Highly efficient generation of single-mode photon pairs from a crystalline whispering-gallery-mode resonator source

We report a highly efficient source of narrow-band photon pairs based on parametric down-conversion in a crystalline whispering-gallery-mode resonator. Remarkably, each photon of a pair is detected in a single spatial and temporal mode, as witnessed by Glauber's autocorrelation function. We explore the phase-matching conditions in spherical geometries, and determine the requirements for single-mode operation. Understanding these conditions has allowed us to experimentally demonstrate a single-mode pair-detection efficiency of $1.13\times {10}^6$ pairs/s per mW pump power per 26.8 MHz bandwidth.

Figure 1

Possible angular phase-matching solutions. (a) Illustration of a WGMR explaining the mode indices $q,m,l$. (b) Cross sections of different intensity distributions inside a WGMR. (c) Subset of angular phase-matching solutions. Each layer represents a subset of the possible solutions for a given pump mode $p_p$. The individual cluster numbers $a$ are encoded in color.

Figure 2

Spectral distribution. Numerical simulation of the spectral distribution for a subset of possible clusters. (a) Close-up of the $a=4$ cluster. (b) Spectral distribution of the first six clusters phase matched with a fundamental pump mode $(q_p=1,p_p=0)$. The yellow dots represent the measured data points.

Figure 3

Experimental setup. (a) Setup for generating pulsed photon pairs from a crystalline WGMR. (b) Setup for measuring the cross-correlation and pair-detection functions. (c) Setup for measuring the autocorrelation function.

Figure 4

Cross-correlation functions. (a) Pair-production rate and (b) normalized cross correlation for the selected $a=0$ cluster (blue circles) and the unselected case (orange triangles). The bin width is 1 ns. Bandwidth and the peak value are determined by an exponential fit (solid line).

Figure 5

Autocorrelation. Normalized autocorrelation function with a bin size of 1 ns. The peak value is determined using an exponential fit (solid curve) to the experimental data (symbols).