Contact and Momentum Distribution of the Unitary Fermi Gas

Abstract

A key quantity in strongly-interacting resonant Fermi gases is the contact C, which characterizes numerous properties such as the momentum distribution at large momenta or the pair correlation function at short distances. The temperature dependence of C was measured at unitarity, where existing theoretical predictions differ substantially even at the qualitative level. We report accurate data for the contact and the momentum distribution of the unitary gas in the normal phase, obtained by Bold Diagrammatic Monte Carlo and Borel resummation. Our results agree with experimental data within error bars and provide crucial benchmarks for the development of advanced theoretical treatments and precision measurements.PACS numbers: 05.30.Fk, 67.85.Lm, 74.20.Fg The resonant Fermi gas is a fundamental model of quantum many-body physics. It features a smooth crossover between fermionic and bosonic superfluidity, as predicted in the context of condensed matter physics [1][2][3][4] and confirmed by remarkable experiments on ultracold atomic Fermi gases near Feshbach resonances [5]. It is also relevant to neutron matter [6,7] and highenergy physics [8], particularly in the central region of the crossover, around the unitary point where the scattering length diverges. As a result of the vanishing interaction range, resonant Fermi gases feature characteristic ultraviolet singularities governed by a single quantity called contact [4,[9][10][11][12]. In particular, for the homogeneous gas, the density-density correlation function at short distance diverges as(1) and the momentum distribution has the tailHere C is the contact per unit volume,n σ (r) = ψ † σ (r)ψ σ (r) is the density operator, and the spinσ momentum distribution n σ (k) is normalised to n σ (k)d 3 k/(2π) 3 = n σ = n σ (r) . A direct manifestation of Eq. (1) is that in a unit volume, the number of pairs of fermions separated by a distance smaller than s is C s/(4π) in the s→0 limit. Hence C controls the (anomalously high) density of pairs with vanishing interparticle distance [9,11,13].A large variety of experimentally studied observables are directly expressible in terms of the contact: the population of the closed channel molecular state measured by laser molecular spectroscopy [14,15], the largemomentum tail of the static structure factor measured by Bragg spectroscopy [16][17][18], the tail of the momentum distribution measured by non-interacting time-offlight or by momentum-resolved radiofrequency spectroscopy [19], the derivative of the energy with respect to the inverse scattering length [10] extracted from the pressure equation of state measured by in-situ imaging [20], the large-frequency tail in radiofrequency spectroscopy [19,[21][22][23], and the short-distance densitydensity correlation function extracted from the threebody loss rate in presence of a bosonic cloud [24].The experimental study [22] is particularly important because it is spatially resolved and for the first time yields the temperature dependence of the contact for a homogeneous system. R...

Diagrammatic Monte Carlo algorithm for the resonant Fermi gas

“…4. Very recently, these results were confirmed using a much more advanced resumma-tion method, which was found to be necessary for controllability, due to the fact that the series has zero radius of convergence 12 . Contact and momentum distribution were also computed using the new resummation method 13 .…”

“…A crucial separate aspect of the approach is the construction of an appropriate divergent-series resummation method; this was reported in Ref. 12 and will be detailed elsewhere 31 .…”

Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory

“…Note that, these results are equivalent those given by Eqs. (18)(19)(20)(21) of Ref. [92] except that the sign convention for the scattering length is different (i.e.…”

“…Starting from the expansion (21) and making a Taylor expansion of each terms around k = k F (or p = 1), one obtains a systematic approach to compute quasi-particle properties in powers of (a s k F ). For instance using the Taylor expansion:…”

Report on scipost_201910_00037v1

“…In Ref. [54], the equation of state of the homogeneous unitary Fermi gas has been accurately calculated by the diagrammatic Monte Carlo calculation. The authors have found that the equation of state as a function of e βµ shows a non-monotonic behaviour at e βµ ∼ 1, in a similar manner as that explained above to a har-monically trapped system.…”