Controlling Hong-Ou-Mandel Antibunching Via Parity-governed Spectral Shaping Achieves Biphoton State Control with Th Symmetry

The peculiar quantum phenomenon of photon bunching and antibunching challenges our classical understanding of light, and researchers continually seek ways to control it. Mikhail Guselnikov, Alexei Kiselev, and Andrei Gaidash, working at ITMO University with colleagues including George Miroshnichenko and Anton Kozubov, now demonstrate a method for actively switching between these regimes. Their work reveals that the parity, or symmetry, of a biphoton’s spectral properties governs whether photons will bunch together or repel each other, offering a new level of control over this quantum behaviour. By carefully shaping the spectrum of entangled photon pairs using subtle adjustments to their path length, the team achieves precise control over the Hong-Ou-Mandel effect, potentially paving the way for advanced quantum technologies reliant on manipulating single photons.

Entangled Biphotons, Rotation, and Spectral Modulation

This research investigates the entanglement properties of biphoton states created through Spontaneous Parametric Down-Conversion (SPDC), focusing on how changes to the spectral properties affect the degree of entanglement, quantified by the Schmidt number. The study also explores how observing these entangled photons from a rotating frame of reference influences their entanglement, with potential applications in precision sensing devices like gyroscopes. Schmidt decomposition is a key tool in quantum information theory, breaking down a quantum state into fundamental components called Schmidt modes.

The number of significant Schmidt modes directly indicates the level of entanglement. The research considers the Joint Spectral Acceptance (JSA), which describes the spectral characteristics of the entangled photon pairs and how they correlate in frequency and angle, demonstrating that modifying the JSA affects the Schmidt number and, consequently, the degree of entanglement. The research utilizes continuous-variable quantum information, dealing with quantum states described by continuous properties like frequency and phase. It examines how observing entangled photons from a rotating frame of reference alters their entanglement, linking this to relativistic effects and the Sagnac effect, a phenomenon where light interference patterns shift in rotating systems. The findings suggest that exploiting the entanglement of biphotons in rotating frames could lead to the development of more sensitive and precise gyroscopes, with implications for quantum metrology and quantum sensing. This work provides a comprehensive mathematical framework for analyzing the entanglement of biphoton states with modified JSAs in non-inertial frames, contributing to fundamental tests of quantum mechanics and its compatibility with general relativity, and potentially relevant for quantum communication protocols in moving or rotating systems.

Biphoton State Modulation and Entanglement Characterisation

The research team investigated the characteristics of biphoton states by analyzing their joint spectral amplitude, focusing on experimentally observable effects like Hong-Ou-Mandel bunching and antibunching. These phenomena are quantified using a symmetry degree parameter, directly linked to the parity of the spectral function. The study demonstrated that switching between bunching and antibunching regimes is achievable through precise modulation of biphoton states, accomplished by finely tuning the spectral phase via sub-nanometer adjustments to the path length. To characterize entanglement, the researchers employed the Schmidt decomposition technique, expanding the biphoton state in terms of Schmidt modes.

This expansion allows for the calculation of Schmidt eigenvalues, used to determine the Schmidt number, a quantitative measure of entanglement. A state is considered entangled when the Schmidt number exceeds 1, with larger values indicating a higher degree of entanglement. The team applied this decomposition to standard biphotons generated via spontaneous parametric down-conversion. The study derived expressions for the Schmidt modes and eigenvalues, enabling the calculation of the Schmidt number as a function of the parameters defining the biphoton state. The resulting formula reveals that the Schmidt number is independent of any spatial phase shift, a consequence of such shifts being generated by local unitary transformations that do not affect entanglement. By analyzing the relationship between the symmetry degree and the Schmidt number, the researchers found that tuning the pump width provides a practical means of controlling entanglement in experiments.

Spectral Control of Photon Bunching and Antibunching

Scientists have demonstrated precise control over biphoton states, achieving both bunching and antibunching regimes through manipulation of spectral phase modulation. Experiments reveal that switching between these regimes is possible by finely tuning the path length on a sub-nanometer scale, directly influencing the symmetry degree parameter that characterizes the photon correlations. The team measured the symmetry degree, finding that positive values correspond to bunching, while negative values indicate antibunching, with the sign governed by the parity properties of the spectral function. Data shows that the Schmidt number, a measure of entanglement, varies as a function of the modulation parameter, revealing narrow resonance peaks strongly correlated with dips in the symmetry degree where antibunching occurs.

Measurements confirm that when the Schmidt number approaches 1, the parameter related to spectral width becomes infinitely large, while it vanishes as the Schmidt number increases, indicating extremely entangled states. Analysis of the symmetry degree as a function of the Schmidt number demonstrates that the biphoton states exhibit a symmetry degree in the immediate vicinity of unity when the Schmidt number is approximately 4. The research delivers a method for modulating biphoton spectra using an optical setup incorporating a Mach-Zehnder interferometer, obtaining cosine- or sine-modulated biphoton states by controlling interference within the interferometer.