By considering a cigar-shaped trapping potential elongated in a proper curvilinear coordinate, we discover a new form of wave localization that arises from the interplay of geometry and topological protection. The potential is modulated in its shape such that local curvature introduces a trapping potential. The curvature varies along the trap curvilinear axis encodes a topological Harper modulation. The varying geometry maps our system in a one-dimensional Andre-Aubry-Harper grating. We show that a mobility edge exists with topologically protected states. These modes are extremely robust with respect to disorder in the shape of the string. The results may be relevant for localization phenomena in Bose-Einstein condensates, optical fibers and waveguides, and new laser devices, but also for fundamental studies on string theory. Taking into account that the one-dimensional modulation mimics the existence of an additional dimension, our system is the first example of a physically realizable five-dimensional string.
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We show that quantum fluids enable experimental analogs of relativistic orbital precession in the presence of non-paraxial effects. The analysis is performed by the hydrodynamic limit of the Schroedinger equation. The non-commutating variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is formally identical to the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton’s theory. In our case, the corrections are due to the modified uncertainty principle. The results may enable novel relativistic analogs in the laboratory, also including sub Planckian phenomenology.
The cascade of resonant -symmetric topological structures is shown to emit laser light with a frequency comb spectrum. We consider optically active topological lattices supporting edge modes at regularly spaced frequencies. When the amplified resonances in the PT-broken regime match the edge modes of the topological gratings, we predict the emission of discrete laser lines. A proper design enables the engineering of the spectral features for specific applications. Topological protection makes the system very well suited for a novel generation of compact frequency comb emitters for spectroscopy, metrology, and quantum information.