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Register a new userGeometric effects in the effective-mass theory and topological optical superlattices
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Cold atoms tailored by an optical lattice have become a fascinating arena for simulating quantum physics. In this area, one important and challenging problem is creating effective spin-orbit coupling (SOC), especially for fashioning a cold atomic gas into a topological phase, for which prevailing approaches mainly rely on the Raman coupling between the atomic internal states and a laser field. Herein, a strategy for realizing effective SOC is proposed by exploiting the geometric effects in the effective-mass theory, without resorting to internal atomic states. It is shown that the geometry of Bloch states can have nontrivial effects on the wave-mechanical states under external fields, leading to effective SOC and an effective Darwin term, which have been neglected in the standard effective-mass approximation. It is demonstrated that these relativisticlike effects can be employed to introduce effective SOC in a two-dimensional optical superlattice, and induce a nontrivial topological phase.
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Lecture Notes of the 45th IFF Spring School Computing Solids - Models, ab initio methods and supercomputing (Forschungszentrum Juelich, 2014).
The topological Kondo (TK) model has been proposed in solid-state quantum devices as a way to realize non-Fermi liquid behaviors in a controllable setting. Another motivation behind the TK model proposal is the demand to demonstrate the quantum dynamical properties of Majorana fermions, which are at the heart of their potential use in topological quantum computation. Here we consider a junction of crossed Tonks-Girardeau gases arranged in a star-geometry (forming a Y -junction), and we perform a theoretical analysis of this system showing that it provides a physical realization of the topological Kondo model in the realm of cold atom systems. Using computer-generated holography, we experimentally implement a Y-junction suitable for atom trapping, with controllable and independent parameters. The junction and the transverse size of the atom waveguides are of the order of 5 micrometers, leading to favorable estimates for the Kondo temperature and for the coupling across the junction. Since our results show that all the required theoretical and experimental ingredients are available, this provides the demonstration of an ultracold atom device that may in principle exhibit the topological Kondo effect.
We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change in the driving field topology. The transition is associated with an effective geometric phase which is identified from the paths of the magnetic moments in a spherical geometry. The topological transition presents close similarities between SO(3) and SU(2) cases but features differences in, e.g., the adiabatic limits of the geometric phases, being $2pi$ and $pi$ in the classical and the quantum case, respectively. We discuss possible experiments where the effective geometric phase would be observable.
We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static system, i.e. metallic bulk transport with conductivity of order $e^2/h$, is substantially suppressed at some Floquet topological transitions in the clean system. We determine the conditions for this suppression analytically and confirm our results in numerical simulations. Remarkably, introducing disorder dramatically enhances this transport by several orders of magnitude.
We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {it induce} topological order, reducing the need for quasiballistic samples to obtain Majorana fermions. Moreover, we find that the total phase space area of the topological state is conserved for long disordered Rashba wires, and can even be increased in an appropriately engineered superlattice potential.
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