Evidence for Multimodal Superfluidity of Neutrons

Abstract

We present theoretical and experimental evidence for a new phase of matter in neutron-rich systems that we call multimodal superfluidity. Using ab initio lattice calculations, we show that the condensate consists of coexisting s-wave pairs, p-wave pairs in entangled double pair combinations, and quartets composed of bound states of two s-wave pairs. We identify multimodal superfluidity as a general feature of single-flavor spin-1/2 fermionic systems with attractive s-wave and p-wave interactions, provided the system is stable against collapse into a dense droplet. Beyond neutrons at sub-saturation densities, we demonstrate that this phase appears in generalized attractive extended Hubbard models in one, two, and three dimensions. We elucidate the mechanism for this coexistence using self-consistent few-body Cooper models and compare with Bardeen-Cooper-Schrieffer theory. We also derive the form of the effective action and show that spin, rotational, and parity symmetries remain unbroken. Finally, we analyze experimental data to show that p-wave pair gaps and quartet gaps are present in atomic nuclei, and we discuss the consequences of this new phase for the structure and dynamics of neutron star crusts.

Figures (37)

• Figure 1: Momentum-space distributions for the 3D GAE Hubbard model.Ab initio lattice results for an $L^3=10^3$, $A=66$ system with coupling $c=-1.6\times 10^{-6}$ MeV$^{-2}$, local smearing strength $s_{\text{L}}=0.5$, non-local smearing strength $s_{\text{NL}}=0.1$ and Euclidean time $\tau=1.67$ MeV$^{-1}$. The vertical dashed lines indicate the Fermi momentum $k_F$. a: One-body momentum occupation number as function of momentum $k$. b: S-wave pair probability distribution as a function of momentum. c: P-wave pair probability distribution. d: Quartet probability distribution.
• Figure 2: Schematic diagrams for multimodal superfluidity.a: Illustration of an s-wave pair, p-wave pair, and quartet composed of two s-wave pairs bound together. b: The quantum phase diagram for a spin-1/2 fermionic system at zero temperature for different s-wave and p-wave interactions. The diagram is only schematic, and the locations of the phase boundaries will depend on the details of the system.
• Figure 3: Momentum-space distributions for realistic neutron matterAb initio lattice results for at density $\rho = 0.033$ fm$^{-3}$ obtain using high-fidelity chiral N$^3$LO interactions and Euclidean time $\tau=0.2$ MeV$^{-1}$. The legend labels indicate the pairing channels with their corresponding cubic representations: $^1S_0$ ($A_1^+$), $^3P_0$ ($A_1^-$), $^3P_1$ ($T_1^-$), $^3P_2$ ($T_2^-$,$E^-$). The numerical values indicate the total numbers of pairs or quartets counted in the corresponding momentum distributions. As described in Methods, some additional steps are needed to properly count the actual number of quartets. The vertical dashed line indicates the Fermi momentum $k_F$. a: S-wave pair distribution as a function of momentum $k$. b: P-wave pair probability distribution as a function of momentum. c: Quartet probability distribution.
• Figure S1: S-wave momentum distribution: rank-one vs pinhole methods. Momentum-space s-wave pair occupation for an $L^3 = 4^3$, $A = 8$ system at Euclidean time $\tau=2.0$ MeV$^{-1}$ using the self-consistent Cooper-model dispersion relation. Results are obtained with two measurement methods. Left: rank-one operator method. Right: momentum pinhole method.
• Figure S2: Momentum-space pairing and quartet distributions for $A=8$.Ab initio lattice results for an $L^3 = 8^3$, $A = 8$ system using the self-consistent Cooper-model dispersion relation. From left to right, the panels show the momentum distribution of s-wave pairing, p-wave pairing and quartets.