Three-dimensional spin–orbit coupled Fermi gases:Fulde–Ferrell pairing, Majorana fermions, Weyl fermions,and gapless topological superfluidity

We theoretically investigate a three-dimensional Fermi gas with Rashba spin-orbit coupling in the presence of both out-of-plane and in-plane Zeeman fields. We show that, driven by a sufficiently large Zeeman field, either out-of-plane or in-plane, the superfluid phase of this system exhibits a number of interesting features, including inhomogeneous Fulde- Ferrell pairing, gapped or gapless topological order, and exotic quasi-particle excitations known as Weyl fermions that have linear energy dispersions in momentum space （i.e., massless Dirac fermions）. The topological superfluid phase can have either four or two topologically protected Weyl nodes. We present the phase diagrams at both zero and finite temperatures and discuss the possibility of their observation in an atomic Fermi gas with synthetic spin-orbit coupling. In this context, topological superfluid phase with an imperfect Rashba spin-orbit coupling is also studied.

ADS Injector-I 2 K superfluid helium cryogenic system

The Accelerator Driven Sub-critical(ADS)system is a strategic plan to solve the nuclear waste problem for nuclear power plants in China.High-energy particle accelerators and colliders contain long strings of superconducting devices,superconducting radio frequency cavities,and magnets,which may require cooling by 2 K superfluid helium(HeliumⅡ).2 K superfluid helium cryogenic system has become a research hot spot in the field of superconducting accelerators.In this study,the ADS Injector-I 2 K cryogenic system is examined in detail.The cryogenic system scheme design,key equipment,and technology design,such as the 2 K Joule–Thomson(J–T)heat exchanger and cryomodules CM1+CM2 design,are examined,in addition to the commissioning and operation of the cryogenic system.The ADS Injector-I 2 K cryogenic system is the first 100 W superfluid helium system designed and built independently in China.The ADS proton beam reached 10 Me V at 10 m A in July 2016 and 10 Me V at 2 m A in continuous mode in January 2017 and has been operated reliably for over 15,000 h,proving that the design of ADS Injector-I 2 K cryogenic system,the key equipment,and technology research are reasonable,reliable,and meet the requirements.The research into key technologies provides valuable engineering experience that can be helpful for future projects such as CI-ADS(China Initiative Accelerator-Driven System),SHINE(Shanghai High Repetition Rate XFEL and Extreme Light Facility),PAPS(Platform of Advanced Photon Source Technology),and CEPC(Circular Electron-Positron Collider),thereby developing national expertise in the field of superfluid helium cryogenic systems.

How Massive Are the Superfluid Cores in the Crab and Vela Pulsars and Why Their Glitch-Events Are Accompanied with under and Overshootings?

The Crab and Vela are well-studied glitching pulsars and the data obtained so far should enable us to test the reliability of models of their internal structures. Very recently it was proposed that glitching pulsars are embedded in bimetric spacetime: their incompressible superfluid cores (SuSu-cores) are embedded in flat spacetime, whereas the ambient compressible and dissipative media are enclosed in Schwarzschild spacetime. In this letter we apply this model to the Crab and Vela pulsars and show that a newly born pulsar initially of and an embryonic SuSu-core of could evolve into a Crab-like pulsar after 1000 years and into a Vela-like pulsar 10,000 years later to finally fade away as an invisible dark energy object after roughly 10 Myr. Based thereon we infer that the Crab and the Vela pulsars should have SuSu-cores of and , respectively. Furthermore, the under- and overshootings phenomena observed to accompany the glitch events of the Vela pulsar are rather a common phenomenon of glitching pulsars that can be well-explained within the framework of bimetric spacetime.

Tunneling dynamics of superfluid Fermi gas in a triple-well potential

The tunneling dynamics of superfluid Fermi gas in a triple-well potential in the unitarity regime is investigated in the present paper. The fixed points of the （0,0） mode and the （π, π） mode are given. We find that the interaction parameter U and the coupling strength k could have an extreme effect on the quantum tunneling dynamics. We also find that, in the zero mode, only Josophson oscillation appears. However, for the mode, the trapping phenomena take place. An irregular oscillation of the particle number in each well could appear by adjusting the scanning period T. It is noted that if the scanning period is less than a critical point T＊, the particle number will come back to the fixed point with small oscillation, while if T 〉 T＊ the particle number cannot come back to the fixed point, but with irregular oscillations. The dependence of the critical point T＊ on the system parameter of coupling strength k is numerically given.

Superfluidity of Bose Einstein condensates in ultracold atomic gases

Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose-Einstein condensate （BEC）, offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin--orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spinorbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross-Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.

Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional （2D） polarized Fermi gas with spin-orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin-orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen-Cooper-Schrieffer （BCS） mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin-orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here, we focus on the region of BCS pairing and ignore the Fulde-Ferrell-Larkin-Ovchinnikov state.

On the role of the uncertainty principle in superconductivity and superfluidity

We discuss the general interplay between the uncertainty principle and the onset of dissipationless transport phenomena such as superconductivity and superfluidity. We argue that these phenomena are possible because of the robustness of many-body quantum states with respect to the external environment, which is directly related to the uncertainty principle as applied to coordinates and momenta of the carriers. In the case of superconductors, this implies relationships between macroscopic quantities such as critical temperature and critical magnetic field, and microscopic quantities such as the amount of spatial squeezing of a Cooper pair and its correlation time. In the case of ultracold atomic Fermi gases, this should be paralleled by a connection between the critical temperature for the onset of superfluidity and the corresponding critical velocity. Tests of this conjecture are finally sketched with particular regard to the understanding of the behaviour of superconductors under external pressures or mesoscopic superconductors, and the possibility to mimic these effects in ultracold atomic Fermi gases using Feshbach resonances and atomic squeezed states.

^3PF2 neutron superfluidity in neutron stars and three-body force effect

We investigate the ^3PF2 neutron superfluidity in H-stable neutron star matter and neutron stars by using the BCS theory and the Brueckner-Hartree-Fock approach. We adopt the Argonne V18 potential supplemented with a microscopic three-body force as the realistic nucleon-nucleon interaction. We have concentrated on studying the threebody force effect on the ^3PF2 neutron pairing gap. It is found that the three-body force effect is to enhance remarkably the ^3PF2 neutron superfluidity in neutron star matter and neutron stars.

Superfluidity of coherent light in self-focusing nonlinear waveguides

We establish the superfluidity theory of coherent light in waveguides made of nonlinear polar crystals.It is found that the pairing state of photons in a nonlinear polar crystal is the photonic superfluid state.The photon-photon interaction potential is an attractive effective interaction by exchange of virtual optical phonons.In the traveling-wave pairing state of photons,the photon number is conserved,which is similar to the Bose-Einstein condensation（BEC） state of photons.In analogy to the BCS-BEC crossover theory of superconductivity,we derive a set of coupled order parameter and number equations,which determine the solution of the traveling-wave superfluid state of photons.This solution gives the critical velocity of light in a self-focusing nonlinear waveguide.The most important property of the photonic superfluid state is that the system of photon pairs evolves without scattering attenuations.

A space-dependent atomic superfluid current in Bose–Einstein condensates

A space-dependent atomic superfluid current with an explicit analytical expression and its role in Bose-Einstein condensates are studied. The factors determining the intensity and oscillating amplitude of the space-dependent atomic superfluid current are explored in detail. Research findings reveal that the intensity of the current can be regulated by setting an appropriate configuration of the trap and its oscillating amplitude can be adjusted via Feshbach resonance. It is numerically demonstrated that the space-dependent atomic superfluid current can exert great influence on the spatial distribution of condensed atoms, and even force condensed atoms into very complex distributional states with spatial chaos.

Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases. A Kadomtsev-Petviashvili I （KPI） solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Coope-Schrieffer （BCS） regime, Bose-Einstein condensate （BEC） reginle, and unitarity regime. One- lump solution as well as one-line soliton solutions for the KPI equation are obtained, and two-line soliton solutions with the same amplitude are also studied in the limited cases. The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.

Energy spectrum and superfluidity of spin-2 ultracold bosons in optical lattices

This paper studies the superfluidity of ultracold spin-2 Bose atoms with weak interactions in optical lattices by calculating the excitation energy spectrum using the Bogoliubov approach. The energy spectra exhibit the characteristics of the superfluid-phase explicitly and it finds the nonvanishing critical speeds of superfiuid. The obtained results display that the critical speeds of superfiuid are different for five spin components and can be controlled by adjusting the lattice parameters in experiments. Finally it discusses the feasibilities of implementing and measuring superfluid.

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Off-site trimer superfluid on a one-dimensional optical lattice

The Bose-Hubbard model with an effective off-site three-body tunneling,characterized by jumps towards one another,between one atom on a site and a pair atoms on the neighborhood site,is studied systematically on a one-dimensional（1D） lattice,by using the density matrix renormalization group method.The off-site trimer superfluid,condensing at momentum k = 0,emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model.Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from[Phys.Rev.A81,011601（R）（2010）]is stable in the thermodynamic limit.The off-site trimer superfluid phase,the partially off-site trimer superfluid phase and the Mott insulator phase are found,as well as interesting phase transitions,such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase.Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.

