Spectral Function of a Boson Ladder in an Artificial Gauge Field

Roberta Citro,Nicolas Victorin,Stefania De Palo,Anna Minguzzi,Edmond Orignac

doi:10.3390/condmat5010015

Abstract

We calculate the spectral function of a boson ladder in an artificial magnetic field by means of analytic approaches based on bosonization and Bogoliubov theory. We discuss the evolution of the spectral function at increasing effective magnetic flux, from the Meissner to the Vortex phase, focussing on the effects of incommensurations in momentum space. At low flux, in the Meissner phase, the spectral function displays both a gapless branch and a gapped one, while at higher flux, in the Vortex phase, the spectral function displays two gapless branches and the spectral weight is shifted at a wavevector associated to the underlying vortex spatial structure, which can indicate a supersolid-like behavior. While the Bogoliubov theory, valid at weak interactions, predicts sharp delta-like features in the spectral function, at stronger interactions we find power-law broadening of the spectral functions due to quantum fluctuations as well as additional spectral weight at higher momenta due to backscattering and incommensuration effects. These features could be accessed in ultracold atom experiments using radio-frequency spectroscopy techniques.

Highlights

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
In the Vortex phase, we find two sound modes at low energy centered at k = ±q0, as well as weaker branches associated with the folding of the excitation spectrum in the presence of a modulated equilibrium density profile
We have obtained the spectral functions of a two-leg boson ladder in an artificial gauge field

Summary

Introduction

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. The low energy modes are collective excitations [21,22], and in the two-leg ladder, there is a separation between a total density (“charge”) and a density difference (“spin”) mode [2,4] This is analogous to the well-known spin-charge separation in electronic systems [21] and two-component boson systems [23]. One could, for example, consider the “spin-spin” dynamical structure factor This would display a well defined gapped or gapless dispersion, respectively, in the Meissner and in the Vortex phase. We calculate the boson spectral function in the different phases of the boson ladder at incommensurate filling in order to fully characterize the transition under flux. We will focus on the positive-frequency part of the spectral function, given by the first term in Equation (6)

Spectral Function in the Meissner Phase for Weak Interchain Hopping

Spectral Functions in the Weakly Interacting Regime From Bosonization

Spectral Function in the Bogoliubov Theory

Conclusions