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arXiv:1710.08777 · Physical Review A

Resonant persistent currents for ultracold bosons on a lattice ring

Geva Arwas, Doron Cohen, F. W. J. Hekking, Anna Minguzzi

Published Dec 19, 2017• 11 citations
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Abstract

Persistent currents are studied for a one-dimensional bosonic gas in a ring lattice that has a SQUID-like geometry. While generically such currents are expected to be strongly suppressed in the Mott insulator phase, they show a pronounced resonant behavior when the barrier strength becomes of the order of the interparticle interaction energy.

DOI
10.1103/physreva.96.063616

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Persistent currents are studied for a one-dimensional bosonic gas in a ring lattice that has a SQUID-like geometry. While generically such currents are expected to be strongly suppressed in the Mott insulator phase, they show a pronounced resonant behavior when the barrier strength becomes of the order of the interparticle interaction energy.
We present an exact calculation of the persistent current in interacting disordered 1D rings. This system exhibits a variety of interesting behaviors depending on the disorder and the strength of electron-electron interactions. We find that even for the disordered case the current at high values of interactions is strongly suppressed due to the Mott-Hubbard metal-insulator transition. We observe that no dramatic increase of the averaged current or its rms value as a result of interactions is possible for these systems.
We revisit here the Kibble-Zurek mechanism for superfluid bosons slowly driven across the transition toward the Mott-insulating phase. By means of a combination of the time-dependent variational principle and a tree-tensor network, we characterize the current flowing during annealing in a ring-shaped one-dimensional Bose-Hubbard model with artificial classical gauge field on up to 32 lattice sites. We find that the superfluid current shows, after an initial decrease, persistent oscillations which survive even when the system is well inside the Mott insulating phase. We demonstrate that the amplitude of such oscillations is connected to the residual energy, characterizing the creation of defects while crossing the quantum critical point, while their frequency matches the spectral gap in the Mott insulating phase. Our predictions can be verified in future atomtronics experiments with neutral atoms in ring-shaped traps. We believe that the proposed setup provides an interesting but simple platform to study the nonequilibrium quantum dynamics of persistent currents experimentally.
Abstract We study the persistent currents and interspecies entanglement generation in a Bose–Bose mixture formed by two atomic gases (hereafter labeled by the letters A and B) trapped in a one-dimensional ring lattice potential with an artificial gauge field after a sudden quench from zero to strong interactions between the two gases. Assuming that the strength of these interactions is much larger than the single species energies and that the gas A is initially in the Mott-insulator regime, we show that the current of the gas B is reduced with respect to its value prior the interaction quench. Averaging fast oscillations out, the relative decrease of this current is independent of the initial visibility and Peierls phase of the gas B and behaves quadratically with the visibility of the gas A. The second Rényi entropy of the reduced state measuring the amount of entanglement between the two gases is found to scale linearly with the number of sites and to be proportional to the relative decrease of the current.
We study the ground state of two interacting bosonic particles confined in a ring-shaped lattice potential and subjected to a synthetic magnetic flux. The system is described by the Bose-Hubbard model and solved exactly through a plane-wave Ansatz of the wave function. We obtain energies and correlation functions of the system both for repulsive and attractive interactions. In contrast with the one-dimensional continuous theory described by the Lieb-Liniger model, in the lattice case we prove that the center of mass of the two particles is coupled with its relative coordinate. Distinctive features clearly emerge in the persistent current of the system. While for repulsive bosons the persistent current displays a periodicity given by the standard flux quantum for any interaction strength, in the attractive case the flux quantum becomes fractionalized in a manner that depends on the interaction. We also study the density after a long time expansion of the system. Our results can be used to benchmark approximate schemes for the many-body problem such as the density matrix renormalization group or other variational schemes.