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arXiv:cond-mat/0702191 · Physical Review B

Phase transitions and pairing signature in strongly attractive Fermi atomic gases

Xin Guan, Murray T. Batchelor, Chaohong Lee, Michael Bortz

Published Aug 16, 2007• 120 citations
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Abstract

We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization, and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field $H<{H}_{c1}$. A completely ferromagnetic phase without pairing occurs when the external field $H>{H}_{c2}$. In the region ${H}_{c1}<H<{H}_{c2}$, we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.

DOI
10.1103/physrevb.76.085120

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We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.
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Ultracold three-component atomic Fermi gases in one dimension are expected to exhibit rich physics due to the presence of trions and different pairing states. Quantum phase transitions from the trion state into a paired phase and a normal Fermi liquid occur at zero temperature. We derive the analytical thermodynamics of strongly attractive three-component one-dimensional fermions with SU(3) symmetry via the thermodynamic Bethe ansatz method in unequal Zeeman splitting fields H1{H}_{1}H1​ and H2{H}_{2}H2​. We find explicitly that for low temperature the system acts like either a two-component or a three-component Tomonaga-Luttinger liquid dependent on the system parameters. The phase diagrams for the chemical potential and specific heat are presented for illustrative values of the Zeeman splitting. We also demonstrate that crossover between different Tomonaga-Luttinger-liquid phases exhibit singular behavior in specific heat and entropy as the temperature tends to zero. Beyond Tomonaga-Luttinger-liquid physics, we obtain the equation of state which provides a precise description of universal thermodynamics and quantum criticality in three-component, strongly attractive Fermi gases.
Quantum criticality of strongly attractive Fermi gas with SU(3)SU(3)SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential μμμ, effective magnetic field H1H_1H1​, H2H_2H2​ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2z=2z=2 and correlation length exponent ν=1/2ν=1/2ν=1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with SU(N)SU(N)SU(N) symmetry.