Narrow Band Source of Transform-Limited Photon Pairs via Four-Wave Mixing in a Cold Atomic Ensemble

We observe narrow band pairs of time-correlated photons of wavelengths 776 and 795 nm from nondegenerate four-wave mixing in a laser-cooled atomic ensemble of ${}^{87}\mathrm{Rb}$ using a cascade decay scheme. Coupling the photon pairs into single mode fibers, we observe an instantaneous rate of 7700 pairs per second with silicon avalanche photodetectors, and an optical bandwidth below 30 MHz. Detection events exhibit a strong correlation in time [$g^{(2)}(\tau =0)\approx 5800$] and a high coupling efficiency indicated by a pair-to-single ratio of 23%. The violation of the Cauchy-Schwarz inequality by a factor of $8.4\times {10}^6$ indicates a strong nonclassical correlation between the generated fields, while a Hanbury Brown–Twiss experiment in the individual photons reveals their thermal nature. The comparison between the measured frequency bandwidth and $1/e$ decay time of $g^{(2)}$ indicates a transform-limited spectrum of the photon pairs. The narrow bandwidth and brightness of our source makes it ideal for interacting with atomic ensembles in quantum communication protocols.

Figure 1

(a) Schematic of the experimental setup, with $P1–P3$, polarization filters; $F1$, $F2$, interference filters; $E$, solid etalon; $D1–D4$, avalanche photodetectors. A 795 nm seed beam is used to determine the phase-matched direction of coherent 762 nm emission. (b) Cascade level configuration in ${}^{87}\mathrm{Rb}$. (c) Timing sequence for one experimental cycle.

Figure 2

(a) Histogram of coincidence events $G_{SI}^{(2)}(\tau )$ for a total integration time of $T=47\mathrm{s}$ as a function of time delay $\tau$ between the detection of idler and signal photons sampled into $\Delta \tau =1\mathrm{ns}$ wide time bins, and its normalized version $g_{SI}^{(2)}$ according to Eq. (1). The solid line is a fit to the model $g_{SI}^{(2)}(\tau )=B+A\exp (-\tau /{\tau }_0)$, where $B=1.20\pm 0.07$ is the mean $g_{SI}^{(2)}(\tau )$ for $\tau$ from 125 ns to $1\mu \mathrm{s}$, resulting in $A=5800\pm 76$ and ${\tau }_0=6.7\pm 0.2\mathrm{ns}$. (b) Time-resolved coincidence histogram $G_{SS}^{(2)}(\tau )$ and its normalized version in a Hanbury Brown–Twiss experiment on signal photons (detectors $D1$, $D2$) for $T=76.3\mathrm{s}$. The solid line shows a fit to the model $g_{SS}^{(2)}(\tau )=C\times [1+D\exp (-|\tau |/{\tau }_0)]$, resulting in $C=1.08\pm 0.1$, $D=0.93\pm 0.06$, and ${\tau }_0=17.8\pm 1.4\mathrm{ns}$. (c) Same as (b) for idler photons detected on $D3$ and $D4$ for $T=247.3\mathrm{s}$, leading to fit parameters $C=1.04\pm 0.08$, $D=0.96\pm 0.08$, and ${\tau }_0=9.9\pm 1.2\mathrm{ns}$. For all plots, the atomic cloud has an optical density ${\mathrm{OD}}_m\approx 32$.

Figure 3

(a) Spectral profile of idler photons, heralded by the detection of signal photons with an atomic cloud ${\mathrm{OD}}_m\approx 32$. The frequency uncertainty is due to the uncertainty in voltage driving the cavity piezo. The line shows a fit to a model of Lorentzian-shaped photon spectrum, convoluted with the cavity transmission spectrum. The fit gives a bandwidth of $24.7\pm 1.4\mathrm{MHz}$ (FWHM). (b) Same as (a), but without heralding. The resulting bandwidth from the fit is $18.3\pm 1.3\mathrm{MHz}$ (FWHM). (c) Inferred idler spectrum from a two step (nonsuperradiant) decay with $12.4\pm 1.4\mathrm{MHz}$ (FWHM) bandwidth from a fit.

Figure 4

Bandwidth (FWHM) of heralded idler photons (pairs) for different cloud optical densities (${\mathrm{OD}}_m$) (filled circles). The line shows the theoretical model according to Refs. 37, 38. Open circles indicate the bandwidth (FWHM) of unheralded idler light.