Incommensurate phases of a bosonic two-leg ladder under a flux

Abstract

A boson two-leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and density matrix renormalization group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is ρπ and close to it, where ρ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung-rung correlation function and the spin-spin and chargecharge static structure factors.A remarkable characteristic of charged systems with broken U(1) global gauge symmetry such as superconductors is the Meissner-Ochsenfeld effect [1]. In the Meissner phase, below the critical field H c1 , a superconductor behaves as a perfect diamagnet, i.e. it develops surface currents that fully screen the external magnetic field. In a type-II superconductor, for fields above H>H c1 , an Abrikosov vortex lattice phase is formed in the system, where the magnetic field penetrates into vortex cores. In quasi one-dimensional systems, analogues of the Meissner and Abrikosov vortex lattice have been predicted for the bosonic two-leg ladder [2-5], 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 (C-IC) transition [6][7][8]. For ladder systems at commensurate filling, a chiral Mott insulator phase with currents circulating in loops commensurate with the ladder was obtained [9][10][11][12]. Initially, Josephson junction arrays [13][14][15][16] were proposed as experimental realizations of bosonic one-dimensional systems [17,18]. However, Josephson junctions are dissipative and open systems [19-21] that cannot be described using a Hermitian manybody Hamiltonian in a canonical formalism. Moreover, the quantum effects in the vortex phase of the Josephson ladder are weak [22]. Fortunately, with the recent advent of ultracold atomic gases, another route to realize low dimensional strongly interacting bosonic systems has opened [23][24][25]. Atoms being neutral, it is necessary to find a way to realize an artificial magnetic flux acting on the ladder. Alternatively, one can consider the mapping of the two-leg ladder bosonic model to a two-component spinor boson model in which the bosons in the upper leg become spin-up bosons and the bosons in the lower leg spin-down bosons. Under such mapping, the magnetic flux of the ladder becomes a spin-orbit coupling for the spinor bosons. Theoretical proposals to realize either artificial gauge fields or artificial spin-orbit coupling have been put forward [26,27], and an artificial spinorbit coupling has been achieved in a cold atoms experiment [28,29]. Recently, the Meissner effect and the formation of a vortex state have been observed for non-interacting ultracold bosonic atoms bosons on a two leg ladder in artificial gauge fi...

Spin-gap spectroscopy in a bosonic flux ladder

“…In this article, we propose an experimentally feasible method to distinguish the M and V phases in the bosonic FL and to characterize their low-energy excitation spectrum. It is known that the M and V phases can be distinguished qualitatively by time-of-flight methods [9,31,32,45,56,57]. We show that they also respond differently to a periodic 'spin' modulation, and we interpret our results as a measure of the spin gap in the M phase.…”

“…We begin by reviewing a method to study the phase diagram [20,23,28,31,32], which can be easily implemented in experiments [9]. We focus on the momentum distribution functions (MDF), both leg-resolved and the total.…”

Precursor of the Laughlin state of hard-core bosons on a two-leg ladder

“…A comparison of this study with our own is the subject of future work. References [89] and [90] discuss the appearance of an incommensuration in the vortex state when the flux per plaquette is χ = πn 0 , where n 0 is the boson filling per rung. That parameter choice is nevertheless distinct from the one chosen in this paper, χ = 2πn 0 .…”

Quantum phase transitions of a two-leg bosonic ladder in an artificial gauge field

“…where σ =↑, ↓ represents the leg index, b j,σ annihilates a boson on leg σ on the j−th site, n jα = b † jα b jα , t is the hopping amplitude along the chain, Ω is the tunneling between the legs, λ is the Peierls phase of the effective magnetic field associated to the gauge field, U ↑↑ = U ↓↓ is the repulsion between bosons on the same leg, U ↓↑ = U ⊥ the interaction between bosons on opposite legs. This model can be mapped to a spin-1/2 bosons with spin-orbit interaction model 37 , where Ω is the transverse magnetic field, λ measures the spin-orbit coupling, U ↑↑ = U ↓↓ is the repulsion between bosons of identical spins, U ↓↑ = U ⊥ the interaction between bosons of opposite spins.…”