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arXiv:1803.02718 · Physical Review A

Bosonic double ring lattice under artificial gauge fields

Nicolas Victorin, F. W. J. Hekking, Anna Minguzzi

Published Nov 26, 2018• 11 citations
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Abstract

We consider a system of weakly interacting bosons confined on a planar double ring lattice subjected to two artificial gauge fields. We determine its ground state by solving coupled discrete nonlinear Schr\"odinger equations at mean-field level. At varying inter-ring tunnel coupling, flux, and interactions, we identify the vortex, Meissner, and biased-ladder phases also predicted for a bosonic linear ladder by a variational ansatz. We also find peculiar features associated to the ring geometry, in particular parity effects in the number of vortices, and the appearance of a single vortex in the Meissner phase. We show that the persistent currents on the rings carry precise information on the various phases. Finally, we propose a way of observing the Meissner and vortex phases via spiral interferogram techniques.

DOI
10.1103/physreva.98.053626

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We consider a system of weakly interacting bosons confined on a planar double ring lattice subjected to two artificial gauge fields. We determine its ground state by solving coupled discrete nonlinear Schr"odinger equations at mean-field level. At varying inter-ring tunnel coupling, flux, and interactions, we identify the vortex, Meissner, and biased-ladder phases also predicted for a bosonic linear ladder by a variational ansatz. We also find peculiar features associated to the ring geometry, in particular parity effects in the number of vortices, and the appearance of a single vortex in the Meissner phase. We show that the persistent currents on the rings carry precise information on the various phases. Finally, we propose a way of observing the Meissner and vortex phases via spiral interferogram techniques.
We consider a system of weakly interacting bosons confined on a planar double lattice ring subjected to two artificial gauge fields. This system is known to display three phases: the Meissner phase, where the flow of particles is carried at the edges of the system without transverse current; a vortex phase, characterized by nonzero transverse current; and a biased-ladder phase, characterized by an imbalance of the population of the two rings. We use the Bogoliubov approximation to determine the excitation spectrum in the three phases, the dynamic structure factor, and the quantum fluctuation corrections to the first-order correlation function. Our analysis reveals supersolid features as well as Josephson modes, corresponding to out-of-phase modes of the finite ring.
We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.
We consider a two-leg boson ladder in an artificial U(1) gauge field and show that, in the presence of interleg attractive interaction, the flux induced vortex state can be melted by dislocations. For increasing flux, instead of the Meissner to vortex transition in the commensurate-incommensurate universality class, first, an Ising transition from the Meissner state to a charge density wave takes place, then, at higher flux, the melted vortex phase is established via a disorder point where incommensuration develops in the rung current correlation function and in momentum distribution. Finally, the quasi-long-range ordered vortex phase is recovered for sufficiently small interaction. Our predictions for the observables, such as the spin current and the static structure factor, could be tested in current experiments with cold atoms in bosonic ladders.
We investigate interacting bosons in a two-leg lattice, which is subject to an uniform artificial magnetic field. Its Hamiltonian takes into account the next nearest neighbor kinetic tunneling term, along the principal diagonal direction. With the help of an inhomogeneous dynamical Gutzwiller mean-field theory, we figure out four novel quantum phases of the system site by site, three of which are the dual vortex lattice, the triplet vortex lattice, and the composite vortex lattice. They particularly present parallelogram vortical particle currents, inside those conventional rectangular vortical currents, due to the import of next nearest neighbor kinetic tunneling. Under certain parameters, we further identify the crossed circulation lattice featuring alternating sequences on local currents and occupancies, whose minimal periods are determined by the value of flux quanta.
We study the persistent currents of an interacting Fermi gas confined in a tightly confining ring trapand subjected to an artificial gauge field. For attractive interactions, we study the currents all through the BCS-BEC crossover. At weak attractions, on theBCS side, fermions display a parity effect in the persistent currents, i.e. their response to the gauge fieldis paramagnetic or diamagnetic depending on the number of pairs on the ring. At resonance and on theBEC side of the crossover, we find a halving of the periodicity of the ground-state energy as a function ofthe artificial gauge field and disappearance of the parity effect, indicating that persistent currents can beused to infer the formation of tightly-bound bosonic pairs. We analyze then the readout of current states by spiral interferograms, showing that Fermi gases display an intrinsic reduction of coherence. We finally show that the spin-resolved density-density correlator obtained from the expansion of the fermions at long times allows to probe the halving of the periodicity of the persistent currents and also yields information on quasi-off diagonal long range order.