Cold atoms at unitarity and inverse square interaction

Abstract

Consider two identical atoms in a spherical harmonic oscillator interacting with a zero-range interaction which is tuned to produce an s-wave zero-energy bound state. The quantum spectrum of the system is known to be exactly solvable. We note that the same partial wave quantum spectrum is obtained by the one-dimensional scale-invariant inverse square potential. Long known as the Calogero–Sutherland–Moser (CSM) model, it leads to the fractional exclusion statistics (FES) of Haldane and Wu. The statistical parameter is deduced from the analytically calculated second virial coefficient. When FES is applied to a Fermi gas at unitarity, it gives good agreement with experimental data without the use of any free parameter.

Joule-Thomson coefficient of ideal anyons within fractional exclusion statistics

“…The strongly interacting Fermi gas is called the unitary Fermi gas [40][41][42][43]. As a hypothesis, the three-dimensional ideal anyons with fractional exclusion statistics can be used to model the statistical behavior of a real unitary Fermi system [32][33][34][35][36]. This fractional exclusion statistics hypothesis is found to be in good agreement with the experimental results in a harmonic trap [36].…”

“…If ideal anyons are considered as quasiparticles to describe interactions [32][33][34][35][36], the effective mass is a significant physical quantity in the fractional exclusion statistics model.…”

“…According to Landau's phenomenological theory, there is an important parameter called effective mass which is used to characterize the quasiparticle and is determined by the low-temperature isochore heat capacity. If ideal anyons are considered as quasiparticles to describe interactions [32][33][34][35][36], the effective mass is a significant physical quantity in the fractional exclusion statistics model.…”

Orthogonality catastrophe and fractional exclusion statistics

“…The Sutherland model (SM) can be used to describe a one-dimensional Bose gas in an harmonic potential where the particles interact with each other through an inverse-square potential. Recent advances in the field of ultra cold atoms and optical lattices have opened up the possibility of simulating such a system in the laboratory [54,[58][59][60][61]. In particular, it has been argued in Ref.…”

Cold atoms at unitarity and semiclassical ground state of a Fermi gas for Haldane-Wu exclusion statistics

“…Bhaduri et al [4,5,6] assume that FES simulates interactions between particles at unitarity and give the analytical expression of the unitary occupancy factor g u = 1 − √ 2/2 ≈ 0.29 for a 3D IHO confinement V (r) = mω 2 r 2 /2 with |r| = r. They compute observables in the extended TF limit leading to smooth variations only. Generalizing their method, we introduce oscillating corrections that depend on for g = g u .…”