Scientific Report - BEC

Quantum Monte Carlo methods 24the critical behavior of a gas of hard disks and we calculated the Kosterlitz-Thoulesstransition temperature as a function of the interaction strength.In the following we describe in some more details the main results obtained fromthe quantum Monte Carlo simulations mentioned above.Normal state of a polarized Fermi gas at unitarityWe study the polarized normal phase in the unitary limit by adopting an approachinspired by the theory of dilute solutions of 3 He in 4 He. We assume that the majorityspecies (↑) forms a background experienced by the minority species (↓) and that thelatter behaves as a gas of weakly interacting fermionic quasiparticles even though the↑−↓atomic interaction is very strong.We begin by writing the expression for the energy E of a homogeneous system inthe limit of very dilute mixtures and at zero temperature. The concentration of ↓ atomsis given by the ratio of the densities x = n ↓ /n ↑ and we will take it to be small. If only ↑atoms are present then the energy is that of an ideal Fermi gas E(x =0)=3/5E F ↑ N ↑ ,where N ↑ is the total number of ↑ atoms and E F ↑ = 2 /2m(6π 2 n ↑ ) 2/3 is the ideal gasFermi energy. When we add a ↓ atom with a momentum p (|p| ≪p F ↑ ), we shallassume that the change in E is given byδE =p22m ∗ − 3 5 E F ↑A. (1)When we add more ↓ atoms, creating a small finite density n ↓ , they will forma degenerate gas of quasiparticles at zero temperature occupying all the states withmomentum up to the Fermi momentum p F ↓ = (6π 2 n ↓ ) 1/3 . The energy of the systemcan then be written in a useful form in terms of the concentration x as (see also theSection on Polarized Fermi gases in this report):E(x)N ↑= 3 5 E F ↑(1 − Ax + m m ∗ x5/3 + Bx 2) . (2)Eq.(2) is valid for small values of the concentration x, i.e. when interactions between↓ quasiparticles as well as further renormalization effects of the parameters can beneglected.We calculate A and m ∗ using a fixed-node diffusion Monte Carlo (FN-DMC) approach[3]. For a single ↓ atom in a homogeneous Fermi sea of ↑ atoms the trial wavefunction ψ T , which determines the nodal surface used as an ansatz in the FN-DMC