Superfluid Pairing in Neutrons and Cold Atoms

Ultracold atomic gases and low-density neutron matter are unique in that they exhibit pairing gaps comparable to the Fermi energy which in this sense are the largest in the laboratory and in nature, respectively. This strong pairing regime, or the crossover between BCS and BEC regimes, requires non-perturbative treatments. We describe Quantum Monte Carlo results useful to understand the properties of these systems, including infinite homogeneous matter and trapped inhomogeneous gases.Comment: 14 pages, 4 figures; chapter in "50 Years of Nuclear BCS", edited by R. A. Broglia and V. Zelevinsk

Quantum Monte Carlo calculations of neutron matter with chiral three-body forces

Chiral effective field theory (EFT) enables a systematic description of low-energy hadronic interactions with controlled theoretical uncertainties. For strongly interacting systems, quantum Monte Carlo (QMC) methods provide some of the most accurate solutions, but they require as input local potentials. We have recently constructed local chiral nucleon-nucleon (NN) interactions up to next-to-next-to-leading order (N$^2$LO). Chiral EFT naturally predicts consistent many-body forces. In this paper, we consider the leading chiral three-nucleon (3N) interactions in local form. These are included in auxiliary field diffusion Monte Carlo (AFDMC) simulations. We present results for the equation of state of neutron matter and for the energies and radii of neutron drops. In particular, we study the regulator dependence at the Hartree-Fock level and in AFDMC and find that present local regulators lead to less repulsion from 3N forces compared to the usual nonlocal regulators.Comment: 10 pages, 8 figures, 1 table, published versio

Contact interaction in an unitary ultracold Fermi gas

An ultracold Fermi atomic gas at unitarity presents universal properties that in the diluted limit can be well described by a contact interaction. By employing a guide function with correct boundary conditions and making simple modifications to the sampling procedure we are able to handle for the first time a true contact interaction in a quantum Monte Carlo calculation. The results are obtained with small variances. Our calculations for the Bertsch and contact parameters are in excellent agreement with published experiments. The possibility of using a more faithfully description of ultracold atomic gases can help uncover features yet unknown of the ultracold atomic gases. In addition, this work paves the way to perform quantum Monte Carlo calculations for systems interacting with contact interactions, where in many cases the description using potentials with finite effective range might not be accurate

The equation of state of neutron matter, symmetry energy, and neutron star structure

We review the calculation of the equation of state of pure neutron matter using quantum Monte Carlo (QMC) methods. QMC algorithms permit the study of many-body nuclear systems using realistic two- and three-body forces in a nonperturbative framework. We present the results for the equation of state of neutron matter, and focus on the role of three-neutron forces at supranuclear density. We discuss the correlation between the symmetry energy, the neutron star radius and the symmetry energy. We also combine QMC and theoretical models of the three-nucleon interactions, and recent neutron star observations to constrain the value of the symmetry energy and its density dependence.Comment: 11 pages, 11 figure

Equation of state of superfluid neutron matter and the calculation of 1S0^1S_0 pairing gap

We present a Quantum Monte Carlo study of the zero temperature equation of state of neutron matter and the computation of the $^1S_0$ pairing gap in the low-density regime with $\rho<0.04$ fm$^{-3}$. The system is described by a non-relativistic nuclear Hamiltonian including both two-- and three--nucleon interactions of the Argonne and Urbana type. This model interaction provides very accurate results in the calculation of the binding energy of light nuclei. A suppression of the gap with respect to the pure BCS theory is found, but sensibly weaker than in other works that attempt to include polarization effects in an approximate way

Quantum Monte Carlo Calculations of Light Nuclei Using Chiral Potentials

We present the first Green's function Monte Carlo calculations of light nuclei with nuclear interactions derived from chiral effective field theory up to next-to-next-to-leading order. Up to this order, the interactions can be constructed in a local form and are therefore amenable to quantum Monte Carlo calculations. We demonstrate a systematic improvement with each order for the binding energies of $A=3$ and $A=4$ systems. We also carry out the first few-body tests to study perturbative expansions of chiral potentials at different orders, finding that higher-order corrections are more perturbative for softer interactions. Our results confirm the necessity of a three-body force for correct reproduction of experimental binding energies and radii, and pave the way for studying few- and many-nucleon systems using quantum Monte Carlo methods with chiral interactions.Comment: 5 pages, 3 figures, 4 tables. Updated references. Cosmetic changes to figures, tables, and equations; added a sentence clarifying the correspondence between our real-space cutoffs and momentum-space cutoffs. Other sentences were reworded for clarit