Strong correlation effects in a two-dimensional Bose gas with quartic dispersion

TL;DR

This paper investigates the ground states of a two-dimensional Bose gas with quartic dispersion, revealing strongly correlated condensates with unique energy scaling and properties, distinct from traditional weakly interacting Bose gases.

Contribution

It introduces and analyzes the ground state properties of a 2D Bose gas with quartic dispersion, showing the emergence of strongly correlated condensates with novel energy scaling behaviors.

Findings

Strongly correlated states have energy per particle scaling as n^{4/3}

A variational Jastrow-type wave function has the lowest energy among considered states

The ground state exhibits a reduced condensate fraction but retains off-diagonal long-range order

Abstract

Motivated by the fundamental question of the fate of interacting bosons in flat bands, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This type of band structure can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jim\'{e}nez-Garcia, and I. B. Spielman, Nature $\textbf{471}$, 83 (2011)], in the regime where the lower band dispersion has the form $\varepsilon_{\textbf{k}} \sim k_{x}^{4}/4+k_{y}^{2}+\ldots$, or using the shaken lattice scheme of Parker $\textit{et al.}$ [C. V. Parker, L.-C. Ha and C. Chin, Nature Physics $\textbf{9}$, 769 (2013)]. We numerically compare the ground state energies of the mean-field Bose-Einstein condensate (BEC) and various trial wave-functions, where bosons avoid each other at short distances. We discover that, at low densities, several types of strongly correlated states have an energy per particle ($\epsilon$), which scales with density ($n$) as $\epsilon \sim n^{4/3}$, in contrast to $\epsilon \sim n$ for the weakly interacting Bose gas. These competing states include a Wigner crystal, quasi-condensates described in terms properly symmetrized fermionic states, and variational wave-functions of Jastrow type. We find that one of the latter has the lowest energy among the states we consider. This Jastrow-type state has a strongly reduced, but finite condensate fraction, and true off-diagonal long range order, which suggests that the ground state of interacting bosons with quartic dispersion is a strongly-correlated condensate reminiscent of superfluid Helium-4. Our results show that even for weakly-interacting bosons in higher dimensions, one can explore the crossover from a weakly-coupled BEC to a strongly-correlated condensate by simply tuning the single particle dispersion or density.