M. D. Girardeau, G. E. Astrakharchik
The ground state of a one-dimensional (1D) quantum gas of dipoles oriented perpendicular to the longitudinal axix, with a strong $1/x^3$ repulsive potential, is studied at low densities $n$. Near contact the dependence of the many-body wave function on the separation $x_{j\ell}$ of two particles reduces to a two-body wave function $Psi_\text{rel}(x_{j\ell})$. Immediately after a sudden rotation of the dipoles so that they are parallel to the longitudinal axis, this wave function will still be that of the repulsive potential, but since the potential is now that of the attractive potential, it will not be stationary. It is shown that as $nd^2\to 0$ the rate of change of this wave function approaches zero. It follos that for small values of $nd^2$, this state is metastable and is an analog of the super Tonks-Girardeau (STG) state of bosons with a strong zero-range attraction. The dipolar system is equivalent to a spinor Fermi gas with spin $z$-components $\sigma_{\uparrow}=\perp$ (perpendicular to longitudinal axis) and $\sigma_{\downarrow}=\parallel$ (parallel to longitudinal axis). A Fermi-Fermi mapping from spinor Fermi to spinless Fermi followed by the standard 1960 Fermi-Bose mapping reduces the Fermi system to a Bose gas. Potential experiments realizing the sudden spin rotation with ultracold dipolar gases are discussed, and a few salient properties of these states are accurately evaluated by a Monte Carlo method.
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http://arxiv.org/abs/1206.6042
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