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We theoretically investigate non-Hermitian $p$-wave Fermi superfluidity in one-dimensional spin-polarized Fermi gases which is relevant to recent ultracold atomic experiments. Considering an imaginary atom-dimer coupling responsible for the three-body recombination process in the Lindblad formalism, we discuss the stability of the superfluid state against the atomic loss effect. Within the two-channel non-Hermitian BCS-Leggett theory, the atomic loss is characterized by the product of the imaginary atom-dimer coupling and the $p$-wave effective range. Our results indicate that for a given imaginary atom-dimer coupling, a smaller magnitude of the effective ranges of $p$-wave interaction is crucial for reaching the non-Hermitian $p$-wave Fermi superfluid state., Comment: 9 pages, 3 figures

We investigate thermomagnetic transport in an ultracold atomic system with two ferromagnets linked via a magnetic quantum point contact. Using nonequilibrium Green's function approach, we show a divergence in spin conductance and a slowing down of spin relaxation that manifest in the weak effective-Zeeman-field limit. These anomalous spin dynamics result from the magnonic critical point at which magnons become gapless due to spontaneous magnetization. Our findings unveil untapped dynamics in ultracold atomic systems, opening new avenues in thermomagnetism., Comment: 16 pages, 6 figures

We explore the theoretical possibility of $^3P_0$ neutron superfluid in dilute spin-polarized neutron matter, which may be relevant to the crust region of a magnetized neutron star. In such a dilute regime where the neutron Fermi energy is less than 1 MeV, the $^1S_0$ neutron superfluid can be suppressed by a strong magnetic field of the compact star. In the low-energy limit relevant for dilute neutron matter, the $^3P_0$ interaction is stronger than the $^3P_2$ one which is believed to induce the triplet superfluid in the core. We present the ground-state phase diagram of dilute neutron matter with respect to the magnetic field and numerically estimate the critical temperature of the $^3P_0$ neutron superfluid, which is found to exceed $10^7$ K., Comment: 7 pages, 3 figures

We investigate the spectrum of spin conductivity for a miscible two-component Bose-Einstein condensate (BEC) that exhibits spin superfluidity. By using the Bogoliubov theory, the regular part being the spin conductivity at finite ac frequency and the spin Drude weight characterizing the delta-function peak at zero frequency are analytically computed. We demonstrate that the spectrum exhibits a power-law behavior at low frequency, reflecting gapless density and spin modes specific to the binary BEC. At the phase transition points into immiscible and quantum-droplet states, the change in quasiparticle dispersion relations modifies the power law. In addition, the spin Drude weight becomes finite, indicating zero spin resistivity due to spin superfluidity. Our results also suggest that the Andreev-Bashkin drag density is accessible by measuring the spin conductivity spectrum., Comment: 13 pages, 4 figures

We theoretically discuss the non-Hermitian superfluid phase transition in one-dimensional two-component Fermi gases near the $p$-wave Feshbach resonance accompanied by the two-body loss associated with the dipolar relaxation. For the first time we point out that this system gives us an opportunity to explore the interplay among various non-trivial properties such as universal thermodynamics at divergent $p$-wave scattering length, topological phase transition at vanishing chemical potential, and non-Hermitian Bardeen-Cooper-Schrieffer(BCS) to Bose-Einstein condensate (BEC) transition, in a unified manner. In the BCS phase, the loss-induced superfluid-normal transition occurs when the exceptional point appears in the effective non-Hermitian Hamiltonian. In the BEC phase, the diffusive gapless mode can be regarded as a precursor of the instability of the superfluid state. Moreover, we show that the superfluid state is fragile against the two-body loss near the topological phase transition point., Comment: 7 pages, 5 figures

We theoretically propose the laser-induced Andreev reflection between two-component Fermi superfluid and normal states via spatially-uniform Rabi couplings. By analyzing the tunneling current between the superfluid and normal states up to the fourth order in the Rabi couplings, we find that the Andreev current exhibits unconventional non-Ohmic transport at zero temperature. Remarkably, the Andreev current gives the only contribution in the synthetic junction system at zero detunings regardless of the ratio of the chemical potential bias to the superfluid gap, which is in sharp contrast to that in the conventional superconductor-normal metal junction. Our result may also pave a way for understanding the black hole information paradox through the Andreev reflection as a quantum-information mirror., Comment: 7 pages, 5 figures

