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

TL;DR

This work addresses how Hong-Ou-Mandel antibunching can be controlled by parity-guided spectral shaping of biphoton states. By formulating a symmetry degree $D_S$ that governs the two-photon coincidence probability and decomposing the joint spectral amplitude into even and odd parity components, the authors derive parity conditions under which antibunching can be induced or suppressed, showing that standard SPDC cannot exhibit antibunching. They introduce experimentally feasible modulated biphoton states via a Mach–Zehnder interferometer, deriving analytic expressions for $D_S$ and the Schmidt number $K$ as functions of the modulation parameter $\beta$, and reveal sharp resonances where $D_S$ reaches $-1$ and $K$ peaks, evidencing a strong $D_S$–$K$ correlation. The results demonstrate a pathway to entanglement control and ultra-sensitive phase measurements, with potential applications in quantum metrology and micro- to nano-scale optical gyroscopy; the approach enables switching between bunching and antibunching by spectral shaping while tracking entanglement via the Schmidt formalism.

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.

Figures (7)

• Figure 1: Conceptual scheme of the HOM interferometer under consideration. A nonlinear crystal (NC) is pumped by the radiation with central frequency $2\Omega$ in order to produce a biphoton state. At the output of the NC, the photons are separated spatially and directed to the different optical-fiber channels, characterized by creating operators $\hat{b}^{\dagger}_1(\omega_1)$ and $\hat{b}^{\dagger}_2(\omega_2)$, respectively. The biphoton state passes through an arbitrary scheme consisting of phase shifters. After the scheme, the biphoton state interferes at the output beamsplitter BS and is detected by photodetectors $D_1$ and $D_2$.
• Figure 2: Dependence of the symmetry degree, $D_S$, of SPDC biphoton joint spectral amplitude with the Schmidt modes \ref{['eq:eq3.1.3']} on the Schmidt number $K$ computed from Eqs. \ref{['eq:eq2.2.11']} and \ref{['eq:eq3.1.4']} at different values of the variance ratio $\sigma_2/\sigma_1$ with $\Delta \tau = 0$.
• Figure 3: Conceptual scheme of optical setup to modulate biphoton states.
• Figure 4: Dependence of the symmetry degree $D_S$ on the time-delay parameter $\beta$ computed for the biphoton state with the cosine-modulated JSA in the three different regions. The parameters are: $\sigma_1 = \sigma_2 = 2\pi\times10$ THz, $\Omega = 2\pi\times 844.5$ THz, $\sigma_p=0.01\sigma_1$, $\Delta\tau =0$.
• Figure 5: The Schmidt number, $K$, and the symmetry degree, $D_S$, as a function of the time-delay parameter $\beta$ for the biphoton state with the cosine-modulated JSA. The parameters are listed in the caption of Fig. \ref{['fig:fig4']}. The insets display a zoomed-in view of the first resonant peak in the Schmidt number and the symmetry degree profiles.