Generation of an exponentially rising single-photon field from parametric conversion in atoms

We prepare heralded single photons from a photon pair source based on nondegenerate four-wave mixing in a cold atomic ensemble via a cascade decay scheme. Their statistics shows strong antibunching with a value for the second order correlation at zero delay less than 0.03, indicating a near single photon character. In an optical homodyne experiment, we directly measure the temporal envelope of these photons and find, depending on the heralding scheme, an exponentially decaying or rising profile. Such a rising envelope is required for the efficient interaction between a single photon and a two level system. At the same time, their observation illustrates the breakdown of a realistic interpretation of the heralding process in terms of defining an initial condition of a physical system.

Figure 1

(a) Cascade level scheme for four-wave mixing in ${}^{87}\mathrm{Rb}$. (b) Setup of the heralded single photon source. Polarizers (P1, P2, Pi, Ps) and interference filters (Fi, Fs) separate the signal and idler photons from the residual pump light before coupling into single mode fibers (SMF). An etalon (E) in the idler arm removes uncorrelated photons from a decay to the $5S_{1/2},F=1$ level. Signal photons detected by Ds, an avalanche photodiode (APD), trigger a Hanbury-Brown–Twiss measurement between idler photons distributed to two detectors, Di1 and Di2, via a 50:50 fiber beam splitter (BS).

Figure 2

(a) The correlation function $g_{i1i2|s}^{\left(2\right)}$ of idler photons separated by a time difference $\Delta t_{12}$, conditioned on detection of a heralding event in the signal mode, shows strong photon antibunching over a time scale of $\pm 20$ ns, indicating the single photon character of the heralded photons. The error bars indicate the propagated Poissonian counting uncertainty from $G_{i1i2|s}^{\left(2\right)}$ and $N_{i1i2|s}$. (b) Same measurement, but with the signal and idler modes swapped.

Figure 3

Field measurement setup. One of the photons (idler in this figure) is combined with a coherent laser field as a local oscillator on a polarizing beam splitter (PBS1), and sent to a balanced pair of pin photodiodes D+ and D- for a homodyne measurement. The photocurrent difference as a measure of the optical field strength is amplified by a transimpedance amplifier (G) and recorded with an oscilloscope on the arrival of a heralding event from the avalanche photodetector in the signal arm.

Figure 4

Optical homodyne results. (a) Exponential decay of the field variance of heralded idler photons. (b) Exponential rise of the field variance of heralded signal photons.