Controlling Hong-Ou-Mandel antibunching via parity governed spectral shaping of biphoton states

TL;DR

This paper demonstrates how spectral phase modulation of biphoton states can control Hong-Ou-Mandel antibunching and bunching effects, with experimental feasibility and detailed spectral symmetry analysis.

Contribution

It introduces a method to switch between HOM bunching and antibunching regimes using spectral phase modulation based on parity properties of the biphoton spectral function.

Findings

Spectral phase modulation can switch HOM regimes.

The symmetry degree is governed by spectral parity properties.

Resonance peaks correlate with HOM antibunching dips.

Abstract

We investigate into experimentally detectable effects such as the Hong-Ou-Mandel (HOM) bunching and antibunching. These regimes can be characterized using the symmetry degree parameter $D_S$ that enters the two-photon coincidence probability $P_{2c}=(1-D_S)/2$. In the case of HOM bunching (antibunching), $D_S$ is positive (negative). Though the symmetry degree can generally be expressed in terms of the difference between the contributions coming from the symmetric and antisymmetric parts of the biphoton joint spectral amplitude (JSA), $\psi(\omega_1,\omega_2)$, for a certain physically realizable class of the JSA, where $\psi(\omega_1,\omega_2)$ is proportional to the product of amplitudes $\varphi_1(\omega_1)\varphi_2(\omega_2)$ multiplied by a Gaussian shaped entangling factor, we find the sign of $D_S$ is primarily governed by the parity properties of the spectral function, $\varphi_{12}(\omega)=\varphi_1(\omega)\varphi_2^*(\omega)$. It is the even (odd) part of $\varphi_{12}=\varphi_{12}^{(+)}+\varphi_{12}^{(-)}$ that meets the parity condition $\varphi_{12}^{(+)}(\omega-\Omega)=\varphi_{12}^{(+)}(\Omega-\omega)$ ($\varphi_{12}^{(-)}(\omega-\Omega)=- \varphi_{12}^{(-)}(\Omega-\omega)$) to yield the positive (negative) contribution, $D_S^{(+)}$ ($-D_S^{(-)}$), to the symmetry degree parameter: $D_S=D_S^{(+)}-D_S^{(-)}$. We have shown that switching between the bunching and antibunching regimes can be realized using the experimentally accessible family of modulated biphoton states produced using the spectral phase modulation fine-tuned via the sub-nanometer scale variation of the path length. For this class of modulated states, the Schmidt number has been computed as a function of the modulation parameter. This dependence reveals the structure of narrow resonance peaks strongly correlated with the corresponding narrow dips of the symmetry degree where the HOM antibunching occurs.