Exact Eigenstates and Magnetic Response of Spin-1 and Spin-2 Vectorial Bose-Einstein Condensates

TL;DR

This paper derives exact eigenstates and spectra of spin-1 and spin-2 vector Bose-Einstein condensates, revealing their magnetic responses and quantum correlations, especially under weak magnetic fields.

Contribution

It provides the first exact solutions for eigenstates and spectra of spinor BECs, highlighting differences from mean-field predictions and uncovering quantum correlations in spin-2 BECs.

Findings

Zero magnetic-quantum-number component becomes populated at low magnetic fields in spin-1 BECs.

Spin-2 BECs show complex magnetic responses due to quantum correlations among three bosons.

Exact eigenspectra differ from mean-field predictions, especially in low-field regimes.

Abstract

The exact eigenspectra and eigenstates of spin-1 and spin-2 vectorial Bose-Einstein condensates (BECs) are found, and their response to a weak magnetic field is studied and compared with their mean-field counterparts. Whereas mean-field theory predicts the vanishing population of the zero magnetic-quantum-number component of a spin-1 antiferromagnetic BEC, the component is found to become populated as the magnetic field decreases. The spin-2 BEC exhibits an even richer magnetic response due to quantum correlation between 3 bosons.