Quantum lattice gas model of spin-2 Bose-Einstein condensates and closed-form analytical continuation of nonlinear interactions in spin-2 superfluids

TL;DR

This paper introduces a unitary operator splitting method for spinor Bose-Einstein condensates, providing an analytical continuation of nonlinear interactions in spin-2 superfluids, enabling improved quantum simulation of complex spin interactions.

Contribution

It presents an infinite-order expansion of the quantum evolution operator for spin-2 BECs using analytical continuation, addressing nonperturbative superfluid phases.

Findings

Derived a closed-form analytical continuation of nonlinear spin interactions.

Enabled accurate quantum simulation of non-Abelian superfluid phases.

Provided a new computational method for spin-2 Bose-Einstein condensates.

Abstract

Presented is an unitary operator splitting method for handling the spin-density interaction in spinor Bose-Einstein condensates. The zero temperature behavior of a spinor BEC is given by mean field theory, where the Hamiltonian includes a nonlinear hyperfine spin interaction. This hyperfine interaction has a diagonal probability-density term (leading to the usual Gross-Pitaevskii type equation of motion) but also has a nondiagonal spin-density term. Since the F=2 spinor BEC (spin-2 BEC) has a non-Abelian superfluid phase (nonperturbative cyclic phase in the strong spin-density coupling regime), an infinite-order expansion of the quantum evolution operator is needed for quantum simulation applications. An infinite-order expansion, obtained by analytical continuation and expressed in analytically closed form, for the spin-2 BEC is presented.