Interference between distinguishable photons

Abstract

Two-photon interference (TPI) lies at the heart of photonic quantum technologies. TPI is generally regarded as quantum interference stemming from the indistinguishability of identical photons, hence a common intuition prevails that TPI would disappear if photons are distinguishable. Here we disprove this perspective and uncover the essence of TPI. We report the first demonstration of TPI between distinguishable photons with their frequency separation up to $10^4$ times larger than their linewidths. We perform time-resolved TPI between an independent laser and single photons with ultralong coherence time ($>10\ μ$s). We observe a maximum TPI visibility of $72\%\pm 2\%$ well above the $50\%$ classical limit indicating the quantum feature, and simultaneously a broad visibility background and a classical beat visibility of less than $50\%$ reflecting the classical feature. These visibilities are independent of the photon frequency separation and show no difference between distinguishable and indistinguishable photons. Based on a general wave superposition model, we derive the cross-correlation functions which fully reproduce and explain the experiments. Our results reveal that TPI as the fourth-order interference arises from the second-order interference of two photons within the mutual coherence time and TPI is not linked to the photon indistinguishability. This work provides new insights into the nature of TPI with great implications in both quantum optics and photonic quantum technologies.

Figures (5)

• Figure 1: (color online) Experimental setup for time-resolved TPI measurement between single photons and an independent laser (Toptica CTL-950). Single photons with ultralong coherence time are generated by a single QD in an optical microcavity driven by a tunable cw Ti:sapphire laser (M SQUARED) with a linewidth $<100\ $kHz. The sample is placed inside a closed-cycle cryostat (attocube attoDry 800). Time-resolved correlation measurements are performed with an 8-channel time-correlated single photon counter (Swabian Instruments) with a time jitter of $3\ $ps. BS, $\mathrm{BS_A}$ and $\mathrm{BS_B}$: beam splitters, LP1 and LP2: linear polarizers, HWP: half-wave plate, SNSPD1 and SNSPD2: superconducting nano-wire single-photon detectors (Scontel) with a time jitter of $20\ $ps.
• Figure 2: (color online) Generation of single photons with ultralong coherence time ($>10\ \mu$s). (a) Reflection spectra measured by scanning the laser's wavelength. The QD-cavity coupled system (i.e., hot cavity) at low driving fields (red, solid line) exhibits different reflection spectra from the cold or empty cavity at high driving fields where the QD gets saturated (blue, dashed line). (b) Measured second-order autocorrelation $\mathrm{g}^{(2)}(\tau)$ of reflected light with the laser frequency fixed at the QD resonance. $\mathrm{g}^{(2)}(0)=0.030\pm 0.002$ is achieved. (c) Measured degree of first-order coherence $|\mathrm{g}^{(1)}(\tau)|$ versus time delay at different driving powers with a Michelson interferometer. The solid curves represent calculated results using the master equation li24. We choose a low driving power with the saturation parameter $S=0.01$ for TPI experiments in this work. (d) Cross-correlation measurements for the superimposed light of laser and single photons in cross-polarization (blue dot) and parallel-polarization (red solid) configurations. (e) Magnified detail of the single-photon anti-bunching dip at zero time delay. (f) HOM visibility versus the time delay. In (d)-(f), the photon frequency separation is kept at $\Delta f=0\ $MHz and the intensity ratio of laser to single photons is fixed to $0.2$.
• Figure 3: (color online) Dependence of cross-correlation measurements on the intensity ratio of laser light to single photons. (a) $\mathrm{g}^{(2)}_{\parallel}(0)$ and $\mathrm{g}^{(2)}_{\perp}(0)$ versus the intensity ratio. (b) $V_{HOM}(0)$ and the peak value of visibility background versus the intensity ratio. Dots represent the experimental data and solid lines represent the calculated results in (a) using Eqs.(\ref{['eq1']})-(\ref{['eq2']}) and (b) using Eq. (\ref{['eq3']}). The photon frequency separation is kept at $\Delta f=0\ $MHz.
• Figure 4: (color online) Cross-correlation measurements in parallel-polarization configuration at different frequency separations which are larger than the single-photon linwidth ($<100\ $kHz): (a) $\Delta f=10\ $MHz; (b) $\Delta f=50\ $MHz; (c) $\Delta f=500\ $MHz. HOM visibility at different frequency separations: (d) $\Delta f=10\ $MHz; (e) $\Delta f=50\ $MHz; (f) $\Delta f=500\ $MHz. (g) $V_{HOM}(0)$ versus the frequency separation between laser light and single photons. (h) The peak of the broad background visibility versus the frequency separation between laser light and single photons. In both (g) and (h), red dots represent the experimental data and solid lines represent the calculated results using Eq.(\ref{['eq3']}).
• Figure 5: (color online) Photon bunching induced by interference. (a) Experimental setup to measure the bunching of two photons on BS1. LP1 and LP2: linear polarizers, HWP: half-wave plate, BS1 and BS2: 50/50 non-polarizing beam splitters, D1 and D2: superconducting nanowire single photon detectors. (b) Auto-correlation function $\mathrm{g}^{(2)}_{\parallel}(\tau)$ versus the time delay. (c) Auto-correlation function $\mathrm{g}^{(2)}_{\perp}(\tau)$ versus the time delay . (d) Visibility versus the time delay. The visibility is defined as $V(\tau)=[\mathrm{g}^{(2)}_{\parallel}(\tau)-\mathrm{g}^{(2)}_{\perp}(\tau)]/\mathrm{g}^{(2)}_{\perp}(\tau)$. In (b)-(d), the photon frequency separation is kept at $\Delta f=0\ $MHz and the intensity ratio of laser light to single photons is fixed to $0.2$.