Reversing the Temporal Envelope of a Heralded Single Photon using a Cavity

We demonstrate a way to prepare single photons with a temporal envelope that resembles the time reversal of photons from the spontaneous decay process. We use the photon pairs generated from a time-ordered cascade decay: the detection of the first photon of the cascade is used as a herald for the ground-state transition resonant second photon. We show how the interaction of the heralding photon with an asymmetric Fabry-Perot cavity reverses the temporal shape of its twin photon from a decaying to a rising exponential envelope. This single photon is expected to be ideal for interacting with two-level systems.

Figure 1

Schematic of the four-wave mixing experiment in collinear geometry. ${\mathrm{IF}}_1$, ${\mathrm{IF}}_2$: interference filters, used to combine pump beams and to separate the photons pairs. SMF: Single-mode optical fibers. $M_1$, $M_2$: cavity mirrors. The incoming and outgoing modes of the cavity are separated by a polarizing beam splitter (PBS) and a quarter wave plate ($\lambda /4$). $D_1$, $D_2$: silicon avalanche photodiodes (APD). The inset shows the cascade level scheme for the generation of photon pairs in ${}^{87}\mathrm{Rb}$.

Figure 2

Transformation of the temporal envelope of the heralded idler photon from exponential decay to rise when the cavity is in the signal mode. The $y$ axis shows the coincidence rate $G_{si}^{(2)}$ between the detectors $D_1$ and $D_2$ as a function of the detection time difference. The dashed lines represent ${|\tilde{\psi }(t_s,t_i)|}^2$, obtained from the model described by Eq. (4) for the indicated cavity detunings $\delta$, with amplitude $A$ as the only free parameter used to fit the experimental points.

Figure 3

Temporal envelope of the idler photon when the cavity is aligned and tuned to resonance with the idler mode. The dashed line represents ${|\tilde{\psi }(t_s,t_i)|}^2$ obtained from Eq. (3) by swapping $i$ and $s$. Also in this case, the amplitude is the only free parameter used in the fit.

Figure 4

Mean photon number in the cavity estimated using Eq. (6). On the left, the detection of an idler photon is used as a herald, and the cavity is in the signal mode. In this case, we observe the interaction of an exponentially rising waveform with the cavity. On the right, the roles of signal and idler are swapped, and the cavity interacts with an exponentially decaying incident photon.