Vortex patterns in moderately rotating Bose-condensed gas

Abstract

Using exact diagonalization, we investigate the many-body ground state for 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 Lz, 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 4N ≤ Lz < 5N for N = 16 bosons. In response to externally impressed rotation, 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.

Many-body quantum dynamics in the decay of bent dark solitons of Bose–Einstein condensates

“…This availability of rotation in BECs stirred numerous theoretical works that investigated vortex nucleation and interactions both at [42][43][44][45] and beyond the MF approximation [46][47][48][49][50][51][52]. Weak [46], moderate [53], and rapid [47] rotating regimes have been explored, leading to the formation of one to few singly quantized vortices, and progressively (with increased stirring) of regular vortex patterns forming canonical polygons and vortex lattices. For the MB treatment of these coherent structures, diagonalization techniques have been developed [53,54] which, however, bear the limitation of tackling few boson systems.…”

“…Weak [46], moderate [53], and rapid [47] rotating regimes have been explored, leading to the formation of one to few singly quantized vortices, and progressively (with increased stirring) of regular vortex patterns forming canonical polygons and vortex lattices. For the MB treatment of these coherent structures, diagonalization techniques have been developed [53,54] which, however, bear the limitation of tackling few boson systems. The MB effects on vortex formation in rotating BECs for larger bosonic ensembles have been considered very recently [55,56] where modes of hidden vorticity not visible in the total density of the system, have been identified.…”

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

“…Appendix A: Computational scheme Since the system being studied here is rotationally invariant in the x-y plane, the z-component of the total angular momentum L z is a good quantum number leading to block diagonalization of the N -body Hamiltonian matrix in subspaces of quantized total angular momentum [36]. To obtain the many-body eigenstates, we carry out exact diagonalization of the Hamiltonian matrix in different subspaces of L z with inclusion of lowest as well as higher Landau levels of the single-particle basis states in constructing the N -body basis states [36,37,40]. The associated Hilbert space may be restricted to the space spanned by the normalized single-particle basis functions u n,m (r, θ) u nz (z) ≡ u n,m,nz (r) spanning the quasi-2D plane, where (n, m, n z ) is set of single-particle quantum numbers.…”

“…On the theoretical front, the rotational properties of BEC and creation of vortices in a harmonic trap have been analyzed mostly by the mean-field approach like Gross-Pitaevskii scheme as in Refs. [26][27][28][29][30][31][32] or beyond the mean-field approximation [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. A review of basic results on BEC vortices can be found in Ref.…”

Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions

“…That's why we employ Exact Diagonalizaton. Variation of average energy spectrum with interaction range σ and zero relative angular momentum is studied, where the energy per particles first increases and the decreases within the system size [9], Variation of Hilbert space with decreasing interaction strength g 2 > 0 for many-body systems in this article [10]. Dependence of single particle energy spectrum with angular momentum quantum number is discussed for spin-1 bosons where energy increases linearly for higher relative particle angular momentum m [11,12], later discussed the different relative angular momentum in attractive BECs .…”