Generalised quantum interference

Technical Summary: Generalised Quantum Interference

Problem and Context
The Hong-Ou-Mandel (HOM) effect is a foundational signature of quantum behavior where two indistinguishable photons entering a balanced beam splitter from different ports always exit together (bunching), suppressing the coincidence outcome where they exit separately. While the standard HOM effect is a well-established tool for characterizing photon indistinguishability and sources, it represents only a specific instance of two-photon quantum interference. Theoretical work (Ref. [36]) suggests that linear optics allows for a broader class of "generalised" interference effects. In this framework, by manipulating the input state and the beam splitter transformation, destructive interference can be tuned to suppress not just the coincidence term, but one of the two bunching terms instead. This would result in an asymmetric quantum interference regime where photons may exit separately or bunch in one port, but are forbidden from bunching in the other.

Methodology
The authors experimentally demonstrate this generalised interference using the Ascella programmable integrated photonic quantum processing unit (QPU). The experimental protocol involves the following steps:

1. State Preparation: Two single photons generated by a quantum dot source are first interfered on a balanced (50:50) beam splitter to create a standard HOM bunched state.
2. Imbalance Generation: Controlled attenuation is applied to one arm of the interferometer. This prepares an imbalanced two-photon input state of the form $a |2, 0\rangle + \sqrt{1-a^2} |0, 2\rangle$, where the coefficient $a$ is determined by the transmissivity $\gamma$ of the attenuation.
3. Variable Interference: This imbalanced state is then directed into a variable beam splitter with tunable reflectivity $R$.
4. Detection: The three possible two-photon output configurations ($|2, 0\rangle$, $|1, 1\rangle$, and $|0, 2\rangle$) are resolved using pseudo-photon-number-resolving (PPNR) detection. This involves splitting each output arm on an additional balanced beam splitter and monitoring with pairs of superconducting nanowire detectors. Coincidences within a single arm identify bunching events, while clicks in different arms identify the coincidence ($|1, 1\rangle$) outcome.

Key Contributions and Results
The study successfully demonstrates the continuous reshaping of the two-photon output distribution by tuning the input-state imbalance ($\gamma$) and the beam splitter reflectivity ($R$).

• Asymmetric Interference Point: The authors identified and realized the specific conditions for asymmetric quantum interference. By setting the attenuation to $\gamma \approx 0.7327$ (yielding an imbalance coefficient $a \approx 0.966$) and the beam splitter reflectivity to $R \approx 78.9\%$, they achieved a state where the $|0, 2\rangle$ bunching term is destructively suppressed.
• Experimental Data: At this asymmetric point, the measured probability of the suppressed $|0, 2\rangle$ output was $(1.9 \pm 0.8) \times 10^{-3}$. In contrast, the remaining outputs, $|2, 0\rangle$ and $|1, 1\rangle$, occurred with nearly equal probabilities ($0.479 \pm 0.009$ and $0.519 \pm 0.009$, respectively). This represents a 250-fold suppression of the forbidden channel compared to the allowed channels.
• Generalised Behavior: By scanning $R$ across a range for three different attenuation settings, the authors showed that the output probabilities evolve continuously, matching theoretical predictions for generalised interference. The results deviate significantly from predictions based on a decohered (classical particle) model, confirming the quantum nature of the effect.
• Discrepancies: Minor deviations between measured and theoretical probabilities were attributed to finite photon indistinguishability, calibration errors in the programmed circuit, and background noise, particularly at high reflectivities.

Significance and Claims
The paper claims to provide the first experimental demonstration of generalised quantum interference on a programmable integrated photonic processor. The primary significance lies in expanding the understanding of the HOM effect from a single, fixed phenomenon to a tunable family of interference effects accessible via linear optics.

The authors state that this work places the standard HOM effect within a broader context of two-photon quantum interference. They suggest that the ability to suppress a selected output channel in a controlled manner could be useful for preparing entangled photon number states with linear optics. The study confirms that by varying input-state imbalance and beam splitter parameters, one can access arbitrary two-photon, two-mode states, with the asymmetric point serving as a limiting case where a specific bunching channel is forbidden.