Coupled-cluster theory for trapped bosonic mixtures

TL;DR

This paper develops a coupled-cluster theory tailored for binary bosonic mixtures in traps, enabling highly accurate many-body physics modeling of Bose-Einstein condensates with promising results validated against exact solutions.

Contribution

The paper introduces a coupled-cluster framework for bosonic mixtures, including explicit equations and simplified forms, tested successfully against exact models for various interaction regimes.

Findings

Remarkable agreement with exact solutions

Effective for balanced and imbalanced boson numbers

Works well for weak to moderate interactions

Abstract

We develop a coupled-cluster theory for bosonic mixtures of binary species in external traps, providing a promising theoretical approach to demonstrate highly accurately the many-body physics of mixtures of Bose-Einstein condensates. The coupled-cluster wavefunction for the binary species is obtained when an exponential cluster operator $e^T$, where $T=T^{(1)}+T^{(2)}+T^{(12)}$ and $T^{(1)}$ accounts for excitations in species-1, $T^{(2)}$ for excitations in species-2, and $T^{(12)}$ for combined excitations in both species, acts on the ground state configuration prepared by accumulating all bosons in a single orbital for each species. We have explicitly derived the working equations for the bosonic mixtures by truncating the cluster operator upto the single and double excitations and using an arbitrary sets of orthonormal orbitals for each of the species. Further, the comparatively simplified version of the working equations are formulated using the Fock-like operators. Finally, using an exactly solvable many-body model for bosonic mixtures that exists in the literature allows us to implement and test the performance and accuracy of the coupled-cluster theory for situations with balanced as well as imbalanced boson numbers and for weak to moderately strong intra- and inter-species interaction strengths. The comparison between our computed results using coupled-cluster theory with the respective analytical exact results displays remarkable agreement exhibiting excellent success of the coupled-cluster theory for bosonic mixtures. All in all, the correlation exhaustive coupled-cluster theory shows encouraging results and it could be a promising approach in paving the way for high-accuracy modelling of various bosonic mixture systems.