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arXiv:1602.01363 · Physical Review A

Geometrically induced complex tunnelings for ultracold atoms carrying orbital angular momentum

Juan Polo, J. Mompart, V. Ahufinger

Published Mar 7, 2016• 31 citations
arXivHTMLPDF

Abstract

We investigate the dynamics of angular momentum states for a single ultracold atom trapped in two-dimensional systems of sided coupled ring potentials. The symmetries of the system show that tunneling amplitudes between different ring states with variation of the winding number are complex. In particular, we demonstrate that in a triangular ring configuration the complex nature of the cross-couplings can be used to geometrically engineer spatial dark states to manipulate the transport of orbital angular momentum states via quantum interference.

DOI
10.1103/physreva.93.033613

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We investigate the dynamics of angular momentum states for a single ultracold atom trapped in two-dimensional systems of sided coupled ring potentials. The symmetries of the system show that tunneling amplitudes between different ring states with variation of the winding number are complex. In particular, we demonstrate that in a triangular ring configuration the complex nature of the cross-couplings can be used to geometrically engineer spatial dark states to manipulate the transport of orbital angular momentum states via quantum interference.
We study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of l=1l=1l=1 orbital angular momentum (OAM) states of an optical lattice with a diamond-chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net $\ensuremath{\pi}$ flux through the plaquettes. These effects give rise to a topologically nontrivial band structure and protected edge states which persist everywhere in the parameter space of the model, indicating the absence of a topological transition. By taking advantage of these analytical mappings, we also show that this system constitutes a realization of a square-root topological insulator. In addition, we demonstrate that quantum interferences between the different tunneling processes involved in the dynamics may lead to Aharanov-Bohm caging in the system. All these analytical results are confirmed by exact diagonalization numerical calculations.
We demonstrate how quantum interference may lead to the appearance of robust edgelike states of a single ultracold atom in a two-dimensional optical ribbon. We show that these states can be engineered within the manifold of either local ground states of the sites forming the ribbon or states carrying one unit of angular momentum. In the former case, we show that the implementation of edgelike states can be extended to other geometries, such as tilted square lattices. In the latter case, we suggest using the winding number associated to the angular momentum as a synthetic dimension.
We study the generation of angular momentum carrying states for a single cold particle by breaking the symmetry of a spatial adiabatic passage process in a two-dimensional system consisting of three harmonic potential wells. By following a superposition of two eigenstates of the system, a single cold particle is completely transferred to the degenerate first excited states of the final trap, which are resonantly coupled via tunneling to the ground states of the initial and middle traps. Depending on the total time of the process, angular momentum is generated in the final trap, with values that oscillate between $\ifmmode\pm\else\textpm\fi{}\ensuremath{\hbar}$. This process is discussed in terms of the asymptotic eigenstates of the individual wells and the results are checked by simulations of the full two-dimensional Schr\"odinger equation.
We investigate the dynamics of neutral fermions trapped in a one-dimensional ring. We construct an effective magnetic field in the ring using the adiabatic motion of dark states created by light beams carrying an orbital angular momentum. We illustrate the effect of the orbital angular momentum by looking at the induced mass current and show how the Aharonov–Bohm effect manifests itself in an atomic Fermi gas as a periodic mass current as a function of the optically induced artificial magnetic flux.