subabsorption signal. We also present a theoretical model whose results are in reasonable agreement with the experimental observations. The model uses density-dependent dephasing rate of the long-range dipole-dipole correlations as a single adjustable parameter. Experiment-theory comparison indicates a dephasing coefficient of $β/2 π= 4.9 \times 10^{-5}$ Hz~cm$^3$, which is more than two orders of magnitude larger than the known dipole-dipole line broadening coefficient in $^{87}$Rb.

Figures (11)

• Figure 1: Qualitative description of superabsorption and subabsorption. With all the atoms starting in their ground state, when a resonant laser pulse is turned on sharply at $t=0$, the absorption does not instantaneously jump to its steady-state value. Instead, the absorption has an associated rise-time, since the atoms transition to the excited level and establish a dipole moment. Without any collective interaction, this rise-time is exactly determined by the lifetime of the excited level, and is $2 \tau_a$ (solid curve). With collective interaction, the rise-time can be faster (superabsorption, blue dashed curve) or slower (subabsorption, black dashed curve). Our experiments demonstrate subabsorption in an ultracold disordered ensemble at a low optical depth and density.
• Figure 2: (a) Simplified schematic of the experiment. The experiment starts with a magneto-optical trap (MOT) of laser-cooled ultracold rubidium ($^{87}$Rb) atoms. With the atoms trapped and optically pumped to the $F=2$ ground level, we turn on a weak excitation laser which is tuned to the $F=2 \rightarrow F'=3$ cycling transition. After passing through the atomic ensemble, the excitation laser pulse is detected using a single-photon counting module (SPCM). The measurement is performed by detecting the excitation laser pulse on the photon counter with and without the atomic ensemble, and thereby time-resolving the amount of absorbed light in the cloud. (b) The relevant energy level diagram of $^{87}$Rb. The excitation laser is near a wavelength of 780 nm and is tuned to the cycling transition between the $5 S_{1/2}$ to $5P_{3/2}$ electronic states (D2 line).
• Figure 3: A sample dataset where we measure absorption as a function of time, $\sigma(t)$, for an atomic cloud with a steady-state optical depth of $\sigma_{ss} =0.87$. The trigger for the excitation laser is turned on at $t=0$, after which the excitation laser rises to its steady state value in about 8 ns. We fit the data to an exponential rise between $\tau_a< t < 8 \tau_a$. The fit for this specific dataset is shown in solid red curve. We refer to the rise-time of the exponential fit as the absorption rise-time and we denote this quantity with $\tau$. See text for further details.
• Figure 4: (a) Experimentally measured absorption rise-time, $\tau$ (normalized to $2 \tau_a$), as the steady-state optical depth of the ensemble is varied from $\sigma_{ss} = 0.024$ to $\sigma_{ss} = 1.11$. The solid red curve is a numerical calculation that treats the atomic ensemble as a non-interacting gas (Maxwell-Bloch propagation code). The experimental measurements agree well with the non-interacting gas calculation at low optical depths, $\sigma_{ss} < 0.05$, and at optical depths $\sigma_{ss} > 0.5$. In the intermediate region, absorption rise-time $\tau$ is increased considerably near $\sigma_{ss} \sim 0.1$, showing clear evidence of subabsorption. (b) Numerical calculation including dipole-dipole correlations using density-dependent dephasing as a single adjustable fitting parameter. See text for details.
• Figure 5: Experimentally observed absorption rise-time as a function of the temperature of the atomic ensemble at three different optical depths, $\sigma_{ss}=0.1$, $\sigma_{ss}=0.6$, and $\sigma_{ss}=1$, respectively. The subabsorption signal at $\sigma_{ss}=0.1$ is highly susceptible to motional dephasing and vanishes when the atomic temperature is increased to about 100 $\mu$K (corresponding to a motional dephasing of $\sim \lambda_a/100$ in an atomic lifetime). At higher optical depths, $\sigma_{ss}=0.6$, and $\sigma_{ss}=1$, there is not significant variation of the rise-time as the temperature is increased. In each plot, the horizontal dashed line is the expected rise-time from the Maxwell-Bloch propagation code.