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

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), $ψ(ω_1,ω_2)$, for a certain physically realizable class of the JSA, where $ψ(ω_1,ω_2)$ is proportional to the product of amplitudes $\varphi_1(ω_1)\varphi_2(ω_2)$ 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, $\varphi_{12}(ω)=\varphi_1(ω)\varphi_2^*(ω)$. It is the even (odd) part of $\varphi_{12}=\varphi_{12}^{(+)}+\varphi_{12}^{(-)}$ that meets the parity condition $\varphi_{12}^{(+)}(ω-Ω)=\varphi_{12}^{(+)}(Ω-ω)$ ($\varphi_{12}^{(-)}(ω-Ω)=- \varphi_{12}^{(-)}(Ω-ω)$) 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.