We theoretically investigate optical (frequency-dependent) bulk spin transport properties in a spin-1/2 topological Fermi superfluid. We specifically consider a one-dimensional system with an interspin {\it p}-wave interaction, which can be realized in ultracold atom experiments. Developing the BCS-Leggett theory to describe the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) evolution and the $\mathbb{Z}_2$ topological phase transition in this system, we show how the spin transport reflects these many-body aspects. We find that the optical spin conductivity, which is a small AC response of a spin current, shows the spin gapped spectrum in the wide parameter region and the gap closes at $\mathbb{Z}_2$ topological phase transition point. Moreover, the validity of the low-energy effective model of the Majorana zero mode is discussed along the BCS-BEC evolution in connection with the scale invariance at {\it p}-wave unitarity., Comment: 10 pages, 5 figures, accepted version for publication in Phys. Rev. B

We show that the optical spin conductivity being a small AC response of a bulk spin current and elusive in condensed matter systems can be measured in ultracold atoms. We demonstrate that this conductivity contains rich information on quantum states by analyzing experimentally achievable systems such as a spin-1/2 superfluid Fermi gas, a spin-1 Bose-Einstein condensate, and a Tomonaga-Luttinger liquid. The obtained conductivity spectra being absent in the Drude conductivity reflect quasiparticle excitations and non-Fermi liquid properties. Accessible physical quantities include the superfluid gap and the contact for the superfluid Fermi gas, gapped and gapless spin excitations as well as quantum depletion for the Bose-Einstein condensate, and the spin part of the Tomonaga-Luttinger liquid parameter elusive in cold-atom experiments. Unlike its mass transport counterpart, the spin conductivity serves as a probe applicable to clean atomic gases without disorder and lattice potentials. Our formalism can be generalized to various systems such as spin-orbit coupled and nonequilibrium systems., Comment: 17 pages, 3 figures; published version

We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which are closely connected with each other by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosons includes only a two-body interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-body coupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of the sum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in the sense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed., Comment: 18 pages, 8 figures; published version

We investigate a mesoscopic spin current for strongly interacting Fermi gases through a quantum point contact. Under the situation where spin polarizations in left and right reservoirs are same in magnitude but opposite in sign, we calculate the contribution of quasiparticles to the current by means of the linear response theory and many-body $T$-matrix approximation. For a small spin-bias regime, the current in the vicinity of the superfluid transition temperature is strongly suppressed due to the formation of pseudogaps. For a large spin-bias regime where the gases become highly polarized, on the other hand, the current is affected by the enhancement of a minority density of states due to Fermi polarons. We also discuss the broadening of a quasiparticle peak associated with an attractive polaron at a large momentum, which is relevant to the enhancement., Comment: 12 pages, 12 figures

Ultracold atoms offer valuable opportunities where interparticle interactions can be controlled at will. In particular, by extinguishing the two-body interaction, one can realize unique systems governed by the three-body interaction, which is otherwise hidden behind the two-body interaction. Here we study one-dimensional bosons with a weak three-body attraction and show that they form few-body bound states as well as a many-body droplet stabilized by the quantum mechanical effect. Their binding energies relative to that of three bosons are all universal and the ground-state energy of the dilute droplet is found to grow exponentially as $E_N/E_3\to\exp(8N^2/\sqrt3\pi)$ with increasing particle number $N\gg1$. The realization of our system with coupled two-component bosons in an optical lattice is also discussed., Comment: 5 pages; published version

One-dimensional spinless Bose and Fermi gases with contact interactions have the close interrelation via Girardeau's Bose-Fermi mapping, leading to the correspondences in their energy spectra and thermodynamics. However, correlation functions are in general not identical between these systems. We derive in both systems the exact universal relations for correlation functions, which hold for any energy eigenstate and any statistical ensemble of the eigenstates with or without a trapping potential. These relations include the large-momentum behaviors of static structure factors and of momentum distributions as well as energy relations, which connect the sums of kinetic and interaction energies to the momentum distributions. The relations involve two- and three-body contacts, which are the integrals of local pair and triad correlations, respectively. We clarify how the relations for bosons and fermions differ and are connected with each other. In particular, we find that the three-body contact makes no contribution to the bosonic energy relation, but it plays a crucial role in the fermionic one. In addition, we compute the exact momentum distribution for any number of fermions in the unitary limit., Comment: 8 pages, no figure; published version