arXiv subjects

Yong-Kai Liu

Publications and source records attributed to Yong-Kai Liu.

6 recordsLinked to original sources

arXiv2024

Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes

Thouless pumping with nontrivial topological phases provides a powerful means for the manipulation of matter waves in one-dimensional lattice systems. The band topology is revealed by the quantization of pumped charge. In the context of Thouless pumping, we present a graphical representation for the topological phases characterized by the Chern number of an effective two-dimensional band. We illustrate how the two topological phases with distinct Zak phase is connected in the pumping process. Such a visual depiction exhibits typical patterns that is directly related to a linking number and to the Chern number, allowing for the construction of Thouless pumping schemes in a practical way. As a demonstration, we present a generalized Creutz model with tunable Peierls phase, inter-leg imbalance and diagonal hopping. Various modulation schemes for Thouless pumping are studied, focusing on their graphical representations in Bloch space, as well as the quantized pumping phenomenon in real space.

cond-mat.quant-gas↗

arXiv2014

Exact solitons and manifold mixing dynamics in the spin-orbit-coupled spinor condensates

We derive exact static as well as moving solitonic solutions to the one-dimensional spin-orbit-coupled F=1 Bose-Einstein condensates. The static polar soliton is shown to be the ground state by the imaginary-time evolution method. It shows a helical modulation of the order parameter due to the spin-orbit coupling. In particular, the moving soliton exhibits a periodic oscillation among the particle numbers of the hyperfine states. We further explore the temporal evolution of the static polar soliton and find that the spin-polarization exhibits dynamical oscillations. This disappearance and re-emergence of the ferromagnetic state indicates the mixing of the ferromagnetic and the antiferromagnetic manifolds.

cond-mat.quant-gas↗

arXiv2014

Stable knots in the trapped Bose-Einstein condensates

The knot of spin texture is studied within the two-component Bose-Einstein condensates which are described by the nonlinear Gross-Pitaevskii equations. We start from the non-interacting equations including an axisymmetric harmonic trap to obtain an exact solution, which exhibits a non-trivial topological structure. The spin-texture is a knot with an integral Hopf invariant. The stability of the knot is verified by numerically evolving the nonlinear Gross-Pitaevskii equations along imaginary time.

cond-mat.quant-gas↗

arXiv2013

Half-knot in the spinor condensates

We present an exact solution to the stationary coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor Bose-Einstein condensates. The solitonic solution is a twisted half-skyrmion in the three-dimension (3D) space. By making a map from and the Cartesian coordinates to the toroidal coordinates, we demonstrate it is a linked half-unknot with a fractional Hopf charge.

cond-mat.quant-gas↗

arXiv2013

Fractional windings of the spinor condensates on a ring

We study the uniform solutions to the one-dimensional spinor Bose-Einstein condensates on a ring. These states explicitly display the associated motion of the super-current and the spin rotation, which give rise to fractional winding numbers according to the various compositions of the hyperfine states. It simultaneously yields a fractional factor to the global phase due to the gauge-spin symmetry. Our method can be applied to explore the fractional vortices by identifying the ring as the boundary of two-dimensional spinor condensates.

cond-mat.quant-gas↗

arXiv2012

Exact solutions to the spin-2 Gross-Pitaevskii equations

We present several exact solutions to the coupled nonlinear Gross-Pitaevskii equations which describe the motion of the one-dimensional spin-2 Bose-Einstein condensates. The nonlinear density-density interactions are decoupled by making use of the properties of Jacobian elliptical functions. The distinct time factors in each hyperfine state implies a "Lamor" procession in these solutions. Furthermore, exact time-evolving solutions to the time-dependent Gross-Pitaevskii equations are constructed through the spin-rotational symmetry of the Hamiltonian. The spin-polarizations and density distributions in the spin-space are analyzed.

cond-mat.quant-gas↗