A Realistic Model for Observing Spin-Balanced Fulde-Ferrell Superfluid in Honeycomb Lattices

The combination of spin-orbit coupling （SOC） and in-plane Zeeman field breaks time-reversal and inversion symmetries of Fermi gases and becomes a popular way to produce single plane wave Fulde-Ferrell （FF） superfluid. However, atom loss and heating related to SOC have impeded the successful observation of FF state until now. In this work, we propose the realization of spin-balanced FF superfluid in a honeycomb lattice without SOC and the Zeeman field. A key ingredient of our scheme is generating complex hopping terms in original honeycomb lattices by periodical driving. In our model the ground state is always the FF state, thus the experimental observation has no need of fine tuning. The other advantages of our scheme are its simplicity and feasibility, and thus may open a new route for observing FF superfluids.

Superfluid phases and excitations in a cold gas of d-wave interacting bosonic atoms and molecules

Motivated by recent advances in orbitally tuned Feshbach resonance experiments, we analyze the ground-state phase diagram and related low-energy excitation spectra of a d-wave interacting Bose gas. A two-channel model with d-wave symmetric interactions and background s-wave interactions is adopted to characterize the gas. The ground state is found to have three interesting superfluid phases: atomic, molecular, and atomic–molecular. In great contrast to what was previously known about the p-wave case, the atomic superfluid is found to be momentum-independent for the d-wave case discussed here. The Bogoliubov spectra above each superfluid phase are obtained both analytically and numerically.

Spin-orbit coupling adjusting topological superfluid of mass-imbalanced Fermi gas

Topological superfluid state is different from the normal superfluid one due to the excitation energy gap on the boundary.How to obtain the topological superfluid state by using spin-orbit coupling to control the s-waves paired mass-imbalanced Fermi gas is a recent novel topic.In this paper,we study the topological superfluid phase diagram of two-dimensional mass-imbalanced Fermi gas with Rashba spin-orbit coupling at zero temperature.We find that due to the competition among mass imbalance,pairing interaction and spin-orbit coupling,there is a double-well structure in the thermodynamic potential,which affects the properties of the ground state of the system.We comprehensively give the phase diagrams of the system on the plane of spin-orbit coupling and chemical potential,and the phase diagrams on the plane of the reduced mass ratio and two-body binding energy.This study not only points out the stable region of topolog-ical superfluid state of mass-imbalanced Fermi gas,but also provides a detailed theoretical basis for better observation of topological superfluid state in experiments.

Superfluid to Mott-insulator transition in a one-dimensional optical lattice

Bose–Einstein condensates(BEC)of sodium atoms are transferred into one-dimensional(1D)optical lattice potentials,formed by two laser beams with a wavelength of 1064 nm,in a shallow optical trap.The phase coherence of the condensate in the lattice potential is studied by changing the lattice depth.A qualitative change in behavior of the BEC is observed at a lattice depth of~13.7Er,where the quantum gas undergoes a transition from a superfluid state to a state that lacks well-to-well phase coherence.

Dipole Oscillation in a Bose–Fermi Superfluid Mixture of ^(41)K and ~6Li

We study the relation between the bosonic frequency shift of a dipole oscillation and the fermionic compressibility in a Bose-Fermi super fluid mixture. Our results show that the A transition occurs in such a system, which interprets the perplexing phenomenon observed in the recent experiment [arXiv：1705.04496]. In that experiment,the frequency shift of the bosonic gas was measured with different fermion-fermion s-wave scattering lengths af. The most striking feature of their measurement is that the frequency shift shows a puzzling non-monotonic behavior around 1/kFaf（？）-0.2 with kF being the Fermi momentum. In the present work, the relation between the bosonic frequency shift and the compressibility of the Fermi gas is revealed by means of the equation of state of the super fluid mixture. Making use of the relation, we find that the compressibility of Fermi gas shows a ∧-like shape around 1/kFaf（？）-0.2. We would like to stress that no free parameter is used in our calculation and our results can be further testified in a future experiment.

Superfluid states in α–T_(3) lattice

The superfluid states of attractive Hubbard model in α–T_(3) lattice are investigated. It is found that one usual needs three non-zero superfluid order parameters to describe the superfluid states due to three sublattices. When two hopping amplitudes are equal, the system has particle–hole symmetry. The flat band plays an important role in superfluid pairing near half filling. For example, when the filling factor falls into the flat band, the large density of states in the flat band favors superfluid pairing and the superfluid order parameters reach relatively large values. When the filling factor is in the gap between the flat band and upper band, the superfluid order parameters take small values due to the vanishing of density of states. The superfluid order parameters show nonmonotonic behaviors with the increase of filling factor. At last, we also investigate the edge states with open boundary conditions. It is shown that there exist some interesting edge states in the middle of quasi-particle bands.