We present a coupled-pair approach for studying few-body physics in harmonically trapped ultracold gases. The method is applied to a two-component Fermi system of
N particles. A stochastically variational Gaussian expansion method is applied, focusing on optimization of the two-body correlations present in the strongly interacting, or unitary, limit. The ground-state energy of the four-, six- and eight-body problem with equal spin populations is calculated with high accuracy and minimal computational effort. We also calculate the structural properties of these systems and discuss their implication for the many-body ultracold gas and other few-body calculations.
Using two different numerical methods, we study the behavior of two-component Fermi gases interacting through short-range
s-wave interactions in a harmonic trap. A correlated Gaussian basis-set expansion technique is used to determine the energies and structural properties, i.e., the radial one-body densities and pair distribution functions, for small systems with either even or odd
N, as functions of the
s-wave scattering length and the mass ratio $\ensuremath{\kappa}$ of the two species. Particular emphasis is put on a discussion of the angular momentum of the system in the BEC-BCS crossover regime. At unitarity, the excitation spectrum of the four-particle system with total angular momentum
L=0 is calculated as a function of the mass ratio $\ensuremath{\kappa}$. The results are analyzed from a hyperspherical perspective, which offers unique insight into the problem. Additionally, fixed-node diffusion Monte Carlo calculations are performed for equal-mass Fermi gases with up to
N=30 atoms. We focus on the odd-even oscillations of the ground-state energy of the equal-mass unitary system having up to
N=30 particles, which are related to the excitation gap of the system. Furthermore, we present a detailed analysis of the structural properties of these systems.
The properties of two-component Fermi gases with zero-range interactions are universal. We use an explicitly correlated Gaussian basis set expansion approach to investigate small equal-mass two-component Fermi gases under spherically symmetric external harmonic confinement. At unitarity, we determine the ground-state energy for systems with up to 10 particles interacting through finite-range two-body potentials for both even and odd numbers of particles. We extrapolate the energies to the zero-range limit using a novel scheme that removes the linear and, in some cases, also the quadratic dependence of the ground-state energies on the two-body range. Our extrapolated zero-range energies are compared with results from the literature. We also calculate the two-body Tan contact and structural properties.
We theoretically investigate equal-mass spin-balanced two-component Fermi gases in which pairs of atoms with opposite spins interact via a short-range isotropic model potential. We probe the distinction between two-dimensional and quasi-two-dimensional harmonic confinement by tuning the effective range parameter within two-dimensional scattering theory. Our approach, which yields numerically exact energetic and structural properties, combines a correlated Gaussian basis-set expansion with the stochastic variational method. For systems containing up to six particles, we: 1) Present the ground- and excited-state energy spectra; 2) Study non-local correlations by analysing the one- and two-body density matrices, extracting from these the occupation numbers of natural orbitals, the momentum distributions of atoms and pairs, and the molecular `condensate fraction’; 3) Study local correlations by computing the radial and pair distribution functions. This paper extends current theoretical knowledge on the properties of trapped few-fermion systems as realised in state-of-the-art cold-atom experiments.
We consider one-dimensional tubes containing bosonic polar molecules. The long-range dipole–dipole interactions act both within a single tube and between different tubes. We consider arbitrary values of the externally aligned dipole moments with respect to the symmetry axis of the tubes. The few-body structures in this geometry are determined as a function of polarization angles and dipole strength by using both essentially exact stochastic variational methods and the harmonic approximation. The main focus is on the three-, four- and five-body problems in two or more tubes. Our results indicate that in the weakly coupled limit the intertube interaction is similar to a zero-range term with a suitable rescaled strength. This allows us to address the corresponding many-body physics of the system by constructing a model where bound chains with one molecule in each tube are the effective degrees of freedom. This model can be mapped onto one-dimensional Hamiltonians for which exact solutions are known.
Dipolar Bose and Fermi gases, which are currently being studied extensively experimentally and theoretically, interact through anisotropic, long-range potentials. Here, we replace the long-range potential by a zero-range pseudopotential that simplifies the theoretical treatment of two dipolar particles in a harmonic trap. Our zero-range pseudopotential description reproduces the energy spectrum of two dipoles interacting through a shape-dependent potential under external confinement very well, provided that sufficiently many partial waves are included, and readily leads to a classification scheme of the energy spectrum in terms of approximate angular momentum quantum numbers. The results may be directly relevant to the physics of dipolar gases loaded into optical lattices.