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We present another topological superfluid with s-wave pairing for ultracold fermionic atoms in addition to the chiral topological superfluid proposed by Sato et al (2009 Phys. Rev. Lett. 103 020401), of which edge dislocations host Majorana zero modes that may be utilized as decoherence-free qubits, and quantized vortices trap zero energy modes. The quantum phase fluctuations for topological superfluids and Berezinsky–Kosterlitz–Thouless transition are also discussed.

The evolution of the field entropy and the entanglement between the atom and the field for the system of a single-mode vacuum field interacting with a -type three-level atom have been studied by using the reduced quantum entropy. The influences of the detuning of the light field and the setting of the initial state of the atom on the field entropy and entanglement of the system under consideration are discussed emphatically. It is showed that the detuning of the light field and the setting of the initial state of the atom play an important role for the evolution of the field entropy and the entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.

The elastic scattering phase shifts to the two-particle energy levels in a finite cubic box is related by the Lüscher’s formula. In this paper, based on the nonrelativistic quantum mechanics model which is usually assumed to be the low energy scattering case in lattice simulations, we confirmed the generalized Lüscher’s formula for the case of two-particle scattering with arbitrary spin in Ref. 1. In particular, Lüscher’s formula is synthesized for two-spin-3/2-particle scattering, i.e. [Formula: see text] scattering on lattice that may help us study the promising dibaryon states.

For a three-dimensional non-harmonic oscillator potential 12r2+A2r 2, the s-wave bound solutions of both Dirac equation and Klein-Gordon equation are giv en when the scalar potential is equal to the vector potential. We find that the radial component equations for both two-dimensional Dirac equation and three-dimensional one are the same when the scalar potential equals to the vector potenti al, and the corresponding s-wave bound solutions for the two-dimensional system are also obtained.