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.

This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb- Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe's hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb-Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang-Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb-Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability.

The Boltzmann constant k_B is a fundamental physical constant in thermodynamics. The present CODATA recommended value of k_B is 1.3806488(13)× 10^-23 J/K (relative uncertainty 0.91 ppm), which is mainly determined by acoustic methods. Doppler broadening thermometry (DBT) is an optical method which determines k_BT by measuring the Doppler width of an atomic or molecular transition. The methodology and problems in DBT are reviewed, and DBT measurement using the sensitive cavity ring-down spectroscopy (CRDS) is proposed. Preliminary measurements indicate that CRDS-based DBT measurement can potentially reach an accuracy at the 1 ppm level.

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 spin–orbit 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.

In this paper, we overview recent advances in high-precision structure calculations of the hydrogen molecular ions (H₂⁺ and HD⁺), including nonrelativistic energy eigenvalues and relativistic and quantum electrodynamic corrections. In combination with high-precision measurements, it is feasible to precisely determine a molecular-based value of the proton-to-electron mass ratio. An experimental scheme is presented for measuring the rovibrational transition frequency (v,L):(0,0)→(6,1) in HD⁺, which is currently underway at the Wuhan Institute of Physics and Mathematics.

Development of atom interferometry and its application in precision measurement are reviewed in this paper. The principle, features and the implementation of atom interferometers are introduced, the recent progress of precision measurement with atom interferometry, including determination of gravitational constant and fine structure constant, measurement of gravity, gravity gradient and rotation, test of weak equivalence principle, proposal of gravitational wave detection, and measurement of quadratic Zeeman shift are reviewed in detail. Determination of gravitational redshift, new definition of kilogram, and measurement of weak force with atom interferometry are also briefly introduced.

Precision measurement of the 4s ²S_1/2–3d ²D_5/2 clock transition based on ⁴⁰Ca⁺ ion at 729 nm is reported. A single ⁴⁰Ca⁺ ion is trapped and laser-cooled in a ring Paul trap, and the storage time for the ion is more than one month. The linewidth of a 729 nm laser is reduced to about 1 Hz by locking to a super cavity for longer than one month uninterruptedly. The overall systematic uncertainty of the clock transition is evaluated to be better than 6.5× 10^-16. The absolute frequency of the clock transition is measured at the 10^-15 level by using an optical frequency comb referenced to a hydrogen maser which is calibrated to the SI second through the global positioning system (GPS). The frequency value is 411 042 129 776 393.0(1.6) Hz with the correction of the systematic shifts. In order to carry out the comparison of two ⁴⁰Ca⁺ optical frequency standards, another similar ⁴⁰Ca⁺ optical frequency standard is constructed. Two optical frequency standards exhibit stabilities of 1× 10^-14τ^-1/2 with 3 days of averaging. Moreover, two additional precision measurements based on the single trapped ⁴⁰Ca⁺ ion are carried out. One is the 3d ²D_5/2 state lifetime measurement, and our result of 1174(10) ms agrees well with the results reported in [Phys. Rev. A 62 032503 (2000)] and [Phys. Rev. A 71 032504 (2005)]. The other one is magic wavelengths for the 4s ²S_1/2–3d ²D_5/2 clock transition; λ_|mj|= 1/2= 395.7992(7) nm and λ_|mj|= 3/2= 395.7990(7) nm are reported, and it is the first time that two magic wavelengths for the ⁴⁰Ca⁺ clock-transition have been reported.

Developments of the micro-Gal level gravimeter based on atom interferometry are reviewed, and the recent progress and results of our group are also presented. Atom interferometric gravimeters have shown high resolution and accuracy for gravity measurements. This kind of quantum sensor has excited world-wide interest for both practical applications and fundamental research.