Energy spectrum of harmonically trapped two-component Fermi gases: Three- and Four-Particle Problem

Abstract

Trapped two-component Fermi gases allow for the investigation of the so-called BCS-BEC crossover by tuning the interspecies atom-atom $s$-wave scattering length scattering $a^{(aa)}$ 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 crossover-like 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 momentum as well as with natural and unnatural parity 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 for the straightforward assignment of quantum numbers and furthermore provides great insights into the strongly-interacting unitary regime.

11 figures

References in corpus (27)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Theory of ultracold Fermi gases
• Observation of Bose-Einstein Condensation of Molecules
• Weakly bound dimers of fermionic atoms
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Observation of an Efimov spectrum in an atomic system
• General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Evidence for Universal Four-Body States Tied to an Efimov Trimer
• Universal Properties of the Four-Body System with Large Scattering Length
• Virial expansion for a strongly correlated Fermi gas
• The potential energy of a ${}^{40}$K Fermi gas in the BCS-BEC crossover
• Scattering Length Scaling Laws for Ultracold Three-Body Collisions
• Universal properties of a trapped two-component Fermi gas at unitarity
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Diatomic molecules in ultracold Fermi gases - Novel composite bosons
• Effective Theory for Trapped Few-Fermion Systems
• Energetics and Structural Properties of Trapped Two-Component Fermi Gases
• Four-boson scale near a Feshbach resonance
• Spectrum and Dynamics of the BCS-BEC crossover from a few-body perspective
• BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
• Energetics and structural properties of three-dimensional bosonic clusters near threshold
• 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
• Efimov Trimer Formation via Ultracold Four-body Recombination
• Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions

Cited by in corpus (34)

• Few-body physics with ultracold atomic and molecular systems in traps
• Comparing and contrasting nuclei and cold atomic gases
• Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases
• Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap
• Three attractively interacting fermions in a harmonic trap: Exact solution, ferromagnetism, and high-temperature thermodynamics
• Four-body Efimov effect
• Exact few-body results for strongly correlated quantum gases in two dimensions
• Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient
• Symmetries of Three Harmonically-Trapped Particles in One Dimension
• Breakdown of universality for unequal-mass Fermi gases with infinite scattering length
• Path integral Monte Carlo ground state approach: Formalism, implementation, and applications
• Probing strongly interacting atomic gases with energetic atoms
• Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations
• Trapped two-component Fermi gases with up to six particles: Energetics, structural properties, and molecular condensate fraction
• Universality of the unitary Fermi gas: A few-body perspective
• Universal dynamic structure factor of a strongly correlated Fermi gas
• Few-body resonances of unequal-mass systems with infinite interspecies two-body s-wave scattering length
• Harmonically trapped Fermi gas: Temperature dependence of the Tan contact
• Degeneracies in trapped two-component Fermi gases
• The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas
• Small two-component Fermi gases in a cubic box with periodic boundary conditions
• Two-body quench dynamics of harmonically trapped interacting particles
• Analytical solution for the spectrum of two ultracold atoms in a completely anisotropic confinement
• Universality and itinerant ferromagnetism in rotating strongly interacting Fermi gases
• Coupled pair approach for strongly-interacting trapped fermionic atoms
• A new effective interaction for the trapped fermi gas: the BEC-BCS crossover
• Quench dynamics of mass-imbalanced three-body fermionic systems in a spherical trap
• Three-body contact for fermions. I. General relations
• Effects of Efimov states on quench dynamics in a three-boson trapped system
• Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
• Observability of modified threshold behavior near unitarity
• When does a Fermi puddle become a Fermi sea? Emergence of pairing in two-dimensional trapped mesoscopic Fermi gases
• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement
• Universality in rotating strongly interacting gases