# Periodic Ultranarrow Rods as 1D Subwavelength Optical Lattices

## TL;DR

This paper investigates the ground state properties of a one-dimensional Bose gas in a periodic multi-rod potential, providing semi-analytical solutions and analyzing band structures and interactions at zero temperature.

## Contribution

It introduces a semi-analytical approach to solve the Gross-Pitaevskii equation for a 1D Bose gas in a periodic rod structure, including elliptic function solutions and band spectrum analysis.

## Key findings

- Identification of energy band loops at strong interactions.
- Dependence of ground state energy and chemical potential on potential height and interactions.
- Prediction of subwavelength optical lattice band structures.

## Abstract

We report on ground state properties of a one-dimensional, weakly-interacting Bose gas constrained by an infinite multi-rods periodic structure at zero temperature. We solve the stationary Gross-Pitaevskii equation (GPE) to obtain the Bloch wave functions from which we give a semi-analytical solution for the density profile, as well as for the phase of the wave function in terms of the Jacobi elliptic functions, and the incomplete elliptic integrals of the first, second and third kind. Then, we determine numerically the energy of the ground state, the chemical potential and the compressibility of the condensate and show their dependence on the potential height, as well as on the interaction between the bosons. We show the appearance of loops in the energy band spectrum of the system for strong enough interactions, which appear at the edges of the first Brillouin zone for odd bands and at the center for even bands. We apply our model to predict the energy band structure of the Bose gas in an optical lattice with subwavelength spatial structure. To discuss the density range of the validity of the GPE predictions, we calculate the ground state energies of the free Bose gas using the GPE, which we compare with the Lieb-Liniger exact energies.