The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.
The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.
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.
We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the s-wave scattering length and the Fermi wave vector, akF. We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy EFG. When a>0, the interaction is strong enough to form bound molecules with energy Emol. For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.
Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform T=0 ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.
The ground state energy and pairing gap of the interacting Fermi gases calculated by the ab initio stochastic method are compared with those estimated from the Bardeen-Cooper-Schrieffer pairing Hamiltonian. We discuss the ingredients of this Hamiltonian in various regimes of interaction strength. In the weakly interacting (1∕akF⪡0) regime the BCS Hamiltonian should describe Landau quasiparticle energies and interactions, on the other hand, in the strongly pairing regime, that is, $1∕a{k}_{F}\ensuremath{\gtrsim}0$, it becomes part of the bare Hamiltonian. However, the bare BCS Hamiltonian is not adequate for describing atomic gases in the regime of weak to moderate interaction strength $\ensuremath{-}\ensuremath{\infty}<1∕a{k}_{F}<0$ such as $a{k}_{F}\ensuremath{\sim}\ensuremath{-}1$.
PACS. 03.75.Hh – Static properties of condensates; thermodynamical, statistical and structural properties. PACS. 03.75.Ss – Degenerate Fermi gases. PACS. 05.30.Fk – Fermion systems and electron gas. Abstract. – We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available. The recent experimental realization of strongly interacting Fermi gases of 6 Li and 40 K atoms near a Feshbach resonance has opened up the exciting possibility of investigating the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) [1–5]. In these systems, the inter-atomic interaction strength can be varied by tuning
We study the system of a dilute gas of fermions in 3-dimensions, with attractive interactions tuned to the unitarity point, using the non-perturbative Restricted Path Integral Monte Carlo (R-PIMC) method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state Quantum Monte Carlo calculations. We identify the temperature T � � 0.70ǫF below which pairing correlations develop, and estimate the critical temperature for the superfluid transition Tc � 0.25ǫF from a finite size scaling analysis of the superfluid density. PACS numbers: The recent experiments, starting with generating a degenerate gas of cold atoms[3], the use of Feshbach resonance to tune the effective interaction between the fermions[4, 5], the measurements of the gap to identify a pairing scale[6] and the measurements of vortices[7] to identify the superfluid state, have all given an impetus to the study of superfluidity in the BCS-BEC crossover regime. The nature of superconductivity or superfluidity in a many-particle system with an increasing pairing attraction was shown [1, 2] to interpolate smoothly between the BCS regime for weak attraction between the fermions, and the Bose-Einstein condensation (BEC) regime for strong coupling. In the weak coupling regime, the Cooper pair size is much larger than the interparticle spacing, and the simultaneous pairing and condensation of fermions is well described by the BCS theory. In the strong coupling regime, fermions form strongly bound bosonic molecules at a pairing temperature scale T ∗ that is considerably higher than the BEC temperature Tc. In a two species system of fermions with an attractive interaction between them, the unitary point is defined by the divergence of the zero energy s-channel scattering length, as, for two particles in free space. The unitary point is interesting since it describes a strongly correlated system with universal properties[8]. In general, there are two length scales that define the system: the interparticle spacing ∝ n −1/3 , and the scattering length as which contains information about the interaction potential. At the unitary point however, since as diverges, all the properties of the system are described by a single length scale k −1