Edge states of the long-range Kitaev chain: an analytical study

We analyze the properties of the edge states of the one-dimensional Kitaev model with long-range anisotropic pairing and tunneling. Tunneling and pairing are assumed to decay algebraically with exponents $\alpha$ and $\beta$, respectively, and $\alpha,\beta>1$. We determine analytically the decay of the edges modes. We show that the decay is exponential for $\alpha=\beta$ and when the coefficients scaling tunneling and pairing terms are equal. Otherwise, the decay is exponential at sufficiently short distances and then algebraic at the asymptotics. We show that the exponent of the algebraic tail is determined by the smallest exponent between $\alpha$ and $\beta$. Our predictions are in agreement with numerical results found by exact diagonalization and in the literature.Comment: 8 pages, 3 figure

Adiabatic Control of Decoherence-Free-Subspaces in an Open Collective System

We propose a method to adiabatically control an atomic ensemble using a decoherence-free subspace (DFS) within a dissipative cavity. We can engineer a specific eigenstate of the system's Lindblad jump operators by injecting a field into the cavity which deconstructively interferes with the emission amplitude of the ensemble. In contrast to previous adiabatic DFS proposals, our scheme creates a DFS in the presence of collective decoherence. We therefore have the ability to engineer states that have high multi-particle entanglements which may be exploited for quantum information science or metrology. We further demonstrate a more optimized driving scheme that utilizes the knowledge of possible diabatic evolution gained from the so-called adiabatic criteria. This allows us to evolve to a desired state with exceptionally high fidelity on a time scale that does not depend on the number of atoms in the ensemble. By engineering the DFS eigenstate adiabatically, our method allows for faster state preparation than previous schemes that rely on damping into a desired state solely using dissipation.Comment: 15 pages and 8 Figure

Coherence Properties of the Repulsive Anyon-Hubbard Dimer

One-dimensional anyonic models of the Hubbard type show intriguing ground-state properties, effectively transmuting between Bose-Einstein and Fermi-Dirac statistics. The simplest model that one can investigate is an anyonic version of the bosonic Josephson junction, the repulsive anyon-Hubbard dimer. In the following we find an exact duality relation to the Bethe-solvable Bose-Hubbard dimer, which is well known from quantum optics and information theory and has interesting connections to spin squeezing and entangled coherent states. Conversely, we show that the anyonic Hubbard dimer has non-trivial coherence properties for large particle numbers, which can potentially be probed by cold atom experiments. We find that the statistical interactions act as excitation-selective filters or amplifiers for large particle numbers $N$, determining the fate of multi-body coherences depending on their commensurability with respect to the exchange parameter $\theta$.Comment: 8 pages, 2 figures, for more information and latest version see https://www.physik.uni-kl.de/eggert/papers