Ground state properties of trapped boson system with finite-range Gaussian repulsion: Exact diagonalization study

Abstract

We use exact diagonalization to study an interacting system of $N$ spinless bosons with finite-range Gaussian repulsion, confined in a quasi-two-dimensional harmonic trap with and without an introduced rotation. The diagonalization of the Hamiltonian matrix using Davidson algorithm in subspaces of quantized total angular momentum $L_z$ is carried out to obtain the $N$-body lowest eigenenergy and eigenstate. To bring out the effect of quantum (Bose) statistics and consequent phase stiffness (rigidity) of the variationally obtained many-body wavefunction on various physical quantities, our study spans from few-body ($N=2$) to many-body ($N=16$) systems. Further, to examine the finite-range effect of the repulsive Gaussian potential on many-body ground state properties of the Bose-condensate, we obtain the lowest eigenstate, the critical angular velocity of single vortex state and the quantum correlation (measured) in terms of von Neumann entanglement entropy and degree of condensation. It is found that for small values of the range (measured by the parameter $\sigma$) of Gaussian potential, the ground state energy increases for few-boson ($2\le N\le 8$) systems but decreases for many-boson ($N>8$) systems. On the other hand for relatively large values of the range of Gaussian potential, the ground state energy exhibits a monotonic decrease, regardless of the number of bosons $N$. For a given $N$, there is found an optimal value of the range of Gaussian potential for which the first vortex (with $L_z=N$) nucleates at a lower value of the rotational angular velocity ${\Omega }_{c1}$ compared to the zero-range ($\delta$-function) potential. Further, we observe that the inter-particle interaction and the introduced rotation are competing effects with latter being dominant over the former.

11 pages, 06 figures, Accepted for publication in J.Phys.B. (https://doi.org/10.1088/1361-6455/ab7fbf)

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Measuring entanglement entropy through the interference of quantum many-body twins
• Fragmentation of Bose-Einstein Condensates
• Quantum Hall physics in rotating Bose-Einstein condensates
• Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and high-temperature thermodynamics
• Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions
• Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions
• Many-body tunneling dynamics of Bose-Einstein condensates and vortex states in two spatial dimensions
• Effective-interaction approach to the many-boson problem
• Breaking the resilience of a two-dimensional Bose-Einstein condensate to fragmentation
• The $s$-wave scattering length of a Gaussian potential
• Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
• Enhanced many-body effects in the excitation spectrum of a weakly-interacting rotating Bose-Einstein condensate
• Particle Entanglement in Rotating Gases
• Symmetry breaking in small rotating cloud of trapped ultracold Bose atoms
• Exact Diagonalization Study of Bose-Condensed Gas with Finite-Range Gaussian Interaction
• Ground and Low-Lying Collective States of Rotating Three-Boson System
• Vortex patterns in moderately rotating Bose-condensed gas

Cited by in corpus (1)

• Novel phases in rotating Bose-condensed gas: vortices and quantum correlation