Multi-vortex Bose-Einstein condensate: examining the role of interaction range using Gaussian potential

TL;DR

This study uses exact diagonalization to analyze how the interaction range in a rotating Bose-Einstein condensate affects vortex formation, energy, entanglement, and internal structure, revealing systematic dependencies and stability features.

Contribution

It provides a detailed analysis of the effects of Gaussian interaction range on vortex states, energy, entanglement, and stability in a finite Bose-Einstein condensate using exact diagonalization.

Findings

Increased interaction range decreases energy.

Larger interaction range raises critical angular velocity for vortex states.

Quantum entanglement decreases with increasing interaction range.

Abstract

We present exact diagonalization study on a system of $10 \leq N \leq 24$ spinless bosons interacting via repulsive Gaussian potential, harmonically confined in $xy$-plane with an externally impressed rotation about the $z$-axis. The two-body interaction strength in the Gaussian potential is taken in the strongly interacting regime with values of interaction range in the regime $0\leq \sigma \leq 1$. The diagonalization of the $N$-body Hamiltonian matrix, in subspaces of total angular momentum in the regime $0\le L_{z} \le 4N$ corresponds to the filling fraction $\nu\lesssim 3.2$ is carried out to obtain the variationally exact ground-state wavefunction and the corresponding eigenvalue. It is found that an increase in interaction range $\sigma$ leads to (a) a systematic decrease in energy, (b) an increase in the critical angular velocity $\Omega_{c_{i}}$ of the $i${th} vortex state and (c) an increase in the largest eigenvalue $\lambda_{1}$, (condensate fraction), of one-particle reduced density matrix (OPRDM). The von Neumann entropy $S_{1}\left(L_{z},\sigma\right)$, quantifying the quantum entanglement between the particles in the many-body ground state, is largely found to decrease with increase in $\sigma$. Crossings in von Neumann entropy for several of the angular momentum states are observed with variation in $\sigma$. The response of the Bose-Einstein condensate to rotation is examined through $L_{z}\left(\sigma\right)-\Omega\left(\sigma\right)$ stability graph for several values of $\sigma$. A vortex state with larger plateau length on the $L_{z}-\Omega$ graph is considered to be more stable. The internal structure of the condensate, as depicted by the conditional probability distribution (CPD) in the body-fixed frame, exhibits characteristic features with interaction range $\sigma$. One such feature is the merging of the cores of the two-vortex state.