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 < Hc1. A completely ferromagnetic phase without pairing occurs when the external field H > Hc2. In the region Hc1 < H < Hc2 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.

We study the dynamics of a single spin 1/2 coupled to a bath of spins 1/2 by inhomogeneous Heisenberg couplings including a central magnetic field. This central-spin model describes decoherence in quantum bit systems. An exact formula for the dynamics of the central spin is presented, based on the Bethe ansatz. For initially completely polarized bath spins and small magnetic field, we find persistent oscillations of the central spin about a nonzero mean value. For a large number of bath spins Nb, the oscillation frequency is proportional to Nb, whereas the amplitude behaves as 1/Nb, to leading order. No asymptotic decay of the oscillations due to the nonuniform couplings is observed, in contrast to some recent studies

Abstract. We provide evidence in support of a recent proposal by Astrakharchik et al for the existence of a super Tonks-Girardeau gas-like state in the attractive interaction regime of quasi-one-dimensional Bose gases. We show that the super TonksGiradeau gas-like state corresponds to a highly-excited Bethe state in the integrable interacting Bose gas for which the bosons acquire hard-core behaviour. The gas-like state properties vary smoothly throughout a wide range from strong repulsion to strong attraction. There is an additional stable gas-like phase in this regime in which the bosons form two-body bound states behaving like hard-core bosons. § Corresponding author (Murray.Batchelor@anu.edu.au)

We extend the exact periodic Bethe Ansatz solution for onedimensional bosons and fermions with δ-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits. PACS numbers: 03.75.Ss, 05.30.Fk, 67.60.-g,71.10.Pm IntroductionOne-dimensional quantum gases with two-particle δ-interaction have long been of fascination. The most simple model of δ-interacting spinless bosons in a periodic box was solved in terms of the Bethe Ansatz by Lieb and Liniger [1]. This quantum mechanical model is not only one of the oldest integrable models after the Heisenberg spin chain, but arguably also one of the most important test beds for exploring new ideas and methods, e.g., the Thermodynamic Bethe Ansatz [2] was pioneered for this model. Earlier Girardeau [3] discussed a mapping from strongly repulsive interacting bosons to fermions, corresponding to the limit c → ∞, where c features as the arbitrary interaction strength in the Lieb-Liniger model. Later in seminal work McGuire [4] discussed δ-interaction particles via an optical analogue. Gaudin [5] and Yang [6] then considered spin-1 2 fermions with periodic boundary conditions, the first model with internal states. Sutherland [7] applied the nested Bethe Ansatz, which allowed the treatment of periodic quantum gases with arbitrary spin by repeated application of the Bethe Ansatz, reducing the number of internal states in each step. Gaudin [8] solved the model of spinless bosons with hard wall boundary conditions.The special form of δ-interaction is at the heart of the integrability of the quantum gases. Models tweaking the type of interaction have been considered, but so far are less prominent [9]. Non-integrable models, like the harmonically trapped gas with tunable interaction strength, have to be treated by approximate methods and simulations. One integrable model, the mixture of fermionic and bosonic particles, solved by Lai and Yang [10] has long been dormant in the literature, but is enjoying new interest ‡

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