Intensity-Based Criterion for Determining Exceptional Point in Parity-Time (PT) Symmetric Coupled Array of Optical Waveguides

Abstract

In this study, we investigated the propagation pattern and the site-to-site correlation function in a PT-symmetric waveguide array with different input quantum states. Recognizing the stark difference in propagation pattern before and after the PT symmetry-breaking point, we have developed a novel, straightforward intensity-based criterion to determine the exceptional point (EP). This new criterion shows excellent agreement with those obtained by directly computing the Hamiltonian's eigenvalues. Given the computational complexity of Hamiltonian diagonalization, our proposed criterion provides a highly efficient and valuable alternative for identifying the PT symmetry-breaking point. Importantly, the proposed criterion is not restricted to the specific system studied here, but is generally applicable to a wide class of systems that can be described within the tight-binding framework.

Figures (11)

• Figure 1: PT-symmetric system for (a) even number, and (b) odd, number of waveguides. The waveguides exhibit cylindrical symmetry and are located at equal distances. The colors red, green, and gray correspond to gain (G), loss (L), and neutral (N) conditions, respectively. In these figures, the yellow arrow shows how light enters the system.
• Figure 2: Propagation pattern of a waveguide array with $N = 50$ waveguides in the Hermitian regime ($g = 0$) for: (a) number state $|n\rangle_p$ with $n = 1$, (b) coherent state $|\alpha\rangle_p$ with $\alpha^2 = 1$, (c) squeezed state $|\xi\rangle_p$ with $\sinh^2(\xi) = 1$, (d) entangled state between the 1st and 2nd waveguides, and (e) entangled state between the 24th and 25th waveguides.
• Figure 3: Propagation pattern of a waveguide array with $N = 50$ waveguides in the PT-symmetry regime ($g = 0.03$) for: (a) number state $|n\rangle_p$ with $n = 1$, (b) coherent state $|\alpha\rangle_p$ with $\alpha^2 = 1$, (c) squeezed state $|\xi\rangle_p$ with $\sinh^2(\xi) = 1$, (d) entangled state between the 1st and 2nd waveguides, and (e) entangled state between the 24th and 25th waveguides.
• Figure 4: Propagation pattern of a waveguide array with $N = 50$ waveguides in the broken PT-symmetry regime ($g = 0.6$) for: (a) number state $|n\rangle_p$ with $n = 1$, (b) coherent state $|\alpha\rangle_p$ with $\alpha^2 = 1$, (c) squeezed state $|\xi\rangle_p$ with $\sinh^2(\xi) = 1$, (d) entangled state between the 1st and 2nd waveguides, and (e) entangled state between the 24th and 25th waveguides.
• Figure 5: Site-to-site correlation a waveguide array with $N = 50$ waveguides in the Hermitian regime ($g = 0$) for: (a) number state $|n\rangle_p$ with $n = 2$, (b) coherent state $|\alpha\rangle_p$ with $\alpha^2 = 2$, (c) squeezed state $|\xi\rangle_p$ with $\sinh^2(\xi) = 2$, (d) entangled state between the 1st and 2nd waveguides, and (e) entangled state between the 24th and 25th waveguides at propagation distance $z=10$.