Multiphoton Interference in the Spectral Domain by Direct Heralding of Frequency Superposition States

Multiphoton interference is central to photonic quantum information processing and quantum simulation, usually requiring multiple sources of nonclassical light followed by a unitary transformation on their modes. We observe interference in the four-photon events generated by a single silicon waveguide, where the different modes are six frequency channels. Rather than requiring a unitary transformation, the frequency correlations of the source are configured such that photons are generated in superposition states across multiple channels, and interference effects can be seen without further manipulation. The frequency correlations of the source also mean that it is effectively acting as multiple pair photon sources, generating photons in different spectral modes, which interfere with each other in a nontrivial manner. This suggests joint spectral engineering is a tool for controlling complex quantum photonic states without the difficulty of implementing spatially separate sources or a large unitary interferometer, which could have practical benefits in various applications of multiphoton interference.

Figure 1

(a) A photon-pair source with a complex pump laser spectrum is used to herald photons in frequency superposition states. Two heralding photons close in frequency give rise to overlapping superpositions where multiphoton interference can be seen. (b) The four-photon generation probability can be related to the permanent of a $2\times 2$ matrix containing four points from the two-photon JSA. (c) The experimental JSA consists of up to five diagonal lines created by FWM from different pump components. The six output frequency channels are marked with blue lines. (d) Experimental setup, consisting of pump pulse preparation using a mode-locked laser (MLL), spectral pulse shapers (SPSs) and erbium-doped fiber amplifier (EDFA); photon pair generation in a silicon nanowire (SiNW), with a cross section shown in the inset; wavelength division (WDMs); and detection, using superconducting nanowire single photon detectors (SPDs) and a time-to-digital converter (TDC).

Figure 2

(a) Single pump component, two-photon counts, showing that idler channel $i1$ ($i2$) heralds signal channel 2 (3), according to energy matching. (b) Four-photon counts involving both idler channels and two out of the four signal channels. Signal photons in channels 2 and 3 are heralded. Error bars denote uncertainty due to Poissonian count statistics.

Figure 3

(a) Two pump components, two-photon counts; $i1$ and $i2$ now herald overlapping superposition states across the signal channels. (b) Four-photon counts; multiphoton interference is expected to increase the 2 and 3 combination slightly.

Figure 4

(a) Three pump components; variation in two-photon count rates as a function of the phase of the center pump. Blue squares, $i1$ and 1; red circles, $i1$ and 2; yellow diamonds, $i1$ and 3. (b) All two-photon combinations, with the phase fixed at 1.3 rad. $i1$ and $i2$ now herald highly overlapping superpositions across the signal channels, and some amplitudes carry a $\pi /2$ phase shift not apparent here.

Figure 5

(a) Four-photon counts, displaying constructive interference for signal channels 2 and 4 and 1 and 3, but destructive interference in the other combinations. (b) These features are absent in the expected counts without multiphoton interference, inferred from the two-photon counts.