Single-photon superradiance in cold atoms

The interaction of an ensemble of atoms with common vacuum modes may lead to an enhanced emission into these modes. This phenomenon, known as superradiance, highlights the coherent nature of spontaneous emission, resulting in macroscopic entangled states in mundane situations. The complexity of the typical observations of superradiance, however, masks its quantum nature, allowing alternative classical interpretations. Here we stress how this picture changed with the implementation ten years ago of a new process for single-photon generation from atomic ensembles. We present then the last piece of evidence for the superradiant nature of such a process, reporting the observation of an accelerated emission of the photon with a rate that may be tuned by controllably changing the number of atoms in the ensemble. We hope such an investigation will help open up a new bottom-up approach to the study of superradiance.

Figure 1

(a) Typical superradiant cascade in an ensemble of atoms with two levels $|g\rangle$ and $|e\rangle .S\{|\cdots \rangle \}$ indicates symmetrical entangled states generated along the cascade. (b) Minimal superradiant cascade of the DLCZ protocol, involving atoms with three levels: $|g\rangle ,|s\rangle$, and $|e\rangle$. Spontaneous emissions on fields 1 and 2 are observed after excitation of the ensemble by write and read pulses, respectively. (c) Spatial configuration for fields in (b). Write and read are large beams counterpropagating to each other. Fields 1 and 2 are defined by the optical fibers (in blue) carrying them to detectors $D_1$ and $D_2$. The detected modes, forming a small angle with the excitation fields, define the region in the atomic cloud that stores the collective entangled state. PF and FF denote polarization and frequency filters, respectively.

Figure 2

Timing for the first series of measurements on the threshold for superradiance.

Figure 3

Squares provide the total conditional probability $P_c$ for extracting the second photon, once the first was detected, as a function of the ensemble's optical depth. The dashed blue line connects the respective results for $P_2$, the unconditional probability to detect a photon in field 2. The employed read pulse was 180-ns long. The inset provides a log-log graph for $\Delta P_c=P_c-P_2$ versus $D_{\mathrm{opt}}$. The red line is a linear fit of slope $s=1.9\pm 0.3$ such that $\Delta P_c\propto D_{\mathrm{opt}}^s$.

Figure 4

Conditional $P_c$ and unconditional $P_2$ probabilities of detecting the second photon as a function of the probability $P_1$ of detecting the first photon.

Figure 5

Conditional $P_c$ and unconditional $P_2$ probabilities of detecting the second photon as a function of the delay between write and read pulses.

Figure 6

Open circles provide the normalized conditional probability as a function of time for six different read powers (in milliwatts): (a) 2.1, (b) 1.2, (c) 0.6, (d) 0.3, (e) 0.15, and (f) 0.075. Solid red curves are the theoretical results of Eq. (1) with $\chi =3.8$ and $\alpha =9.0$. Dashed blue lines provide the corresponding results for the normalized unconditional probability $p_2\left(t\right)/P_c$.

Figure 7

Measurement of optical depth for the outgoing photon throughout the whole 0.5-ms interval at which trials are taken with the trap off.

Figure 8

Open circles provide the normalized conditional probability as a function of time for six different optical depths: (a) 4.8, (b) 4.0, (c) 3.4, (d) 2.6, (e) 1.6, and (f) 1.0. Solid red curves are the theoretical results for independent fits using Eq. (1). The fit parameters $\chi$ and $\alpha$ for each $D_{\mathrm{opt}}$ are plotted in Fig. 9. Dashed blue lines provide the corresponding results for the normalized unconditional probability $p_2\left(t\right)/P_c$. The read power is 0.3 mW.

Figure 9

Values of $\chi$ and $\alpha$ as a function of $D_{\mathrm{opt}}$ obtained from the fittings in Fig. 8. The red curve is a fit to a function with the same linear dependence as Eq. (2). The inset plots the decay times ${\tau }_{sp}={(\chi \Gamma /2)}^{-1}$.