Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap

Abstract

An asymptotically exact many body theory for spin polarized interacting fermions in a one-dimensional harmonic atom trap is developed using the bosonization method and including backward scattering. In contrast to the Luttinger model, backscattering in the trap generates one-particle potentials which must be diagonalized simultaneously with the two-body interactions. Inclusion of backscattering becomes necessary because backscattering is the dominant interaction process between confined identical one-dimensional fermions. The bosonization method is applied to the calculation of one-particle matrix elements at zero temperature. A detailed discussion of the validity of the results from bosonization is given, including a comparison with direct numerical diagonalization in fermionic Hilbert space. A model for the interaction coefficients is developed along the lines of the Luttinger model with only one coupling constant $K$. With these results, particle densities, the Wigner function, and the central pair correlation function are calculated and displayed for large fermion numbers. It is shown how interactions modify these quantities. The anomalous dimension of the pair correlation function in the center of the trap is also discussed and found to be in accord with the Luttinger model.

19 pages, 5 figures, journal-ref added

References in corpus (10)

• A quasi-pure Bose-Einstein condensate immersed in a Fermi sea
• Bose-Einstein Condensation in a Surface Micro Trap
• Sympathetic cooling of bosonic and fermionic Lithium gases towards quantum degeneracy
• Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions
• Non-Interacting Fermions in a One-Dimensional Harmonic Atom Trap: Exact One-Particle Properties at Zero Temperature
• Stable, Strongly Attractive, Two-State Mixture of Lithium Fermions in an Optical Trap
• Light scattering from a degenerate quasi-onedimensional confined gas of non-interacting fermions
• Luttinger model approach to interacting one-dimensional fermions in a harmonic trap
• Two-component Fermi gas in a one-dimensional harmonic trap
• Momentum flux density, kinetic energy density and their fluctuations for one-dimensional confined gases of non-interacting fermions

Cited by in corpus (10)

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• Density profile of interacting Fermions in a one-dimensional optical trap
• Relaxation and dephasing in a many-fermion generalization of the Caldeira-Leggett model
• Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap
• A many-fermion generalization of the Caldeira-Leggett model
• Phase theory and critical exponents for the Tomonaga-Luttinger model with harmonic confinement
• Dynamic response of interacting one-dimensional fermions in the harmonic atom trap: Phase response and the inhomogeneous mobility
• Pseudospin and spin-spin interactions in ultra-cold alkali atoms