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First order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna (LISA). All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid $^3$He an ideal for test of classical nucleation theory. As Leggett and others have noted the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave (GW) production in the early universe. Here we discuss studies of the AB phase transition dynamics in $^3$He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases., Comment: 34 pp, 4 figures. Based on a talk given at Quantum Fluids and Solids 2023, Manchester, U.K, on behalf of the QUEST-DMC collaboration

Fabrication of superconducting nanomechanical resonators for quantum research, detectors and devices traditionally relies on a lithographic process, resulting in oscillators with sharp edges and a suspended length limited to a few 100 micrometres. We report a low-investment top-down approach to fabricating NbTi nanowire resonators with suspended lengths up to several millimetres and diameters down to 100 nanometres. The nanowires possess high critical currents and fields, making them a natural choice for magnetomotive actuation and sensing. This fabrication technique is independent of the substrate material, dimensions and layout and can readily be adapted to fabricate nanowire resonators from any metal or alloy with suitable ductility and yield strength. Our work thus opens access to a new class of nanomechanical devices with applications including microscopic and mesoscopic investigations of quantum fluids, detecting dark matter and fundamental materials research in one-dimensional superconductors in vacuum., Comment: 19 pages, 4 figures

Because of the extreme purity, lack of disorder, and complex order parameter, the first-order superfluid $^3$He A-B transition is the leading model system for first order transitions in the early universe. Here we report on the path dependence of the supercooling of the A phase over a wide range of pressures below 29.3 bar at nearly zero magnetic field. The A phase can be cooled significantly below the thermodynamic A-B transition temperature. While the extent of supercooling is highly reproducible, it depends strongly upon the cooling trajectory: The metastability of the A phase is enhanced by transiting through regions where the A phase is more stable. We provide evidence that some of the additional supercooling is due to the elimination of B phase seeds formed upon passage through the superfluid transition. A greater understanding of the physics is essential before the $^3$He can be exploited to model transitions in the early universe., Comment: 6 Figures

The composited cosmological defects in superfluids of nafen-disorded 3He are discussed in this review article. In spite of the existence of the half quantum vortices (Alice strings), more novel composited cosmological defects such as Nambu monople, Kibble-Lazarides-Shafi (KLS) string wall, and nexus objects appear in this system in the two-step successive symmetry breaking phase transition. To reveal them, we analyzed symmetry breaking patterns in detail by using the algebraic topology and group theory. It turns out that the fibrations of the degenerate parameter spaces of symmetry breaking patterns dominate the existence of composite cosmological defects in the successive symmetry breaking of nafen-distorted 3He. To compare our model with ROTA's experiment of string wall, we demonstrate how the KLS string wall extend to 1D nexus in equilibrium states. The equilibrium free energies, which determines the configurations 1D nexus, are evaluated by non-linear numerical optimization algorithm. Based on these equilibrium configurations, we calculated the spectrum of spin dynamical response of system under weak magnetic driving. The results exactly coincide with the experimental observations., Comment: Review Artile. arXiv admin note: substantial text overlap with arXiv:2008.09286, arXiv:2002.07578

In this paper we analytically investigate the ground-state properties of a two-dimensional polarized degenerate Fermi gas in a high-finesse optical cavity, which is governed by a generalized Fermi-Dicke model with tunable parameters. By solving the photon-number dependent Bogoliubov-de-Gennes equation, we find rich quantum phases and phase diagrams, which depend crucially on the fermion-photon coupling strength, the fermion-fermion interaction strength, and the atomic resonant frequency (effective Zeeman field). In particular, without the fermion-fermion interaction and with a weak atomic resonant frequency, we find a mixed phase that the normal phase with two Fermi surfaces and the superradiant phase coexist, and reveal a first-order phase transition from this normal phase to the superradiant phase. With the intermediate fermion-fermion interaction and fermion-photon coupling strengths, we predict another mixed phase that the superfluid and superradiant phases coexist. Finally, we address briefly how to detect these predicted quantum phases and phase diagrams in experiments., Comment: 20 pages,10 figures

