Statistical-noise-enhanced multi-photon interference

TL;DR

The paper shows that, contrary to the two-photon HOM paradigm, multi-photon interference in symmetric multiport circuits can be enhanced by carefully engineered photon-number statistics. By analyzing coincidence probabilities in the DFT and a symmetric unitary $U_{\rm sym}$, it demonstrates that super-Poissonian noise can maximize interference visibility beyond the single-photon limit, revealing a statistical complementarity where quantum and classical advantages are mutually exclusive resources. The work provides analytic expressions for $N=2$ and $N=3$ and a general framework for arbitrary $N$, highlighting circuit-dependent, non-monotonic behavior of visibility as a function of $g^{(2)}$ and higher-order correlations. Practically, engineered noise offers a robust, high-counting-method for calibrating and characterizing multi-photon circuits, while also deepening the understanding of the quantum-classical boundary in bosonic interference. The results suggest broader implications for exploiting photon statistics to tailor interference in quantum photonic technologies.

Abstract

Photon statistics plays a governing role in multi-photon interference. While interference visibility in the standard two-photon case, known as Hong-Ou-Mandel interference, monotonically degrades with higher intensity correlation functions, we show that this monotonicity does not hold for three-photon interference in symmetric circuits. We reveal that, in the discrete Fourier transform circuit, engineered super-Poissonian photon-number fluctuations, realized using a modulated laser, maximize the visibility, surpassing the magnitude of the single-photon signature. In addition, by tuning the symmetric circuit parameters, we demonstrate that the visibility hierarchy inverts relative to the benchmark of Poissonian statistics. This trade-off implies that quantum and classical advantages are mutually exclusive resources for interference, indicating a form of statistical complementarity.

Figures (6)

• Figure 1: (a) Schematic of the interferometric scenario. The input fields are not limited to single photons but are characterized by intensity correlation functions. (b, c) Conceptual illustration of the coincidence probabilities in HOM interference (b) with the inputs of indistinguishable photons ($P_{\rm coinc}^{{\rm id}}$) and (c) those of distinguishable photons ($P_{\rm coinc}^{{\rm dist}}$).
• Figure 2: Visibility $V^{(3)}$ in DFT circuit. The red solid curve indicates the upper bound $V^{(3)}_{\rm cl}$ in the classical regime with $g^{(2)}\geq 1$. The green solid curve represents the limit of $V^{(3)}$ for the pure Gaussian-state inputs. For reference, $V^{(2)}=(1+g^{(2)})^{-1}$ with $T=R=1/2$ in Eq. (\ref{['eq:V2']}) is shown as the black dashed curve. The plotted points represent, in ascending order of $g^{(2)}$, inputs with 1, 2, and 4 photons ($\circ$) SM, laser light ($\diamond$), thermal ($g^{(2)}=2, g^{(3)}=6$) and its second-harmonic ($g^{(2)}=6, g^{(3)}=90$) lights ($\triangle$) Loudon2000 in each mode.
• Figure 3: Visibility as a function of the sequential mode overlap parameter $\xi$. The range $0 \leq \xi \leq 1$ corresponds to sweeping the mode overlap $M_{23}$ from 0 to 1 while keeping $M_{12}=M_{31}=0$. The range $1 < \xi \leq 2$ corresponds to sweeping $M_{12}=M_{31}$ from 0 to 1 with $M_{23}=1$. Blue: single photon. Orange: laser light. Green: thermal light. Red: optimized noise ($g^{(2)}\sim 1.9$, $g^{(3)}\sim 3.6$).
• Figure 4: Visibility as a function of phase $\phi$ in $U_{\rm sym}$. Blue: single photon (the dashed curve indicates the absolute value). Orange: laser light. Green: thermal light. Red: optimized noise for the DFT.
• Figure S1: Coincidence probabilities normalized by the input intensities as a function of phase $\phi$. (a) $\tilde{P}_{\rm coinc}^{{\rm id}}$ for indistinguishable case. (b) $\tilde{P}_{\rm coinc}^{{\rm dist}}$ for distinguishable case. The vertical axes are fixed to the same scale to highlight the absolute difference in coincidence probabilities. Blue: single photons. Orange: laser light. Green: thermal light. Red: optimized noise for the DFT.