Quantum dynamics of bosons in a two-ring ladder: Dynamical algebra, vortexlike excitations, and currents

Abstract

We study the quantum dynamics of the Bose-Hubbard model on a ladder formed by two rings coupled by tunneling effect. By implementing the Bogoliubov approximation scheme, we prove that, despite the presence of the inter-ring coupling term, the Hamiltonian decouples in many independent sub-HamiltoniansĤ k associated to momentum-mode pairs ±k. Each sub-HamiltonianĤ k is then shown to be part of a specific dynamical algebra. The properties of the latter allow us to perform the diagonalization process, to find energy spectrum, the conserved quantities of the model, and to derive the time evolution of important physical observables. We then apply this solution scheme to the simplest possible closed ladder, the double trimer. After observing that the excitations of the system are weakly-populated vortices, we explore the corresponding dynamics by varying the initial conditions and the model parameters. Finally, we show that the inter-ring tunneling determines a spectral collapse when approaching the border of the dynamical-stability region. I.arXiv:1705.02115v3 [cond-mat.quant-gas]

Two-species boson mixture on a ring: A group-theoretic approach to the quantum dynamics of low-energy excitations

“…one boson in an atomic species and one in the other) through the terms K ± . We remark that this second process is due to operators K± which were absent in the two-ring model [21]. Some of these microscopic processes are illustrated in Fig.…”

“…In this article, using the method applied to the dynamics of bosons in a tworing ladder [21], we analyze the low-energy excitations in a two-component bosonic mixture described within the BH picture and confined on ring lattice. The ring geometry, designed more than ten years ago in [22], has recently raised a lot of interest in the study of atomtronic devices [23], [24] and its feasibility has been proved to be within the reach of current experimental techniques.…”

Pathway toward the formation of supermixed states in ultracold boson mixtures loaded in ring lattices

“…In this appendix, we derive, by means of a modified version of the Bogoliubov approximation scheme [32,43], the analytical expression of quasiparticles' frequencies of a L = 3-system when its ground state exhibits a supermixed soliton-like structure (namely, when it belongs to phase SM). In this circumstance, in fact, one can recognize that there are two site modes, a 1 , b 1 , that are macroscopically occupied, namely n 1 ≈ N a − n 2 − n 3 and m 1 ≈ N b − m 2 − m 3 while the microscopically occupied ones are a 2 , a 3 , b 2 and b 3 .…”

Spectral Function of a Boson Ladder in an Artificial Gauge Field

“…In quasi-one-dimensional systems, analogs of the Meissner and Vortex phase have been predicted for the bosonic two-leg ladder [1][2][3][4][5], the simplest system where orbital magnetic field effects are allowed. It was shown that in this model, the quantum phase transition between the Meissner and the Vortex phase is a commensurate-incommensurate transition [6][7][8].…”