The type-II Weyl and type-II Dirac points emerge in semimetals and also in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. In this case the horizon with Painleve-Gullstrand metric serves as the surface of the Lifshitz transition. This relativistic analogy allows us to simulate the black hole horizon and Hawking radiation using the fermionic superfluid with supercritical velocity, and the Dirac and Weyl semimetals with the interface separating the type-I and type-II states. The difference between such type of the artificial event horizon and that which arises in acoustic metric is discussed. At the Lifshitz transition between type-I and type-II fermions the Dirac lines may also emerge, which are supported by the combined action of topology and symmetry. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. Different configurations of the Fermi surfaces, involved in such Lifshitz transition, are discussed. In one case the type-II Weyl point connects the Fermi pockets, and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition the Weyl point is released from both Fermi surfaces. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds. For the interacting electrons, the Lifshitz transitions may lead to the formation of the dispersionless (flat) band with zero energy and singular density of states, which opens the route to room-temperature superconductivity., Comment: 18 pages, 8 figures, title changed, prepared for proceeding of ECT workshop "Superfluidity and pairing phenomena"

Motivated by recent experimental development, we investigate spin-orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the density-matrix renormalization group method, we calculate momentum distribution function, gap, and spin-correlation function to reveal rich ground-state properties. We find that spin-orbit coupling (SOC) can generate unconventional momentum distribution, which depends crucially on the filling. We call the corresponding phase with zero gap the SOC-induced metallic phase. We also show that SOC can drive the system from the antiferromagnetic to ferromagnetic Mott insulators with spin rotating. As a result, a second-order quantum phase transition between the spin-rotating ferromagnetic Mott insulator and the SOC-induced metallic phase is predicted at the strong SOC. Here the spin rotating means that the spin orientations of the nearest-neighbor sites are not parallel or antiparallel, i.e., they have an intersection angle $\theta \in (0,\pi )$. Finally, we show that the momentum $k_{\mathrm{peak}}$, at which peak of the spin-structure factor appears, can also be affected dramatically by SOC. The analytical expression of this momentum with respect to the SOC strength is also derived. It suggests that the predicted spin-rotating ferromagnetic ($k_{\mathrm{peak}% }<\pi /2$) and antiferromagnetic ($\pi /2

The non-Abelian gauge fields play a key role in achieving novel quantum phenomena in condensed-matter and high-energy physics. Recently, the synthetic non-Abelian gauge fields have been created in the neutral degenerate Fermi gases, and moreover, generate many exotic effects. All the previous predictions can be well understood by the microscopic Bardeen-Cooper-Schrieffer theory. In this work, we establish an SU(2) Ginzburg-Landau theory for degenerate Fermi gases with the synthetic non-Abelian gauge fields. We firstly address a fundamental problem how the non-Abelian gauge fields, imposing originally on the Fermi atoms, affect the pairing field with no extra electric charge by a local gauge-field theory,and then obtain the first and second SU(2) Ginzburg-Landau equations. Based on these obtained SU(2) Ginzburg-Landau equations, we find that the superfluid critical temperature of the intra- (inter-) band pairing increases (decreases) linearly, when increasing the strength of the synthetic non-Abelian gauge fields. More importantly, we predict a novel SU(2) non-Abelian Josephson effect, which can be used to design a new atomic superconducting quantum interference device., Comment: 9 pages, 2 figures

Understanding novel pairings in attractive degenerate Fermi gases is crucial for exploring rich superfluid physics. In this report, we reveal unconventional pairings induced by spin-orbit coupling (SOC) in a one-dimensional optical lattice, using a state-of-the-art density-matrix renormalization group method. When both bands are partially occupied, we find a strong competition between the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings. In particular, for the weak and moderate SOC strengths, these two pairings can coexist, giving rise to a new phase called the FFLO-BCS phase, which exhibits a unique three-peak structure in pairing momentum distribution. For the strong SOC strength, the intraband BCS pairing always dominates in the whole parameter regime, including the half filling. We figure out the whole phase diagrams as functions of filling factor, SOC strength, and Zeeman field. Our results are qualitatively different from recent mean-field predictions. Finally, we address that our predictions could be observed in a weaker trapped potential., Comment: 16 Pages, 13 Figures

In this paper we explore the spin-orbit-induced bound state and molecular signature of the degenerate Fermi gas in a narrow Feshbach resonance based on a generalized two-channel model. Without the atom-atom interactions, only one bound state can be found even if spin-orbit coupling exists. Moreover, the corresponding bound-state energy depends strongly on the strength of spin-orbit coupling, but is influenced slightly by its type. In addition, we find that when increasing the strength of spin-orbit coupling, the critical point at which the molecular fraction vanishes shifts from zero to the negative detuning. In the weak spin-orbit coupling, this shifting is proportional to the square of its strength. Finally, we also show that the molecular fraction can be well controlled by spin-orbit coupling., Comment: Major modification