Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder

Abstract

We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.Introduction. The quantum states of interacting electrons in the presence of spin-orbit coupling and magnetic fields are attracting significant attention in condensed matter physics because of their connection to Quantum Hall physics [1], topological insulators [2-4] and the emergence of unusual excitations in low dimensions [5,6]. Recent progress with quantum gas experiments has led to the realization of artificial gauge fields [7], both in the continuum [8][9][10] and for bosons in optical lattices [11][12][13][14], paving the way for future experiments on the interplay of interactions, dimensionality, and gauge fields in a systematic manner. This has motivated theoretical research into the physics of strongly interacting particles in the presence of abelian and non-abelian gauge fields and various questions such as the Quantum Hall effect with bosons [15][16][17][18][19][20][21][22], unusual quantum magnetism [23][24][25][26], and the emergence of topologically protected phases [27][28][29] have been addressed.

Chiral currents in one-dimensional fractional quantum Hall states

“…This behaviour of the current is a signature of the emergence fractional chiral excitations. It distinguishes the 1D FQH state from other phases containing chiral currents such as the Mott insulator phases 9,27,[41][42][43][44] . Stabilization of FQH phases for small inter-chain coupling and low filling factors ν < 1/2 requires interaction range beyond on-rung.…”

“…1. The possibility that chiral currents screen the orbital magnetic field in a kind of a Meissner phase, was pointed out [25][26][27] and recently observed experimentally 1,28 ; here we focus on the FQH phase.…”

Topological quasi-one-dimensional state of interacting spinless electrons

“…A useful quantity for determining phase boundaries numerically in the presence of flux is the chiral current 41,42 defined as j c = ∂H ∂φ . In Fig.…”

Density-dependent synthetic magnetism for ultracold atoms in optical lattices

“…Ladders with static fields [i.e., Hamiltonian (1) with density-independent Peierls phases] have been recently realized in several experimental groups [15][16][17] and studied theoretically as well [14,[41][42][43][44][45][46].…”