Temporally multimode four-photon Hong-Ou-Mandel interference

The two-photon Hong-Ou-Mandel (HOM) interference is a pure quantum effect which indicates the degree of indistinguishability of photons. The four-photon HOM interference exhibits richer dynamics in comparison to the two-photon interference and simultaneously is more sensitive to the input photon states. We demonstrate theoretically and experimentally an explicit dependency of the four-photon interference on the number of temporal modes, created in the process of parametric down-conversion. Moreover, we exploit the splitting ratio of the beam splitter to manipulate the interference between bunching and antibunching. Our results reveal that the temporal mode structure (multimodeness) of the quantum states shapes many-particle interference.

Figure 1

Schematic setup. The type-II PDC process generates two signal-idler pairs of photons. After PBS, two horizontally polarized photons are routed to the channel 1 (red line), while two vertically polarized photons are routed to the channel 2 (green line). A half wave plate (HWP) located in the upper channel converts the horizontally polarized photons into vertically polarized ones. An additional path increment $l+\mathrm{\Delta }l$ in the lower channel allows us to compensate the time delay between the signal and idler photons. Then four vertically polarized photons cross the BS at the same time, and the HOM interference occurs. The photons are detected after the BS.

Figure 2

Experimental setup. A femtosecond titanium:sapphire (Ti:Sa) oscillator with repetition rate of 80 MHz is used to pump a PPKTP waveguide designed for type-II PDC. For spectral shaping of the pump, we use a spatial light modulator (SLM) in a folded $4f$ setup to shape the desired spectral amplitude and phase. An 8-nm-wide bandpass filter (BPF) centered at 1532 nm was used to block the pump and phase-matching side lobes. The orthogonally polarized PDC photons were sent to the interferometer setup, where we used a polarizing beamsplitter (PBS), a half wave plate (HWP), and an adjustable time delay stage $\mathrm{\Delta }\tau$ to control the interference. Then the photons were sent to a single-mode fiber coupler with an adjustable coupling ratio where interference occurs. Each output port of the fiber coupler is then connected to a balanced fiber splitter followed by superconducting nanowire single photon detectors (SNSPD).

Figure 3

Spectral-temporal properties of considered PDC states: state A is nearly decorrelated, state B is standard frequency anticorrelated, and state C has spectral phase anticorrelations from a strongly chirped pump. The first column presents measured joint spectral intensity (JSI), which contains no information about the spectral phase. The second column depicts the absolute value and the phase of theoretical joint spectral amplitudes (JSAs). The third column shows the absolute value of theoretical joint temporal amplitudes (JTAs). The fourth column shows the calculated (red solid line) and measured (blue dots) two-photon Hong-Ou-Mandel interference (HOMI), with error bars smaller than the dots. Experimental points on $P_{1,1}$ correspond to twofold coincidences between detectors 1 and 3, with maximum count rates of 1 590 426, 1 583 615, and 1 675 548 per 60 s for states A, B, and C, respectively.

Figure 4

Theoretical coincidence probabilities to detect: (a) two photons per channel, (b) three photons in one channel and one photon in the other channel, and (c) four photons in one channel for different pump spectral bandwidths [states A, B, and C are presented by black, red (dark gray), and dashed green curves, respectively].

Figure 5

Theoretical and experimental $P_{22}$ probabilities for states A, B, and C. Experimental points correspond to maximum counting rates of 3761, 2127, and 2309 per 60 s for states A, B, and C, respectively.

Figure 6

Unbalanced BS configuration. Theoretical coincidence probabilities to detect: (a) two photons per channel, (b) three photons in one channel and one photon in the other channel, and (c) four photons in one channel for different pump spectral bandwidths [states A, B, and C in black, red (dark gray), and dashed green, respectively].

Figure 7

Theoretical and experimental $P_{22}$ probabilities for states A and C in the unbalanced BS configuration. Experimental points correspond to maximum counting rates of 5128 and 2094 per 60 s for states A and C, respectively.

Figure 8

The two-photon HOM dip with a balanced BS and the four-photon HOM dip with an unbalanced BS in the single-mode regime: the pulse duration is 0.29 ps.