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arXiv:1709.05160 · Physical Review C

Static response, collective frequencies, and ground-state thermodynamical properties of spin-saturated two-component cold atoms and neutron matter

Antoine Boulet, Denis Lacroix A

Published Jan 4, 2018• 15 citations
arXivHTMLPDF

Abstract

The thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed density functional theory (DFT) based on the $s$-wave scattering length ${a}_{s}$, effective range ${r}_{e}$, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus, and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the noninfinite scattering length and to a significant influence of effective range, which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in auxiliary-field diffusion Monte Carlo (AFDMC) can be qualitatively reproduced when the $p$-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free-gas response might stem from the compensation of the ${a}_{s}$ effect by the effective range and $p$-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.

DOI
10.1103/physrevc.97.014301

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The thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed density functional theory (DFT) based on the sss-wave scattering length as{a}_{s}as​, effective range re{r}_{e}re​, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus, and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the noninfinite scattering length and to a significant influence of effective range, which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in auxiliary-field diffusion Monte Carlo (AFDMC) can be qualitatively reproduced when the ppp-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free-gas response might stem from the compensation of the as{a}_{s}as​ effect by the effective range and ppp-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.
In this paper I derive the static and dynamic properties of two differnt fermionic cold gas system. I derive the thermodynamic properties of a fully polarized noninteracting fermi gas in a quartic trap using a semiclassical approach and a low temperature series expansion method. I also introduce the recently discovered quantity Contact and derive several universal relations associated with it. In order to derive the contact, I use two different methods: a ground-state energy fucntional based on asymptotic limits and Monte Carlo calculations, and BCS Mean Field Theory. I use the universal relations associated with Contact to derive several static and dynamic properties of a balanced strongly interacting gas of fermions with two spin states and large scattering length. The static properties include the total energy, contact density, and polytropic index of the system, and the dynamic properties include the collective oscillations of the trap, the structure factor, and an alternate derivation of the polytropic index. The collective oscillation frequencies are found using both hydrodynamic theory and a sum rule approach and are presented in terms of the contact and homogenous energy. It is found that the static and dynamic properties derived for this system agree well with experimental data and alternative theoretical approaches.
We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.
We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.
A density-functional theory is proposed for strongly interacting fermions with arbitrary large negative scattering length. The functional has only two parameters that are directly fixed to reproduce the universal properties of unitary gas: the so-called Bertsch parameter ${\ensuremath{\xi}}_{0}$ and a parameter ${\ensuremath{\eta}}_{e}$ related to the possible influence of the effective range re{r}_{e}re​ at infinite scattering length aaa. Using most recent quantum Monte Carlo (QMC) estimates of these two parameters, it is shown that the functional properly reproduces the experimental measurements of interacting Fermi systems not only at unitarity but also away from this limit over a wide range of ${(a{k}_{F})}^{\ensuremath{-}1}$ values. The functional is applied to obtain an expression of Tan's contact parameter including the effect of re{r}_{e}re​. Application is finally made to neutron matter. It is shown that most recent QMC results are well reproduced.
Cold gas experiments can be tuned to achieve strongly-interacting regimes such as that of low-density neutron matter found in neutron-stars' crusts. We report T=0T=0T=0 diffusion Monte Carlo results (i) for the ground state of both spin-1/2 fermions with short-range interactions and low-density neutron matter in a cylindrical container, and (ii) properties of these systems with a vortex line excitation. We calculate the equation of state for cold atoms and low-density neutron matter in the bulk systems, and we contrast it to our results in the cylindrical container. We compute the vortex line excitation energy for different interaction strengths, and we find agreement between cold gases and neutron matter for very low densities. We also calculate density profiles, which allow us to determine the density depletion at the vortex core, which depends strongly on the short-ranged interaction in cold atomic gases, but it is of $\ensuremath{\approx}25%$ for neutron matter in the density regimes studied in this work. Our results can be used to constrain neutron matter properties by using measurements from cold Fermi gases experiments.
Experiments with cold Fermi atoms can be tuned to probe strongly-interacting fluids that are very similar to the low-density neutron matter found in the crusts of neutron stars. In contrast to traditional superfluids and superconductors, matter in this regime is very strongly paired, with gaps of the order of the Fermi energy. We compute the T=0T=0T=0 equation of state and pairing gap for cold atoms and low-density neutron matter as a function of the Fermi momentum times the scattering length. Results of quantum Monte Carlo calculations show that the equations of state are very similar. The neutron matter pairing gap at low densities is found to be very large but, except at the smallest densities, significantly suppressed relative to cold atoms because of the finite effective range in the neutron-neutron interaction.