Orbital elementary excitations as probes of entanglement and quantum phase transitions of collective spins in an entangled Bose-Einstein condensate

TL;DR

This paper investigates how orbital elementary excitations in an entangled Bose-Einstein condensate reveal underlying quantum phase transitions and entanglement properties of collective spins, linking orbital dynamics to spin entanglement.

Contribution

It introduces a novel approach connecting orbital excitations to spin entanglement and phase transitions in a two-species pseudospin-1/2 Bose gas system.

Findings

Orbital excitation energy gap peaks at isotropic spin coupling.

Quantum phase transition occurs in the ground state of the effective spin Hamiltonian.

Maximal entanglement of the collective spins is observed at the transition.

Abstract

A mixture of two species of pseudospin-1/2 Bose gases exhibits interesting interplay between spin and orbital degrees of freedom. Expectation values of various quantities of the collective spins of the two species play crucial roles in the Gross-Pitaevskii-like equations governing the four orbital wave functions in which Bose-Einstein condensation occurs. Consequently, the elementary excitations of these orbital wave functions reflect properties of the collective spins. When the coupling between the two collective spins is isotropic, the energy gap of the gapped orbital excitation peaks, while there is a quantum phase transition in the ground state of the effective Hamiltonian of the two collective spins, which have previously been found to be maximally entangled.