Three s-wave interacting fermions under anisotropic harmonic confinement: Dimensional crossover of energetics and virial coefficients

Abstract

We present essentially exact solutions of the Schroedinger equation for three fermions in two different spin states with zero-range s-wave interactions under harmonic confinement. Our approach covers spherically symmetric, strictly two-dimensional, strictly one-dimensional, cigar-shaped, and pancake-shaped traps. In particular, we discuss the transition from quasi-one-dimensional to strictly one-dimensional and from quasi-two-dimensional to strictly two-dimensional geometries. We determine and interpret the eigenenergies of the system as a function of the trap geometry and the strength of the zero-range interactions. The eigenenergies are used to investigate the dependence of the second- and third-order virial coefficients, which play an important role in the virial expansion of the thermodynamic potential, on the geometry of the trap. We show that the second- and third-order virial coefficients for anisotropic confinement geometries are, for experimentally relevant temperatures, very well approximated by those for the spherically symmetric confinement for all s-wave scattering lengths.

13 figures (multiple subfigures)

References in corpus (16)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Attractive and repulsive Fermi polarons in two dimensions
• Virial expansion for a strongly correlated Fermi gas
• Radio Frequency Association of Efimov Trimers
• Analytical solutions for the dynamics of two trapped interacting ultracold atoms
• Low-energy three-body dynamics in binary quantum gases
• Universal properties of a trapped two-component Fermi gas at unitarity
• Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and high-temperature thermodynamics
• Exact few-body results for strongly correlated quantum gases in two dimensions
• Spectrum and Dynamics of the BCS-BEC crossover from a few-body perspective
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Atom-dimer scattering for confined ultracold fermion gases
• Three-body problem for ultracold atoms in quasi-one-dimensional traps
• Pseudo-potential treatment of two aligned dipoles under external harmonic confinement
• Universality in a 2-component Fermi System at Finite Temperature

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