Dilute Fermi systems with large
s-wave scattering length
as exhibit universal properties if the interparticle spacing
r0 greatly exceeds the range of the underlying two-body interaction potential. In this regime,
r0 is the only relevant length scale and observables such as the energy per particle depend only on
r0 (or, equivalently, the energy
EFG of the free Fermi gas). This paper investigates Bose and Fermi systems with nonvanishing angular momentum
l using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of an
l-dependent length scale ${\ensuremath{\xi}}_{l}$, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite
l. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.
Dilute Fermi systems with large s-wave scattering length a_s exhibit universal properties if the interparticle spacing r_o greatly exceeds the range of the underlying two-body interaction potential. In this regime, r_o is the only relevant length scale and observables such as the energy per particle depend only on r_o (or, equivalently, the energy E_{FG} of the free Fermi gas). This paper investigates Bose and Fermi systems with non-vanishing angular momentum l using the lowest order constrained variational method. We focus on the regime where the generalized scattering length becomes large and determine the relevant length scales. For Bose gases with large generalized scattering lengths, we obtain simple expressions for the energy per particle in terms of a l-dependent length scale ξ_l, which depends on the range of the underlying two-body potential and the average interparticle spacing. We discuss possible implications for dilute two-component Fermi systems with finite l. Furthermore, we determine the equation of state of liquid and gaseous bosonic helium.
Quantum degenerate Fermi gases can be created in the laboratories using alkali atoms. These gases can be in different regimes of density and interaction strength and provide an ideal test bed for the basic properties of the quantum and statistical mechanics. Also some astrophysical objects such as neutron stars can be idealized as interacting fermion systems. In this thesis work, the ground state properties of dilute Fermi gases with attractive short range two-body interactions are reported. Main results of this work are produced by application of quantum Monte Carlo methods. We introduce variational nodal structure to the trial wave function in order to deal with the fermion sign problem. We consider the possibility of Cooper pairing between fermions of different species. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the s-wave scattering length a and the Fermi wave vector kF. We also review some of the conventional variational methods such as the Lowest Order Constrained Variational which is suitable for Fermi fluids without pairing correlation. The ground state energy, pairing gap Δ, quasi-particle spectrum, two-body distribution function, and momentum distribution of the superfluid were studied with greater accuracy using ab initio quantum Monte Carlo techniques. In the case of the two component Fermi fluid, we find that in the weak coupling regime, 1/akF < -1, the system is a Bardeen-Cooper-Schrieffer type superfluid and the energy gap Δ is much smaller than the Fermi gas energy EFG. For 1/akF ≥ 0:5 we find that weakly interacting composite bosons or molecules are formed in the superfluid gas with Δ and gas energy per particle approaching half of the molecular energy jEmolj=2. In this region we seem to have Bose-Einstein condensation of molecules. The behavior of the energy, chemical potential and energy gap in the transition region, -0:5 < 1/akF < 0:5, is discussed. The study is extended to the three component Fermi fluid in relation to the spin polarized alkali gases and color superconductivity of the quark matter. Unlike the two component fluids, zero potential range limit cannot be reached without causing collapse of the system. We also study the scaling behavior of the three-body system. We calculate the threshold of the three-body bound state as a function of the potential range and strength. For the many-body systems, we find that ground state can be achieved by broken symmetry pairing. However, the restored symmetry pairing scenario in the strongly interacting regime is not conclusive. We also discuss the pairing gap as well as the structural properties such as two-body distribution functions.
This work studies zero-temperature Fermi gases with short-ranged and attractive interactions with focus on the dimensionality aspects by confining the system from three to two dimensions. Interacting Fermi gases are superfluids characterized as being strongly correlated if the scattering length is much larger than the other scales present. In the many-body context, this category of systems requires a careful treatment since mean-field approaches are not expected to hold under the conditions which define the strong pairing. For this reason, we employ quantum Monte Carlo methods to study the dimensionality effects in two-component Fermi gases in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover. To be able to investigate such aspects, we consider a three-dimensional gas with periodic boundary conditions in the xy plane and a confining potential in the z direction capable of reducing the dimensionality of the system, which defines a dimensional BCS-BEC crossover. We calculate the equation of state as the energy per particle as a function of the dimensionality and as a function of the interaction parameter, which are characterized by the oscillator length in the z direction and the scattering length respectively. The greater confinement in the system lowers the interparticle distances, which increases the effects of the attractive interactions between antiparallel-spin fermions.We also calculate the density profile in the z direction over the crossover for different confinements and different interaction parameters to quantify their influence on the spatial distribution of the particles. This study connects the perspectives between theoretical and experimental works in low-dimensional ultracold Fermi gases by utilizing an approach that is similar to what it is realized in modern experiments.
We investigate the energy spectrum of systems of two, three, and four spin-
21 fermions with short range attractive interactions both exactly and within the scattering length approximation. The formation of molecular bound states and the ferromagnetic transition of the excited scattering state are examined systematically as a function of the two-body scattering length. Identification of the upper branch (scattering states) is discussed and a general approach valid for systems with many particles is given. We show that an adiabatic ferromagnetic transition occurs, but at a critical transition point
kFa much higher than predicted from previous calculations, almost all of which use the scattering length approximation. In the four-particle system the discrepancy is a factor of 2. The exact critical interaction strength calculated in the four-particle system is consistent with that reported by experiment. To make comparisons with the adiabatic transition, we study the quench dynamics of the pairing instability using the eigenstate wave functions.