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Register a new userStability of spinor Fermi gases in tight waveguides
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The two and three-body correlation functions of the ground state of an optically trapped ultracold spin-1/2 Fermi gas (SFG) in a tight waveguide (1D regime) are calculated in the plane of even and odd-wave coupling constants, assuming a 1D attractive zero-range odd-wave interaction induced by a 3D p-wave Feshbach resonance, as well as the usual repulsive zero-range even-wave interaction stemming from 3D s-wave scattering. The calculations are based on the exact mapping from the SFG to a ``Lieb-Liniger-Heisenberg model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, and indicate that the SFG should be stable against three-body recombination in a large region of the coupling constant plane encompassing parts of both the ferromagnetic and antiferromagnetic phases. However, the limiting case of the fermionic Tonks-Girardeau gas (FTG), a spin-aligned 1D Fermi gas with infinitely attractive p-wave interactions, is unstable in this sense. Effects due to the dipolar interaction and a Zeeman term due to a resonance-generating magnetic field do not lead to shrinkage of the region of stability of the SFG.
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Using the Theory of Scattering in Restricted Geometries developed by A. Lupu-Sax as a starting point, we present a comprehensive multi-channel theory of atom-atom scattering in tight atom waveguides.
A generalized Fermi-Bose mapping method is used to determine the exact ground states of six models of strongly interacting ultracold gases of two-level atoms in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). Three of these models exhibit a quantum phase transition in the presence of an external magnetic field, associated with a cooperative ground state rearrangement wherein Fermi energy is traded for internal excitation energy. After investigation of these models in the absence of an electromagnetic field, one is generalized to include resonant interactions with a single photon mode, leading to a possible thermal phase transition associated with Dicke superradiance.
We consider a mixture of one-dimensional strongly interacting Fermi gases up to six components, subjected to a longitudinal harmonic confinement. In the limit of infinitely strong repulsions we provide an exact solution which generalizes the one for the two-component mixture. We show that an imbalanced mixture under harmonic confinement displays partial spatial separation among the components, with a structure which depends on the relative population of the various components. Furthermore, we provide a symmetry characterization of the ground and excited states of the mixture introducing and evaluating a suitable operator, namely the conjugacy class sum. We show that, even under external confinement, the gas has a definite symmetry which corresponds to the most symmetric one compatible with the imbalance among the components. This generalizes the predictions of the Lieb-Mattis theorem for a fermionic mixture with more than two components.
We investigate the effect of slow light propagating in a degenerate atomic Fermi gas. In particular we use slow light with an orbital angular momentum. We present a microscopic theory for the interplay between light and matter and show how the slow light can provide an effective magnetic field acting on the electrically neutral fermions, a direct analogy of the free electron gas in an uniform magnetic field. As an example we illustrate how the corresponding de Haas-van Alphen effect can be seen in a neutral gas of fermions.
Some thoughts regarding pairing in atomic Fermi gases were considered, meant for starting discussion on the topic.
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