Quantum states of a binary mixture of spinor Bose-Einstein condensates

TL;DR

This paper investigates the quantum states of a binary mixture of spinor Bose-Einstein condensates, highlighting the complexities introduced by inter-species interactions and analyzing special cases where the Hamiltonian simplifies.

Contribution

It provides a detailed analysis of the quantum state structure in spinor BEC mixtures, especially under conditions where the Hamiltonian becomes more tractable.

Findings

Eigenstates depend on intra- and inter-species interactions.

In certain limits, eigenstates are independent of interaction details.

The study clarifies the role of non-commuting terms in the Hamiltonian.

Abstract

We study the structure of quantum states for a binary mixture of spin-1 atomic Bose-Einstein condensates. In contrast to collision between identical bosons, the s-wave scattering channel between inter-species does not conform to a fixed symmetry. The spin-dependent Hamiltonian thus contains non-commuting terms, making the exact eigenstates more challenging to obtain because they now depend more generally on both the intra- and inter-species interactions. We discuss two limiting cases, where the spin-dependent Hamiltonian reduces respectively to sums of commuting operators. All eigenstates can then be directly constructed, and they are independent of the detailed interaction parameters.