Effective nonlinear Schrodinger equations for cigar-shaped and disc-shaped Fermi superfluids at unitarity

Year: 2009

Authors: Adhikari S.K., Salasnich L.

Autors Affiliation: Instituto de Física Teórica, UNESP—São Paulo State University, 01.405-900 São Paulo, São Paulo, Brazil; CNR-INFM and CNISM, Research Unit of Padova, Department of Physics ‘Galileo Galilei’, University of Padua, Via Marzolo 8, 35131 Padova, Italy

Abstract: In the case of tight transverse confinement (cigar-shaped trap), the three-dimensional (3D) nonlinear Schrodinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length vertical bar a vertical bar -> infinity), is reduced to an effective 1D form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces results in good agreement with the original 3D one. In the limit of small and large fermion numbers N, the nonlinearity is of simple power-law type. A similar reduction of the 3D theory to a 2D form is also performed for a tight axial confinement (disc-shaped trap). The resultant effective 2D nonpolynomial equation also produces results in agreement with the original 3D equation and has simple power-law nonlinearity for small and large N. For both cigar- and disc-shaped superfluids, our nonpolynomial Schrodinger equations are quite attractive for phenomenological applications.

Journal/Review: NEW JOURNAL OF PHYSICS

Volume: 11      Pages from: 023011  to: 023011

More Information: We thank Professor Flavio Toigo for useful comments. SKA was partially supported by FAPESP and CNPq (Brazil), and the Institute for Mathematical Sciences of National University of Singapore. This research was partially done when SKA was on a visit to the Institute for Mathematical Sciences of the National University of Singapore in 2007. LS was partially supported by GNFM-INdAM and Fondazione CARIPARO.
DOI: 10.1088/1367-2630/11/2/023011

Citations: 46
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