Subradiance in a Large Cloud of Cold Atoms

Since Dicke’s seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes. Here, we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model.

Figure 1

Principle of the experiment. A large probe laser illuminates the atomic sample for $30\mu \mathrm{s}$ and is switched off rapidly. The fluorescence at $\sim 35°$ is collected by a hybrid photomultiplier (HPM) and recorded on a multichannel scaler (MCS). The experiment is repeated 500 000 times. At each cycle, 12 pulses are recorded during the free expansion of the cloud, allowing the on-resonance optical depth to vary.

Figure 2

Slow decay of the fluorescence after switching off the probe laser. The vertical scale is normalized by the steady-state detected power $P(0)$, and the time scale is normalized by the atomic lifetime of the excited state ${\tau }_{\mathrm{at}}$. Without any collective effect (single-atom physics), the decay would be given by $P(t)=P(0)\exp (-t/{\tau }_{\mathrm{at}})$ (the black dotted line). (a) Several data are shown for different on-resonance optical depths $b_0$ and the same detuning $\delta =-6$ (in units of $\mathrm{\Gamma }$). The time constant increases with $b_0$. (b) Several data are shown for different detunings and the same $b_0=108\pm 5$. The time constant remains unchanged, but the relative amplitude of the subradiant decay decreases as the detuning increases.

Figure 3

Dependence of the subradiance time with the on-resonance optical depth $b_0$ and the laser detuning $\delta$. (a) Subradiant time constant ${\tau }_{\mathrm{sub}}$ (in units of ${\tau }_{\mathrm{at}}$) as a function of $b_0=3N/(k_{0}R{)}^2$ for different detunings of the probe laser. Almost all of the points collapse on a single curve, showing the linear scaling with $b_0$. The dashed line is a linear fit ${\tau }_{\mathrm{sub}}/{\tau }_{\mathrm{at}}=1+\alpha b_0$, with the slope $\alpha$ as a free parameter. Excluding the data with $b_0>120$, we obtain $\alpha =0.8$. (b) From the same data, ${\tau }_{\mathrm{sub}}$ is plotted as a function of the detuning for three different values of $b_0$, illustrating that ${\tau }_{\mathrm{sub}}$ is independent of the detuning. (c) Similarly, the subradiant relative amplitude $A_{\mathrm{sub}}$ is plotted as a function of the detuning for the same three different values of $b_0$. Subradiance is more important near resonance and decreases towards a plateau at large detuning.