Single-Photon Generation from Stored Excitation in an Atomic Ensemble

Single photons are generated from an ensemble of cold Cs atoms via the protocol of Duan et al. [Nature (London) 414, 413 (2001)]. Conditioned upon an initial detection from field 1 at 852 nm, a photon in field 2 at 894 nm is produced in a controlled fashion from excitation stored within the atomic ensemble. The single-quantum character of field 2 is demonstrated by the violation of a Cauchy-Schwarz inequality, namely $w(1_2,1_2|1_1)=0.24\pm 0.05\ngeqq 1$, where $w(1_2,1_2|1_1)$ describes the detection of two events $(1_2,1_2)$ conditioned upon an initial detection $1_1$, with $w\to 0$ for single photons.

Figure 1

Schematic of experiment for conditional generation of single photons. Write and read pulses sequentially propagate into a cloud of cold Cs atoms (MOT), generating the correlated output fields $(1,2)$. A detection event for field 1 at $D_{1A,1B}$ leads to an approximate one-photon state for field 2, as confirmed with detectors $D_{2A,2B}$. (P)BS: (polarization) beam splitter; SM: single mode. The inset illustrates the relevant atomic level scheme.

Figure 2

Left column: (a)–(c) Normalized intensity correlation functions ${\tilde{g}}_{1,1}$, ${\tilde{g}}_{2,2}$, ${\tilde{g}}_{1,2}$ versus observed detection probabilities $p_1$, $p_2$, $\sqrt{p_1{p}_2}$, respectively. Right column: (d)–(f) $q_{1,1}$, $q_{2,2}$, $q_{1,2}$ for joint detection versus $q_1$, $q_2$, $\sqrt{q_1{q}_2}$ for single detection, with $q_l,q_{l,m}$ referenced to the output of the MOT. Statistical uncertainties are indicated by the error bars. The full curves are from the model calculation described in the text with $({\kappa }_1,{\kappa }_2)=(0.17,0.90)$ and $(|v_{1b}{|}^2,|v_{2b}{|}^2)=0.006$.

Figure 3

Ratio $R\equiv [{\tilde{g}}_{1,2}{]}^2/{\tilde{g}}_{1,1}{\tilde{g}}_{22}$ versus the normalized cross correlation ${\tilde{g}}_{1,2}$, where $R>1$ for manifestly quantum (nonclassical) fields. The points are from our experiment with statistical uncertainties indicated by the error bars. The full curve is from the model calculation with $({\kappa }_1,{\kappa }_2)$ and $(|v_{1b}{|}^2,|v_{2b}{|}^2)$ as in Fig. 2.

Figure 4

Threefold correlation function $w$ for detection event $1_1$ for field 1 followed by two events $(1_2,1_2)$ for field 2 versus the normalized cross correlation ${\tilde{g}}_{1,2}$. (a) $w_{i,j}$ for events $(1_1{)}_i$ and $(1_2,1_2{)}_j$ from different trials $i\ne j$ together with points for ${\tilde{g}}_{2,2}$. $w_{i,j}={\tilde{g}}_{2,2}$ for statistically independent trials. (b) $w_{i,i}$ for events from the same trial $i$. $w_{i,i}<1$ for sub-Poissonian fields in support of the single-photon character of field 2. Statistical uncertainties are indicated by the error bars. The full curves are from the model calculation with $({\kappa }_1,{\kappa }_2)$ and $(|v_{1b}{|}^2,|v_{2b}{|}^2)$ as in Figs. 2, 3.