Abstract Superfluid dilute neutron matter and ultracold gas, close to the unitary regime, exhibit several similarities. Therefore, to a certain extent, fermionic ultracold gases may serve as emulators of dilute neutron matter, which forms the inner crust of neutron stars and is not directly accessed experimentally. Quantum vortices are one of the most significant properties of neutron superfluid, essential for comprehending neutron stars’ dynamics. The structure and dynamics of quantum vortices as a function of pairing correlations’ strength are being investigated experimentally and theoretically in ultracold gases. Certain aspects of these studies are relevant to neutron stars. We provide an overview of the characteristics of quantum vortices in s-wave-type fermionic and electrically neutral superfluids. The main focus is on the dynamics of fermionic vortices and their intrinsic structure.
Abstract Superfluid dilute neutron matter and ultracold gas, close to the unitary regime, exhibit several similarities. Therefore, to a certain extent, fermionic ultracold gases may serve as emulators of dilute neutron matter, which forms the inner crust of neutron stars and is not directly accessed experimentally. Quantum vortices are one of the most significant properties of neutron superfluid, essential for comprehending neutron stars’ dynamics. The structure and dynamics of quantum vortices as a function of pairing correlations’ strength are being investigated experimentally and theoretically in ultracold gases. Certain aspects of these studies are relevant to neutron stars. We provide an overview of the characteristics of quantum vortices in s-wave-type fermionic and electrically neutral superfluids. The main focus is on the dynamics of fermionic vortices and their intrinsic structure.
Abstract Fermionic superfluids provide a new realization of quantum turbulence, accessible to both experiment and theory, yet relevant to phenomena from both cold atoms to nuclear astrophysics. In particular, the strongly interacting Fermi gas realized in cold-atom experiments is closely related to dilute neutron matter in neutron star crusts. Unlike the liquid superfluids 4 He (bosons) and 3 He (fermions), where quantum turbulence has been studied in laboratory for decades, superfluid Fermi gases stand apart for a number of reasons. They admit a rather reliable theoretical description based on density functional theory called the time-dependent superfluid local density approximation that describes both static and dynamic phenomena. Cold atom experiments demonstrate exquisite control over particle number, spin polarization, density, temperature, and interaction strength. Topological defects such as domain walls and quantized vortices, which lie at the heart of quantum turbulence, can be created and manipulated with time-dependent external potentials, and agree with the time-dependent theoretical techniques. While similar experimental and theoretical control exists for weakly interacting Bose gases, the unitary Fermi gas is strongly interacting. The resulting vortex line density is extremely high, and quantum turbulence may thus be realized in small systems where classical turbulence is suppressed. Fermi gases also permit the study of exotic superfluid phenomena such as the Larkin–Ovchinnikov–Fulde–Ferrell pairing mechanism for polarized superfluids which may give rise to 3D supersolids, and a pseudo-gap at finite temperatures that might affect the regime of classical turbulence. The dynamics associated with these phenomena has only started to be explored. Finally, superfluid mixtures have recently been realized, providing experimental access to phenomena like Andreev–Bashkin entrainment predicted decades ago. Superfluid Fermi gases thus provide a rich forum for addressing phenomena related to quantum turbulence with applications ranging from terrestrial superfluidity to astrophysical dynamics in neutron stars.
We investigate the Bose-Einstein condensation of fermionic pairs in three different superfluid systems: ultracold and dilute atomic gases, bulk neutron matter, and neutron stars. In the case of dilute gases made of fermionic atoms the average distance between atoms is much larger than the effective radius of the inter-atomic potential. Here the condensation of fermionic pairs is analyzed as a function of the s-wave scattering length, which can be tuned in experiments by using the technique of Feshbach resonances from a small and negative value (corresponding to the Bardeen-Cooper-Schrieffer (BCS) regime of Cooper Fermi pairs) to a small and positive value (corresponding to the regime of the Bose-Einstein condensate (BEC) of molecular dimers), crossing the unitarity regime where the scattering length diverges. In the case of bulk neutron matter the s-wave scattering length of neutron-neutron potential is negative but fixed, and the condensate fraction of neutron-neutron pairs is studied as a function of the total neutron density. Our results clearly show a BCS-quasiunitary-BCS crossover by increasing the neutron density. Finally, in the case of neutron stars, where again the neutron-neutron scattering length is negative and fixed, we determine the condensate fraction as a function of the distance from the center of the neutron star, finding that the maximum condensate fraction appears in the crust of the neutron star.
Abstract From flow without dissipation of energy to the formation of vortices when placed within a rotating container, the superfluid state of matter has proven to be a very interesting physical phenomenon. Here we present the key mechanisms behind superfluidity in fermionic systems and apply our understanding to one of the most exotic systems in the universe: the superfluid interior of a neutron star. The extreme conditions of neutron stars prevent us from directly probing the internal superfluid properties, however, we can experimentally realize conditions resembling the interior through the use of cold atoms prepared in a laboratory and simulated on a computer. Key insights can be gained by simulating the neutron star superfluid using another system with analogous properties: a cold atomic Fermi gas. Computational physicists are leveraging the power of supercomputers to simulate interacting atomic systems with unprecedented accuracy. In this paper we provide a pedagogical introduction to the physics, guiding the reader through the major conceptual steps to understand the relation between cold atoms, superfluids, and neutron stars. We stress the surprising similarity between these systems, which stems from universality, a fundamental notion in many-body physics. These topics are available in advanced textbooks, but introductory materials are harder to come by; this paper is intended to fill the gap for curious undergraduate and graduate students. We will show how cold atoms can help us make significant strides towards understanding the exotic physics found deep within the universe.
In cold atoms and in the crust of neutron stars, the pairing gap can reach values comparable with the Fermi energy. While in nuclei the neutron gap is smaller, it is still of the order of a few percent of the Fermi energy. The pairing mechanism in these systems is due to short range attractive interactions between fermions and the size of the Cooper pair is either comparable to the inter‐particle separation or it can be as big as a nucleus, which is still relatively small in size. Such a strong pairing gap is the result of the superposition of a very large number of particle–particle configurations, which contribute to the formation of the Cooper pairs. These systems have been shown to be the host of a large number of remarkable phenomena, in which the large magnitude of the pairing gap plays an essential role: quantum shock waves, quantum turbulence, Anderson–Bogoliubov–Higgs mode, vortex rings, domain walls, soliton vortices, vortex pinning in neutron star crust, unexpected dynamics of fragmented condensates and role of pairing correlations in collisions on heavy‐ions, Larkin–Ovchinnikov phase as an example of a Fermi supersolid, role of pairing correlations in controlling the dynamics of fissioning nuclei.
Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction (6Li), we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by BardeenCooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are quantitatively measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.
Low-density neutron matter has been studied extensively for many decades, with a view to better understanding the properties of neutron-star crusts and neutron-rich nuclei. Neutron matter is beyond experimental control, but in the past decade it has become possible to create systems of fermionic ultracold atomic gases in a regime close to low-density neutron matter. In both these contexts pairing is significant, making simple perturbative approaches impossible to apply and necessitating ab initio microscopic simulations. Atomic experiments have also probed polarized matter. In this work, we study population-imbalanced neutron matter (possibly relevant to magnetars and to density functionals of nuclei) arriving at the lowest-energy configuration to date. For small-to-intermediate relative fractions, the system turns out to be fully normal, while beyond a critical polarization we find phase coexistence between a partially polarized normal neutron gas and a balanced superfluid gas. As in cold atoms, a homogeneous polarized superfluid is close to stability but not stable with respect to phase separation. We also study the dependence of the critical polarization on the density.