Microwave control of the interaction between two optical photons

A microwave field is used to control the interaction between pairs of optical photons stored in highly excited collective states (Rydberg polaritons). We show that strong dipole-dipole interactions induced by the microwave field destroy the coherence of polariton modes with more than one Rydberg excitation. Consequently, single-polariton modes, which correspond to single stored photons, are preferentially retrieved from the sample. Measurements of the photon statistics of the retrieved light field also reveal nontrivial propagation dynamics of the interacting polaritons.

Figure 1

Control of optical photon statistics by an external microwave field. (a) Optical signal photons are stored in a cold atomic cloud as Rydberg polaritons. Subsequently, an external microwave field controls the state and the interaction between neighboring polaritons. Finally, the optical field is retrieved and the second-order correlation function ${\mathcal{g}}^{\left(2\right)}$ is analyzed using two single-photon counters. The $6\text{−}\mu$s separation between the retrieved pulses, shown in the inset, corresponds to the repetition rate of the experiment. (b) The normalized ${\mathcal{g}}^{\left(2\right)}$ function of the retrieved signal as a function of time delay $\tau$ between the two detectors. No microwave field is applied during the storage interval in this case. The suppression of ${\mathcal{g}}^{\left(2\right)}$ at $\tau =0$ is a consequence of dipole blockade during the photon storage process. (c) The application of a microwave field during the storage interval results in significantly enhanced suppression of ${\mathcal{g}}^{\left(2\right)}$ at $\tau =0$. Note that the entire retrieved pulse has been binned for both sets of ${\mathcal{g}}^{\left(2\right)}$ measurements, and the ${\mathcal{g}}^{\left(2\right)}$ functions are background corrected using the measured signal-to-noise ratio [27].

Figure 2

Photon-number-dependent group delay. (a) The variation of ${\mathcal{g}}^{\left(2\right)}\left(0\right)$ depending on the sampling window of the retrieved pulse. The width of the sampling window is varied, fixing one end at the trailing edge (red circles) or the leading edge (blue squares) of the retrieved pulse. The insets show the retrieved pulse shape with the corresponding sampling window highlighted. Each inset corresponds to the adjacent hollowed data point. No microwave coupling has been applied in this case. The variation of ${\mathcal{g}}^{\left(2\right)}\left(0\right)$ suggests that the group delay of the retrieved pulse depends on the photon number. (b) The retrieved pulse shapes for the case where no microwave coupling is applied (blue, upper curve), and after microwave coupling (red, lower curve). The amplitude of the pulses are scaled in terms of the average number of photons retrieved per store-and-retrieve cycle ${\overline{n}}_{\mathrm{ret}}$. After microwave coupling there is a suppression in the amplitude of the retrieved field due to dephasing of multipolariton states. However, there is a large degree of overlap of the pulses in their trailing edges (purple area). This corresponds to the region where the single-photon mode (corresponding to a single polariton) should dominate. The overlap in the trailing edges is shown more clearly in the inset. Here $\Delta {\overline{n}}_{\mathrm{ret}}$ is the difference between the two retrieved pulses, normalized by the case of no microwave coupling. A larger (40 ns) bin width has been used to calculate the normalized pulse difference to improve the counting statistics.

Figure 3

Collective readout of polariton fields containing different photon numbers. (a) Rabi oscillations of the collective $\mathcal{N}$-polariton state between microwave-coupled Rydberg levels are mapped out by varying the microwave Rabi frequency ${\Omega }_{\mu }$ for fixed time $t=150$ ns. The retrieved photon signal (small filled symbols) is normalized to the case where no microwave coupling is applied. The function $P={\left[{cos}^2({\Omega }_{\mu }t/2)\right]}^{\mathcal{N}}$ is fit to the data, where each peak of the oscillation is fit individually over a region defined by a sliding window. The color and shape of the small symbols indicate regions of data that are used together for a fit; some data points take part in more than one fit, shown by overlapped symbols. The solid curves show the fits to the corresponding data regions, with all parameters (vertical offset, vertical scale, frequency, phase, and $\mathcal{N}$) independently fitted for each region. A portion of these data were previously published as Fig. 3 in Ref. [6], though fitting with variable $\mathcal{N}$ is new to this paper. (b) (Inset) Large hollow symbols: The variation of the fit parameter $\mathcal{N}$ across the Rabi oscillations. In the regime where ${\Omega }_{\mu }<V_{\mathrm{dd}}$, $\mathcal{N}$ approaches 1, suggesting that only a single polariton survives.