Nonreciprocity in Photon Pair Correlations of Classically Reciprocal Systems

Nonreciprocal optical systems have found many applications altering the linear transmission of light as a function of its propagation direction. Here, we consider a new class of nonreciprocity which appears in photon pair correlations and not in linear transmission. We experimentally demonstrate and theoretically verify this nonreciprocity in the second-order coherence functions of photon pairs produced by spontaneous four-wave mixing in a silicon microdisk. Reversal of the pump propagation direction can result in substantial extinction of the coherence functions without altering pump transmission.

Figure 1

Nonreciprocity arises in photon pairs generated by cavity-enhanced spontaneous four-wave mixing (SFWM) via coupled whispering-gallery modes (WGMs). (a) A depiction of a smooth silicon microdisk with a single surface scatterer. Pump laser light (green) is introduced at port 1 and evanescently coupled into the microdisk, exciting a forward-propagating WGM. The scatterer couples this mode to a backward-propagating WGM. If the device were instead pumped from port 2 (translucent green), the backward-propagating WGM would be excited and light could scatter to the forward-propagating WGM. The position of the scatterer crucially affects the relative phase between WGMs in each pumping scenario. (b) A depiction of a rough silicon microdisk. Nanoscale surface roughness acts as a distributed scatterer, coupling WGMs and creating standing wave eigenmodes (blue and orange). (c) The experimental cavity transmission of the pump doublet resonance for a pump field introduced at port 1 (blue) and at port 2 (red), which closely match. (d) A frequency domain representation of SFWM in the silicon microdisk showing several biphoton creation pathways. (e) SFWM in a silicon microdisk with scattering-induced coupling. Generated signal and idler photons may coherently scatter between clockwise- and counterclockwise-propagating modes before exiting the device either forward- or backward-propagating relative to the input pump field. The phase relationship between pump modes and generated biphoton states depends on pump field’s initial propagation direction.

Figure 2

Normalized second-order biphoton coherence functions. (a) and (b) Measured coincidences are plotted as a function of the difference in the detection times of the signal and idler photons produced by a pump input at port 1 (a) and port 2 (b) for all possible biphoton path configurations: signal-forward and idler-forward (SF IF), signal-forward and idler-backward (SF IB), signal-backward and idler-forward (SB IF), and signal-backward and idler-backward (SB IB). The sum of coherence functions for all four path configurations gives the total coherence function, and all coherence functions are normalized to the maximum of the respective total coherence function. (c) and (d) The theoretically obtained coherence functions corresponding to pump port 1 and pump port 2, respectively.

Figure 3

Description of a microdisk with a singlet pump mode. (a) A frequency domain picture of SFWM with a singlet pump. (b) Second-order coherence function (normalized to its maximum) for (b) SF IF, (c) SF IB, (d) SB IF, and (e) SB IB biphoton path configurations from a microdisk with a singlet pump mode.