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Optics Express

Characterization of PT-symmetric quantum interference based on the coupled mode theory

Junhe Zhou

Published Jun 8, 2022• 7 citations
Publisher

Abstract

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.

DOI
10.1364/oe.458881

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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.
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.
It is well known that the Hong–Ou–Mandel (HOM) effect can be realized on beam splitters (BSs) in the form of coupled waveguides. It is believed that in this case, the theory is similar to HOM interference on conventional BSs. In this work, it is shown that if a BS is used in the form of a coupled waveguide, the theory of HOM interference can differ significantly from the known one. It is shown that even in the case of completely identical photons, the visibility of V can essentially differ from unity. The developed theory must be taken into account in quantum optical schemes, where BSs are represented mainly as coupled waveguides.
The Hong-Ou-Mandel (HOM) effect, an effective two-photon interference phenomenon, is a cornerstone of quantum optics and a key tool for linear optical quantum information processing. While the HOM effect has been extensively studied both theoretically and experimentally for various photonic quantum states, particularly in the spectral domain, detailed overviews of its behaviour for structured photons - those with complex spatial profiles - under arbitrary spatial mode measurement schemes are still lacking. This tutorial aims to fill this gap by providing a comprehensive theoretical analysis of the HOM effect for structured photons, including an arbitrary mode projection on quantum interference outcomes. The tutorial also provides analytical, closed-form expressions of the HOM visibility under different measurement conditions.