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arXiv:0707.0613 · Physical Review A

Ferromagnetic behavior in the strongly interacting two-component Bose gas

Xi‐Wen Guan, Murray T. Batchelor, Minoru Takahashi

Published Oct 16, 2007• 71 citations
arXivHTMLPDF

Abstract

We investigate the low-temperature behavior of the integrable one-dimensional two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility, and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat ${c}_{v}\ensuremath{\sim}{T}^{1∕2}$ and the susceptibility $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.

DOI
10.1103/physreva.76.043617

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In this thesis, we investigate thermodynamic properties, magnetic phase transitions and correlation functions of integrable quantum many-body systems in the field of ultracold atomic gases. The scope of our investigation encompasses three models in one-dimension that are integrable by means of the Bethe ansatz method. They are the multi-component 5-interacting Fermi gas, the spin-l Bose gas with antiferromagnetic spin interaction and the SU(2) spinor Bose gas with finite-range Gaussian interaction. We derive the thermodynamic Bethe ansatz equations for the general SU(k) Fermi gas. We illustrate the root patterns and give a quantitative description of the ground state properties for the strongly and weakly interacting regimes. The thermodynamics and magnetic phase transitions are described quantitatively by means of the thermodynamic Bethe ansatz equations. We find that all phase transitions in the attractive regime are of second order with a linear field dependent magnetization in the vicinities of critical points. The SU(2) Fermi gas is studied in more detail. The low temperature thermodynamics for the repulsive case is derived by means of the Wiener-Hopf technique. Finite-size corrections and correlation functions for both the repulsive and attractive cases are derived from the nested Bethe ansatz equations and conformal field theory. In the attractive case, we show that spatial oscillations of the leading terms in the pair correlation function and spin correlation function solely depend on the mismatch between Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristic of a Fulde- Ferrell-Larkin-Ovchinnikov (FFLO) state. For the spin-l Bose gas with antiferromagnetic spin interaction, we find that at zero temperature, the system exhibits three quantum phases: a phase with singlet pairs of bosons, a fully-polarized Tonks-Girardeau gas phase of unpaired ms = 1 bosons, and a mixed phase of singlet pairs and unpaired ms = 1 bosons. Phase transitions in the vicinities of the critical fields are also of second order with a linear field dependent magnetization. Finally, we use the asymptotic Bethe ansatz method to derive the quasimomenta distribution and ground state energy for the SU(2) spinor Bose gas with finite-range Gaussian interaction. We show that finite range potentials are more likely to lead to quasi Bose-Einstein condensation than zero range potentials by studying the spatial density profiles as the interaction width increases.
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