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Optics Express

Analytical formulation of quantum interference inside coupled waveguides with unequal losses

Junhe Zhou

Published Sep 22, 2022• 4 citations
Publisher

Abstract

In this paper, a theoretical framework is proposed to formulate the quantum interference inside the coupled waveguides with unequal losses. The quantum coupled mode equation is added with the Langevin noise terms to account for the impact of unequal losses, which can be solved analytically. A close form formula is derived for the correlation matrix of the Langevin noise terms, which provides full information for the density matrix of the propagation state. The theory is self-consistent and tested with a three-waveguide system, which is considered as anti-parity-time (PT) symmetric and simulated in the previous publications. An 89-waveguide system is analyzed afterwards to further demonstrate the applicability of the theory.

DOI
10.1364/oe.470006

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In this paper, a theoretical framework is proposed to formulate the quantum interference inside the coupled waveguides with unequal losses. The quantum coupled mode equation is added with the Langevin noise terms to account for the impact of unequal losses, which can be solved analytically. A close form formula is derived for the correlation matrix of the Langevin noise terms, which provides full information for the density matrix of the propagation state. The theory is self-consistent and tested with a three-waveguide system, which is considered as anti-parity-time (PT) symmetric and simulated in the previous publications. An 89-waveguide system is analyzed afterwards to further demonstrate the applicability of the theory.
In this paper, we propose a comprehensive quantum theoretical framework to formulate the quantum interference inside the parity-time (PT) symmetric waveguide system which is formed by two coupled optical waveguides with unequal losses. Based on the theory, the expression for the well-known Hong-Ou-Mandel (HOM) dip is derived, which is in an exact agreement with the published results. What's more, a novel one-photon quantum interference phenomenon is predicted according to the model, which suggests a quantum interference process similar to the HOM effect can be observed for the one-photon state, while the other photon is lost due to the waveguide attenuation. Such phenomenon cannot occur in a Hermitian system or in the system formed by the waveguides with equal losses.
We theoretically demonstrate quantum interference in an anti-parity-time (anti-PT) symmetric system based on coupled waveguides. We calculate the coincidence probability in an input polarization-entangled two-photon state, which can be used to simulate different statistical particles. When the birefringence of the waveguides is negligible, our results indicate that the coincidence probabilities of the bosons and fermions decrease exponentially with the propagation distance in both the unbroken and broken anti-PT symmetry regions owing to the dissipation. Particularly, loss-induced transparency is observed for the bosons. Simultaneously, the statistical rule valid in the Hermitian system is violated and the antibunching of bosons is observed. When the birefringence of the waveguides is considered, the coincidence probability of the bosons and fermions is equalized at the exceptional point (EP), whereas that of the bosons is less(greater) than that of the fermions in the broken(unbroken) anti-PT symmetry region. Additionally, we observe the Hong-Ou-Mandel dip for bosons in the broken anti-PT phase. Our research provides a complementary technique for the manipulation of quantum interference compared with the PT symmetric system and may be applied in building quantum devices with anti-PT symmetric quantum mechanics.
We analyze the noise characteristics of an optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers. In such a system, the non-degenerated signal and idler waves co-propagate through the link, interacting with each other in the optical parametric amplifiers. For the first time, we derive a closed-form expression for the accumulated noise using the quantum-mechanical Langevin-equation approach. The derived noise formula allows calculating the noise figure of the optical-amplifier chain under the influence of the internal loss of the amplifiers and the transmission loss of the link, thereby theoretically demonstrating its low-noise characteristics.
We analyze the noise characteristics of an optical transmission system repeated by two-mode phase-sensitive optical parametric amplifiers. In such a system, the non-degenerated signal and idler waves co-propagate through the link, interacting with each other in the optical parametric amplifiers. For the first time, we derive a closed-form expression for the accumulated noise using the quantum-mechanical Langevin-equation approach. The derived noise formula allows calculating the noise figure of the optical-amplifier chain under the influence of the internal loss of the amplifiers and the transmission loss of the link, thereby theoretically demonstrating its low-noise characteristics.
A model is proposed where two ${\ensuremath{\chi}}^{(2)}$ nonlinear waveguides are contained in a cavity suited for second-harmonic generation. The evanescent wave coupling between the waveguides is considered as weak, and the interplay between this coupling and the nonlinear interaction within the waveguides gives rise to quantum violations of the standard quantum limit. Pronounced twin-beam behavior is observed as almost complete noise suppression in the difference as well as the sum of the waveguide intensities close to bistable transitions, self-pulsing instabilities as well as the transition from symmetric to asymmetric states. The correlations imply strong correlations and anticorrelations induced by the coupling. The violations of the standard quantum limit are particularly strong when two instabilities are competing. The results are based on the full quantum Langevin equations derived from the boson operator Hamiltonian and including cavity damping effects. The intensity correlations of the output fields are calculated semianalytically using a linearized version of the Langevin equations derived through the positive-P representation. Confirmation of the analytical results are obtained by numerical simulations of the nonlinear Langevin equations derived using the truncated Wigner representation.
A quantum mechanical analysis of the propagation of coupled modes in integrated optical waveguides is given. The modal orthonormalization property on a cross-section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry are taken into account to derive the quantum momentum operator and Heisenberg's equations giving a quantum-consistent formulation of the coupled mode propagation as a function of forward and backward creation and annihilation operators.