Multipolar exchange in a many-body homonuclear mixture of atoms in different internal states
Abstract
We develop a general method for constructing the many-body Hamiltonian of pairwise interactions describing homonuclear mixtures of atoms occupying states with different total angular momenta or other quantum numbers. This Hamiltonian explicitly accounts for isotropic interactions governed by low-energy s-wave scattering. The advantage of the irreducible spherical tensor operator formalism is demonstrated: these operators give the Hamiltonian an explicit physical structure, account for all scattering channels, and include multipolar exchange interactions. The latter correspond to the exchange of both angular-momentum projections and the total angular momentum. Particular realizations of the general Hamiltonian, widely used in the physics of ultracold gases, are also analyzed. The resulting Hamiltonian provides a universal framework for investigating a broad range of quantum many-body phenomena in bosonic and fermionic atomic gases.
Versions
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BibTeX
@misc{bulakhov2026multipolar,
title = {{Multipolar exchange in a many-body homonuclear mixture of atoms in different internal states}},
author = {M. Bulakhov and A. S. Peletminskii and Yu. V. Slyusarenko},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2605.22375},
eprint = {2605.22375},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.22375},
}
RIS
TY - UNPB
TI - Multipolar exchange in a many-body homonuclear mixture of atoms in different internal states
AU - M. Bulakhov
AU - A. S. Peletminskii
AU - Yu. V. Slyusarenko
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2605.22375
UR - https://arxiv.org/abs/2605.22375
AB - We develop a general method for constructing the many-body Hamiltonian of pairwise interactions describing homonuclear mixtures of atoms occupying states with different total angular momenta or other quantum numbers. This Hamiltonian explicitly accounts for isotropic interactions governed by low-energy s-wave scattering. The advantage of the irreducible spherical tensor operator formalism is demonstrated: these operators give the Hamiltonian an explicit physical structure, account for all scattering channels, and include multipolar exchange interactions. The latter correspond to the exchange of both angular-momentum projections and the total angular momentum. Particular realizations of the general Hamiltonian, widely used in the physics of ultracold gases, are also analyzed. The resulting Hamiltonian provides a universal framework for investigating a broad range of quantum many-body phenomena in bosonic and fermionic atomic gases.
ER -