Bogoliubov excitation spectrum in anharmonic traps

TL;DR

This paper investigates the Bogoliubov excitation spectrum of Bose-Einstein condensates in anharmonic traps, demonstrating reduced inhomogeneous broadening and mode simplification in flat-bottom traps, with validation from numerical simulations.

Contribution

It introduces a comparative analysis of excitation spectra in harmonic and flat-bottom traps, highlighting the reduction of inhomogeneous broadening and the correlation between radial modes and bound states.

Findings

Flat-bottom traps significantly reduce inhomogeneous broadening.

The flat trap supports primarily one radial mode.

Numerical simulations confirm the model's accuracy.

Abstract

We study the linearized Bogoliubov excitation spectrum of infinitely long anharmonically trapped Bose-Einstein condensates, with the aim of overcoming inhomogeneous broadening. We compare the Bogoliubov spectrum of a harmonic trap with that of a theoretical flat-bottom trap and find a dramatic reduction in the inhomogeneous broadening of the lineshape of Bogoliubov excitations. While the Bragg excitation spectrum for a condensate in a harmonic trap supports a number of radial modes, the flat trap is found to significantly support just one mode. We also study the excitation spectrum of realistic anharmonic traps with potentials of finite power dependence on the radial coordinate. We observe a correlation between the number of radial modes and the number of bound states in the effective potential of the quasi-particles. Finally we compare a full numerical Gross-Pitaevskii simulation of a finite-length condensate to our model of infinite, linearized Gross-Pitaevskii excitations. We conclude that our model captures the essential physics.