Superfluid instability in ultra-cold gas of fermionic atoms with attractive potential in a one-dimensional trap

17th International Conference on Recent Progress in Many-Body Theories

Schlottmann, P.^1 ; Zvyagin, A.A.^2,3

Department of Physics, Florida State University, Tallahassee, FL 32306, United States^1

B.I. Verkin Institute for Low Temperature Physics and Engineering, Ukrainian National Academy of Sciences, 47 Lenin Avenue, Kharkov, 61103, Ukraine^2

Max-Planck-Institut für Physik Komplexer Systeme, D-01187, Dresden, Germany^3

关键词: Bethe ansatz solution;    Conformal field theories;    Correlation function;    Ground state phase diagram;    Harmonic confinement;    Josephson tunneling;    Long range orders;    Response functions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/529/1/012013/pdf
DOI  :  10.1088/1742-6596/529/1/012013

来源: IOP

【 摘 要 】

In the context of ultracold fermionic atoms with effective spin S confined to an elongated trap we study the one-dimensional gas interacting via an attractive δ-function potential using the Bethe ansatz solution. There are N 2S + 1 fundamental states: The particles can either be unpaired or clustered in bound states of 2, 3, ..., 2S and 2S + 1 atoms. In a magnetic field, the rich ground state phase diagram consists of these N states and various mixed phases in which combinations of the fundamental states coexist. The phase diagram simplifies considerably in zero-field, where only bound states of N atoms can exist. Due to the harmonic confinement and within the local density approximation, the density profile of bound states decreases along the tube from the center of the trap to its boundaries. In an array of tubes with weak Josephson tunneling superfluid order may arise. In zero-field the response functions determining the superfluid and density wave order are calculated using conformal field theory and the exact Bethe ansatz solution. The response function for superfluidity consists of a power law with distance, while the correlation function for density waves is a power law of distance times a sinusoidal factor oscillating with distance with a period given by two times the Fermi momentum. For S 1/2 superfluidity is a possibility for all densities and density waves can be excluded. For S ≥ 3/2 superfluidity may occur at low densities but at high densities it gives way to density waves. We discuss the scenario of phase separation where for S ≥ 3/2 the system has superfluid long-range order toward the trap boundaries and density waves at its center.