Interference of Temporally Distinguishable Photons Using Frequency-Resolved Detection

We demonstrate quantum interference of three photons that are distinguishable in time by resolving them in the conjugate parameter frequency. We show that the multiphoton interference pattern in our setup can be manipulated by tuning the relative delays between the photons, without the need for reconfiguring the optical network. Furthermore, we observe that the symmetries of our optical network and the spectral amplitude of the input photons are manifested in the interference pattern. We also demonstrate time-reversed Hong-Ou-Mandel-like interference in the spectral correlations using time-bin entangled photon pairs. By adding a time-varying dispersion using a phase modulator, our setup can be used to realize dynamically reconfigurable and scalable boson sampling in the time domain as well as frequency-resolved multiboson correlation sampling.

Figure 1

Schematic of the experimental setup to observe frequency-resolved two-photon interference. Orthogonally polarized photon pairs are generated using Type-II SPDC in a PPKTP crystal, separated using a polarization beam splitter (PBS), delayed and recombined using a beam splitter (BS) after polarization (red arrows) rotation in one of the arms. A chirped Bragg grating (CBG) with a spectral bandwidth more than that of the generated photon pairs, and a time-interval analyzer (TIA) implement a time-of-flight spectrometer (see the Supplemental Material [30]). HWP: half-wave plate (to generate entangled photon pairs), DM: dichroic mirror, PC: polarization controller, PD: photo-diode.

Figure 2

(a)–(d) Measured and (e)–(h) simulated spectral correlations [$\mathrm{\Gamma }({\omega }_1,{\omega }_2,\tau )$] between two photons with varying relative delay $\tau$ at the input. (i)–(l) Measured coincidence counts (maximum normalized to unity) as a function of frequency separation $({\omega }_2-{\omega }_1)$. Measured (blue dots) and simulated (red line) (m) fringe separation, and (n) visibility as function of the delay $\tau$. The delay between the photons was calibrated using HOM interference.

Figure 3

(a) Schematic of the setup to observe frequency-resolved three-photon interference. The PPKTP crystal is strongly pumped to efficiently generate two pairs of photons which are then probabilistically separated using a PBS and two nonpolarizing beam splitters. (b)–(e) Measured and (f)–(i) simulated spectral correlations between three photons (heralded by the fourth photon) with relative delays $({\tau }_{21},{\tau }_{31})\approx (0,15);(20,40);(10,25);(350,175)\mathrm{ps}$. (j)–(m) Fourier transform (FT) of the three-photon correlation function [in (b)–(e)], integrated over ${\omega }_3$. The peaks (highlighted by red dashes) indicate beat notes associated with multiple pairwise interferences.

Figure 4

Measured and simulated spectral correlations for time-bin entangled photon pairs, with the phase factor (a)–(b) $\mathrm{\Delta }\phi =0$ and, (d)–(e) $\mathrm{\Delta }\phi =\pi$. (c), (f) Measured coincidences as a function of $({\omega }_1+{\omega }_2)$.