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Register a new userInstabilities of one- and two-dimensional degenerate atomic Fermi gas against a long-wave perturbation in optical lattice
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Added by
Lyubov' Manakova A.
Publication date
2003
fields
Physics
and research's language is
English
Authors
L.A. Manakova
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A mechanism of both formation of peaks in the density of states near the Fermi surface and phase instabilities of nearly ideal degenerate Fermi gas in low-dimensional optical lattices is proposed. According to this mechanism, peak formation is caused by the quasi-classical quantization of the one- and two-dimensional fermionic spectrum in the neighborhood of its extremal points under interaction with an long-wave periodical perturbation. The new spectra result in the instabilities with respect to spontaneous formation of an equilibrium superstructure. In the one-dimensional case this happens for low enough numbers of fermionic atoms. As a result of such transition, fermions become localized (a transition of the metal-insulator type). In the two-dimensional system the transition is possible for a nearly half-filled band. In this case fermions are localized in the wave direction only. It is briefly discussed the possible influence of the results obtained in the paper on the superfluid transition temperature in high anisotropic lattices possessing quasi-(one,two)-dimensional subsystems of fermionic atoms.
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In the present paper one-dimensional two-component atomic Fermi gas is considered in long-wave limit as a Luttinger liquid. The mechanisms leading to instability of the non-Fermi-liquid state of a Luttinger liquid with two-level impurities are proposed. Since exchange scattering in 1D systems is two-channel scattering in a certain range of parameters, several types of non-Fermi-liquid excitations with different quantum numbers exist in the vicinity of the Fermi level. These excitations include, first, charge density fluctuations in the Luttinger liquid and, second, many-particle excitations due to two-channel exchange interaction, which are associated with band-type as well as impurity fermion states. It is shown that mutual scattering of many-particle excitations of various types leads to the emergence of an additional Fermi-liquid singularity in the vicinity of the Fermi level. The conditions under which the Fermi-liquid state with a new energy scale (which is much smaller than the Kondo temperature) is the ground state of the system are formulated.
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We investigate the effect of the anisotropy between the s-wave scattering lengths of a three-component atomic Fermi gas loaded into a one-dimensional optical lattice. We find four different phases which support trionic instabilities made of bound states of three fermions. These phases distinguish themselves by the relative phases between the 2$k_F$ atomic density waves fluctuations of the three species. At small enough densities or strong anisotropies we give further evidences for a decoupling and the stabilization of more conventional BCS phases. Finally our results are discussed in light of a recent experiment on $^{6}$Li atoms.
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