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arXiv:1101.5081 · Annalen der Physik

Quantum anticentrifugal potential in a bent waveguide

Rossen Dandoloff, Victor Atanasov

Published Sep 20, 2011• 3 citations
arXivHTMLPDF

Abstract

Abstract We show the existence of an anticentrifugal force for a quantum particle in a bent waveguide. This effect may be observed in interference experiments which are sensitive to the additional phase of the wavefunction gained in the bent regions and can find application in distinguishing between straight and bent geometries.
DOI
10.1002/andp.201100136

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In a two-dimensional world, a free quantum particle of vanishing angular momentum experiences an attractive force. This force originates from a modification of the classical centrifugal force due to the wave nature of the particle. For positive energies the quantum anticentrifugal force manifests itself in a bunching of the nodes of the energy wave functions towards the origin. For negative energies this force is sufficient to create a bound state in a two-dimensional \ensuremath{\delta}-function potential. In a counterintuitive way, the attractive force pushes the particle away from the location of the \ensuremath{\delta}-function potential. As a consequence, the particle is localized in a band-shaped domain around the origin.
This chapter aims to address the quantum signal role and properties in optical fiber application mainly in quantum communication. It covers the general discussion on quantum bits and optical waveguiding properties. The highlight of this chapter lies in the discussion of the quantum fictitious force of anti-centrifugal force which was first reported in 2001. Under this condition, the free particle experience an attractive potential towards the rotating center of a bent waveguide structure. A lot of theoretical work has been carried out to observe this quantum phenomenon. However, no intensive experimental work has been carried out to date. With the advancement of nano-fabrication technology and quantum experimental, it provides a bright potential to observe these phenomena. Thus, we proposed a promising material of Lithium Niobate on Insulator to serve as a waveguiding platform to study this quantum effect experimentally. The discussion is extended to perceive the relation between Schrodinger and Helmholtz’s equation corresponding to this effect.
Non-zero curvature in a waveguide leads to the appearance of an attractive quantum potential which crucially affects the dynamics in matter-wave circuits. Using methods of supersymmetric quantum mechanics, pairs of bent waveguides are found whose geometry-induced potentials share the same scattering properties. As a result, reflectionless waveguides, dual to the straight waveguide, are identified. Strictly isospectral waveguides are also found by modulating the depth of the trapping potential. Numerical simulations are used to demonstrate the efficiency of these approaches in tailoring and controlling curvature-induced quantum-mechanical effects.
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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.