Beyond Mean-Field Theory for Attractive Bosons under Transverse Harmonic Confinement
arXiv:cond-mat/0602670 · doi:10.1088/0953-4075/39/7/016
Abstract
We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e. under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wave function which extends the Bethe ansatz proposed by McGuire (J. Math. Phys. {\bf 5}, 622 (1964)) by including a variational transverse Gaussian shape. We investigate the ground state properties of the system comparing them with the ones of the one-dimensional (1D) attractive Bose gas. We find that the gas becomes ultra 1D as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the simmetry-breaking solitonic density profile of the ground-state, which generalize the one deduced by Calogero and Degasperis (Phys. Rev. A {\bf 11}, 265 (1975)). This bright-soliton analytical solution shows near the collapse small deviations with respect to the 3D mean-field numerical solution. Finally, we show that our variational Gauss-McGuire theory is always more accurate than the McGuire theory. In addition, we prove that for small numbers of particles the Gauss-McGuire theory is more reliable than the mean-field theory described by the 3D Gross-Pitaevskii equation.
arXiv commentTo be published in J. Phys. B.: At. Mol. Opt. Phys
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Cited by in corpus (6)
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- One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons
- Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz
- Partially incoherent gap solitons in Bose-Einstein condensates
- Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz