Exceptional-Point-Induced Sensitivity-Robustness Phase Transition in Quantum Interference

Abstract

Quantum interference underpins many quantum information protocols but is typically studied in lossless Hermitian systems. Here, we reveal an exceptional point induced phase transition in two photon Hong Ou Mandel interference within a lossy coupled waveguide system. In the PT symmetric phase. interference is ultrasensitive to coupling strength, yielding sharp bunching antibunching switches. In the PT broken phase. it becomes robust oscillation free and propagation independent with coincidence probability stably tunable via coupling. These regimes enable enhanced quantum sensing and reliable two photon control for robust quantum information processing.

Figures (5)

• Figure 1: Waveguide setup and coincidence probability analysis near the EP. (a) Waveguide setup exhibiting quantum interference near the EP. (b) Three-dimensional plot of coincidence probability as a function of coupling strength $g$, loss parameter $\gamma$, and propagation length $z$, with the line $g=\frac{\gamma}{2}$ marking the EP. The coincidence probability transitions to narrow peaks as the system approaches the EP with increasing $\gamma$ or $z$ in the PT-symmetry phase. (c) Coincidence probability versus $\gamma$ for $g=1$ and $z=\frac{3}{2}\pi$. (d) Coincidence probability versus $g$ for a unitary beam splitter ($\gamma=0$) and a non-unitary beam splitter ($\gamma=2$) at $z=\frac{3}{2}\pi$, comparing Hermitian and non-Hermitian behaviors. (e) Coincidence probability versus $z$ for a unitary beam splitter ($g=1$, $\gamma=0$, top), a non-unitary beam splitter in the PT-symmetric phase ($g=1$, $\gamma=1$, middle), and the PT-symmetry-broken phase ($\gamma=2$, bottom) with $g=1$, $0.5$, $0.1$, and $0$.
• Figure 2: (a) Evolution of the two eigenvectors in the complex plane, showing amplitude distribution between the normal channel (C1) and lossy channel (C2). Red and blue curves trace the two eigenvectors. The amplitude separation between them reflects the relative photon population in each channel. The blue eigenvector rotates clockwise, while the red rotates counterclockwise due to opposite real parts of the eigenvalues. The transition from the lossy channel (before the yellow arrow) to the normal channel (after the arrow) demonstrates the competition between slowed eigenvalue-induced phase accumulation and the shrinking phase-alignment window near the exceptional point, a hallmark of non-Hermitian dynamics. (b, c, d) Photon proportion as a function of propagation length $z$ and coupling strength $g$. The first row shows results for a conventional unitary beam splitter, and the second row shows a non-unitary beam splitter ($\gamma=2$). Green circles, photon bunching events; Purple squares, anti-bunching events; Orange stars, anti-bunching events that vanish in the non-Hermitian case because loss prevents perfect reflection of both photons. (b) PT-symmetric phase ($g=1.1$) with varying $z$. (c) PT-symmetry-broken phase ($g=0.5$) with varying $z$. (d) Varying $g$ at $z=\frac{3}{2}\pi$. (e) Numerical results for the ratios of spacing in $z$ and $g$ between an anti-bunching and the adjacent bunching point, $\Delta z_{\text{NH}}$ and $\Delta g_{\text{NH}}$, relative to those in the Hermitian system $\Delta z_{\text{H}}$ and $\Delta g_{\text{H}}$, respectively.
• Figure 3: Sensing capability of a conventional unitary beam splitter (gray dashed line) versus a non-unitary beam splitter with single-channel loss (blue solid line). (a) Maximum slope of coincidence probability $P_{\text{coin}}$ with respect to coupling strength $g$ as a function of propagation length $z$ in the PT-symmetric phase for $\gamma=2$. (b, c) Fisher information at $z=\frac{3}{2}\pi$ (b) and $z=3\pi$ (c), quantifying sensitivity.
• Figure 4: Coincidence probability variation with $g$ at $z=3\pi$ for a conventional unitary beam splitter (gray dashed line) versus a non-unitary beam splitter with single-channel loss (blue solid line).
• Figure 5: Coincidence probability variation when $g\rightarrow0$. (a, b) show the coincidence probability variation with $g$ at $z=\frac{3}{2}\pi$ for a conventional unitary beam splitter (gray dashed line) versus a non-unitary beam splitter with single-channel loss (blue solid line). (c) shows the coincidence probability variation with $z$ for different $g$ when $g\rightarrow0$.