2016/01/25 by Mohd Imran, Mohd. Imran, M. A. H. Ahsan +1 · 4 citations
Physics and Astronomy · #Angular momentum #Cold Atom Physics and Bose-Einstein Condensates #Ground state #Hamiltonian (control theory) #Moment of inertia #Quantum #Quantum chaos and dynamical systems #Quantum many-body systems #Rotational symmetry #Symmetry (geometry) #Total angular momentum quantum number #Vortex #cond-mat.quant-gas
paper · pdf · doi:10.1088/1361-6455/aa5878
published in Journal of Physics B Atomic Molecular and Optical Physics 50(4), 045301 (IOP Publishing) · 6 pages, 10 figures
arxiv created 2016/01/25 · openalex created_date 2016/06/24 · openalex publication_date 2017/01/10 · arxiv updated 2020/06/02 · openalex updated_date 2026/08/05
Abstract Using exact diagonalization, we investigate the many-body ground state for regular vortex patterns in a rotating Bose-condensed gas of N spinless particles, confined in a quasi-two-dimensional harmonic trap and interacting repulsively via finite-range Gaussian potential. The N -body Hamiltonian matrix is diagonalized in given subspaces of quantized total angular momentum L z , to obtain the lowest-energy eigenstate. Further, the internal structure of these eigenstates is analyzed by calculating the corresponding conditional probability distribution. Specifically, the quantum mechanically stable as well as unstable states in a co-rotating frame are examined in the moderately rotating regime corresponding to angular momenta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>4</mml:mn> <mml:mi>N</mml:mi> <mml:mo>≤</mml:mo> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>z</mml:mi> </mml:mrow> </mml:msub> <mml:mo><</mml:mo> <mml:mn>5</mml:mn> <mml:mi>N</mml:mi> </mml:math> for N = 16 bosons. In response to externally impressed rotation, the patterns of singly quantized vortices are formed, shaping into canonical polygons with a central vortex at the trap center. The internal structure of unstable states reveals the mechanism of entry, nucleation and pattern formation of vortices with structural phase transition, as the condensate goes from one stable vortical state to the other. The stable polygonal vortex patterns having discrete p -fold rotational symmetry with p = 5 and p = 6 are observed. The hexagonal vortex pattern with p = 6 symmetry is a precursor to the triangular vortex lattice of singly quantized vortices in the thermodynamic limit. For unstable states, quantum melting of vortex patterns due to uncertainty in positions of individual vortices, is also briefly discussed.