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Title: Vortex lattices in a rotating Fermi superfluid in the BCS-BEC crossover with many Landau levels

Abstract

We present an explicit analytical analysis of the ground state of vortex lattice structure, based on a minimization of the generalized Gross-Pitaevskii energy functional in a trapped rotating Fermi superfluid gas. By a Bogoliubov-like transformation we find that the coarse-grained average of the atomic density varies as inverted parabola in three dimensional cases; the Fermi superfluid in the BEC regime enters into the lowest Landau level at fast rotation, in which the vortices form an almost regular triangular lattice over a central region and the vortex lattice is expanded along the radial direction in the outer region; the fluid in the unitarity and BCS regimes occupies many low-lying Landau levels, in which a trapped gas with a triangular vortex lattice has a superfluid core surrounded by a normal gas. The calculation is qualitatively consistent with recent numerical and experimental data both in the vortex lattice structure and vortex numbers and in the density profiles versus the stirring frequency in the whole BCS-BEC crossover. - Highlights: Black-Right-Pointing-Pointer We present an analysis of vortex lattice in an interacting trapped rotating Fermi superfluid gas. Black-Right-Pointing-Pointer Decomposing the vortex from the condensate, we can explain the vortex lattice. Black-Right-Pointing-Pointer The calculation is consistent withmore » numerical and experimental data. Black-Right-Pointing-Pointer It can characterize experimentally properties in different regimes of the BCS-BEC crossover.« less

Authors:
; ;
Publication Date:
OSTI Identifier:
22157029
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 327; Journal Issue: 8; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BCS THEORY; BOSE-EINSTEIN CONDENSATION; ENERGY LEVELS; FERMI GAS; GROUND STATES; SUPERFLUIDITY; THREE-DIMENSIONAL CALCULATIONS; TRANSFORMATIONS; TRAPPING; UNITARITY; VORTICES; WAVE EQUATIONS

Citation Formats

Song, Tie-ling, Ma, C.R., and Ma, Yong-li, E-mail: ylma@fudan.edu.cn. Vortex lattices in a rotating Fermi superfluid in the BCS-BEC crossover with many Landau levels. United States: N. p., 2012. Web. doi:10.1016/J.AOP.2012.03.006.
Song, Tie-ling, Ma, C.R., & Ma, Yong-li, E-mail: ylma@fudan.edu.cn. Vortex lattices in a rotating Fermi superfluid in the BCS-BEC crossover with many Landau levels. United States. doi:10.1016/J.AOP.2012.03.006.
Song, Tie-ling, Ma, C.R., and Ma, Yong-li, E-mail: ylma@fudan.edu.cn. 2012. "Vortex lattices in a rotating Fermi superfluid in the BCS-BEC crossover with many Landau levels". United States. doi:10.1016/J.AOP.2012.03.006.
@article{osti_22157029,
title = {Vortex lattices in a rotating Fermi superfluid in the BCS-BEC crossover with many Landau levels},
author = {Song, Tie-ling and Ma, C.R. and Ma, Yong-li, E-mail: ylma@fudan.edu.cn},
abstractNote = {We present an explicit analytical analysis of the ground state of vortex lattice structure, based on a minimization of the generalized Gross-Pitaevskii energy functional in a trapped rotating Fermi superfluid gas. By a Bogoliubov-like transformation we find that the coarse-grained average of the atomic density varies as inverted parabola in three dimensional cases; the Fermi superfluid in the BEC regime enters into the lowest Landau level at fast rotation, in which the vortices form an almost regular triangular lattice over a central region and the vortex lattice is expanded along the radial direction in the outer region; the fluid in the unitarity and BCS regimes occupies many low-lying Landau levels, in which a trapped gas with a triangular vortex lattice has a superfluid core surrounded by a normal gas. The calculation is qualitatively consistent with recent numerical and experimental data both in the vortex lattice structure and vortex numbers and in the density profiles versus the stirring frequency in the whole BCS-BEC crossover. - Highlights: Black-Right-Pointing-Pointer We present an analysis of vortex lattice in an interacting trapped rotating Fermi superfluid gas. Black-Right-Pointing-Pointer Decomposing the vortex from the condensate, we can explain the vortex lattice. Black-Right-Pointing-Pointer The calculation is consistent with numerical and experimental data. Black-Right-Pointing-Pointer It can characterize experimentally properties in different regimes of the BCS-BEC crossover.},
doi = {10.1016/J.AOP.2012.03.006},
journal = {Annals of Physics (New York)},
number = 8,
volume = 327,
place = {United States},
year = 2012,
month = 8
}
  • We present an explicit analytical analysis of the ground state of vortex lattice structures, based on a minimization of the Gross-Pitaevskii energy functional in a fast rotating Bose-Einstein condensate between the Thomas-Fermi and the lowest-Landau-level regimes. By a Bogoliubov-like transformation we find that the coarse-grained average of the atomic density varies as [1-(x{sup 2}+y{sup 2})/R{sub perpendicular}{sup 2}]{sup 3/2} in the xy plane, and that the vortices form an almost regular triangular lattice. Our variational calculation is quantitatively and qualitatively consistent with recent analytical, numerical, and experimental data.
  • We consider a periodic vortex lattice in a rotating Bose-Einstein-condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we numerically solve the two-dimensional (2D) Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which ismore » crucial for the calculation of the Tkachenko frequencies.« less
  • We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a T-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature T{sub c}. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through T{sub c}. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossovermore » region is shown to appear in DOS after the pseudogap disappears below T{sub c}. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas.« less
  • We study the Bogoliubov collective excitations of harmonically trapped superfluid Fermi gases in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to Bose-Einstein condensate (BEC) beyond Thomas-Fermi (TF) limit. Starting from a generalized Gross-Pitaevskii equation and an equation of state valid for the whole crossover, we derive Bogoliubov-de Gennes (BdG) equations for low-lying collective modes at zero temperature. We use a Fetter-like variational ground state wave function to remove the noncontinuity of slope at the boundary of condensate, which appears in the TF limit. We solve the BdG equations analytically and obtain explicit expressions for all eigenvalues and eigenfunctions, valid for variousmore » crossover regimes and for traps with spherical and axial symmetries. We discuss the feature of these collective excitations in the BCS-BEC crossover and show that the theoretical result obtained agrees with available experimental data near and beyond the TF limit.« less