Energy spectrum of harmonically trapped two-component Fermi gases: Three- and four-particle problem

2010/05/17 by K. M. Daily, D. Blume · 1 citation
Physics and Astronomy · #Advanced Frequency and Time Standards #Atomic and Subatomic Physics Research #Cold Atom Physics and Bose-Einstein Condensates #Crossover #Fermi Gamma-ray Space Telescope #Fermion #Parity (physics) #Physics #Quantum mechanics #Scattering #Unitary state #Wave function #cond-mat.quant-gas

paper · pdf · doi:10.1103/physreva.81.053615

published as Phys.Rev.A81:053615,2010 · 11 figures

openalex publication_date 2010/05/17 · arxiv created 2010/06/04 · arxiv updated 2014/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Trapped two-component Fermi gases allow the investigation of the so-called BCS-BEC crossover by tuning the interspecies atom-atom s-wave scattering length a^(aa) from attractive to repulsive, including vanishing and infinitely large values. Here, we numerically determine the energy spectrum of the equal-mass spin-balanced four-fermion system---the smallest few-particle system that exhibits BCS-BEC crossoverlike behavior---as a function of a^(aa) using the stochastic variational approach. For comparative purposes, we also treat the two- and three-particle systems. States with vanishing and finite total angular momenta as well as with natural and unnatural parities are considered. In addition, the energy spectrum of weakly attractive and weakly repulsive gases is characterized by employing a perturbative framework that utilizes hyperspherical coordinates. The hyperspherical coordinate approach allows the straightforward assignment of quantum numbers and furthermore provides great insight into the strongly interacting unitary regime.

Citations

• Universal properties of the four-body system with large scattering length
• Method for solving the many-body bound state nuclear problem
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Generalized virial theorem and pressure relation for a strongly correlated Fermi gas
• Universal relations for a strongly interacting Fermi gas near a Feshbach resonance
• Emergence of a molecular Bose–Einstein condensate from a Fermi gas
• Weakly Bound Dimers of Fermionic Atoms
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Exact Relations for a Strongly Interacting Fermi Gas from the Operator Product Expansion
• Spectrum and Dynamics of the BCS-BEC Crossover from a Few-Body Perspective
• Scattering Length Scaling Laws for Ultracold Three-Body Collisions
• Observation of Bose-Einstein Condensation of Molecules

Cited by

• Separable effective interaction for the trapped Fermi gas: The BEC-BCS crossover