arXiv subjects
Publications and source records attributed to C. Yuce.
We introduce a one dimensional non-Hermitian four band tight binding lattice system. We find stable topological edge states protected by particle-hole and parity-time symmetries. We show that topological phase appears in the system. We discuss that the system can also be used as a topological laser if the gain and loss positions in a unit cell are judiciously arranged.
We consider periodically modulated Su-Schrieffer-Heeger (SSH) model with gain and loss. This model, which can be realized with current technology in photonics using waveguides, allows us to study Floquet topological insulating phase. By using Floquet theory, we find the quasi-energy spectrum of this one dimensional PT symmetric topological insulator. We show that stable Floquet topological phase exists in our model provided that oscillation frequency is large and the non-Hermitian degree is below than a critical value.
Topological edge states appear at the interface of topologically distinct two Hermitian insulators. We study the extension of this idea to non-Hermitian systems. We consider PT symmetric and topologically distinct non-Hermitian insulators with real spectra and study topological edge states at the interface of them. We show that PT symmetry is spontaneously broken at the interface during the topological phase transition. Therefore topological edge states with complex energy eigenvalues appear at the interface. We apply our idea to a complex extension of the Su-Schrieffer-Heeger (SSH) model.
We study self-acceleration in PT and non-PT symmetric systems. We find some novel wave effects that appear uniquely in non-Hermitian systems. We show that integrable self-accelerating waves exist if the Hamiltonian is non-Hermitian. We find that self-accelerating constant intensity waves are possible even when gain and loss are not balanced in the system.
We introduce a new self-accelerating wave packet solution of the Schrodinger equation in one dimension. We obtain an exact analytical parabolic cylinder wave for the inverted harmonic potential. We show that truncated parabolic cylinder waves exhibits their accelerating feature.
We consider a Glauber-Fock oscillator and show that diffraction can be managed. We show how to design arrays of waveguides where light beams experience zero diffraction. We find an exact analytical family of nondiffracting localized solution. We predict discrete parametric oscillation in the Glauber-Fock oscillator.
We consider a non-Hermitian generalization of the Kitaev model and study the existence of stable Majorana zero energy modes. We show that they exist in the limit of zero chemical potential even if balanced gain and loss are randomly distributed along the lattice. We show that Majorana zero modes also appear if the chemical potential is different from zero provided that not the full Hamiltonian but the non-Hermitian part of the Hamiltonian is PT symmetric.
Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight binding lattice if certain conditions are satisfied. We show that pseudo PT symmetry guarantees the reality of the quasi energy spectrum in our system.
In this paper, we study the existence of Floquet topological insulators for PT symmetric non-Hermitian Hamiltonians. We consider an array of waveguide in 1D with periodically changing non-Hermitian potential and predict the existence of Floquet topological insulators in the system. We also extend the concept of Floquet topological phase to a two dimensional non-Hermitian system.
The free particle Schrodinger equation admits a non-trivial self-accelerating Airy wave packet solution. Recently, the Airy beams that freely accelerate in space was experimentally realized in photonics community. Here we present self-accelerating waves for the Bose-Einstein condensate in a time dependent harmonic oscillator potential. We show that parity and time reversal symmetries for self accelerating waves are spontaneously broken.
A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.
We study discrete rogue waves in an array of nonlinear waveguides. We show that very small degree of disorder due to experimental imperfection has a deep effect on the formation of discrete rogue waves. We predict long-living discrete rogue wave solution of the discrete nonlinear Schrodinger equation.
We investigate quantum tunneling phenomena for an optical lattice subjected to a bichromatic ac force. We show that incommensurability of the frequencies leads to super Bloch oscillation. We propose directed super Bloch oscillation for the quasi periodically driven optical lattice. We study the dynamical localization and photon assisted tunneling for a periodical and quasi-periodical ac force.
We study pseudo PT symmetry for a tight binding lattice with a general form of the modulation. Using high-frequency Floquet method, we show that the critical non-Hermitian degree for the reality of the spectrum can be manipulated by varying the parameters of the modulation. We study the effect of periodical and quasi-periodical nature of the modulation on the pseudo PT symmetry.
PT symmetric Aubry-Andre model describes an array of N coupled optical waveguides with position dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of disorder for small number of lattice sites. We obtain the Hofstadter Butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserves the total intensity.
We investigate fast frictionless expansion of an optical lattice with dynamically variable spacing (accordion lattice). We design an expansion trajectory that yields a final state identical to the initial state up to an irrelevant phase factor. We discuss the effect of additional force and nonlinear interaction on the fast frictionless expansion.
We consider a singly quantized off-axis straight vortex in a rotating dipolar ultracold gas in the Thomas-Fermi (TF) regime. We derive analytic results for small displacements and perform numerical calculations for large displacement within the TF regime. We show that the dipolar interaction energy increases (decreases) as the vortex moves from the trap center to the edge in an oblate (a prolate) trap. We find that for an oblate (a prolate) trap, the effect of the dipole-dipole interaction is to lower (raise) both the precession velocity of an off-center straight vortex line and the angular velocity representing the onset of metastability.
Berry's phase is investigated for ultracold atoms in a frequency modulated optical lattice. It is shown that Berry's phase appears due to Bloch oscillation and the periodic motion of the optical lattice. Particularly, Berry's phase for ultracold atoms under the gravitational force in an oscillating tight-binding optical lattice is calculated analytically. It is found that the Berry's phase depends linearly on the amplitude of the oscillation of the optical lattice.