Skin Effect And Ising-like Magnetism In Ultracold Gases

The effective and flexible control of the interaction between laser and atom makes ultracold atomic gas widely used as quantum simulation,which provides a powerful tool for further understanding and realizing some complex phenomena in condensed matter physics.The rapid development of experiments also stimulates the theoretical workers to explore the corresponding system in depth.The two works in this dissertation are skin effect and Ising-like magnetism in quantum gases,both of which are theoretical studies based on the models realized in recent experiments.We first briefly introduce some technical methods which are often involved in theoretical and experimental work,and review and discuss the development of skin effect in cold atoms and Ising-like model in Rydberg system.In the first work,we predict that skin effect can exist in an experimental system described by a spin-orbit coupled model with dissipative behavior.The inconsistencies between the spectra solved numerically at the periodic and open boundary conditions indicate the existence of skin states.In addition,under the different parameters and the external potential with different geometric shapes,the system still has the eigen-skin modes,showing the robustness of their existence.By means of the ideas in non-Bloch band theory with large system size,the combination of generalized wave vector conditions and resultant theory helps us to find two generalized wave vector curves and recover the spectrum at open boundary conditions.By numerically calculating the dynamic evolution of the system,we find the anomalous reflection behavior which is different from Hermitian case.Different incident momentum and dissipation strength have corresponding effects on evolution trajectory.Especially when the incident momentum is small and the dissipation strength is large,the atom will be localized near the boundary after encountering it,that is,the dynamic sticky effect.This phenomenon provides a dynamic signal for the experimental detection of skin effect,which is expected to be observed by in-situ imaging in cold atoms in the future.For the second work,an Ising-like model on a triangular Rydberg array is numerically analyzed by using the quantum Monte Carlo method of stochastic series expansion.This model has a long-range van der Waals interaction,and both transverse-and longitude-field components.At zero temperature,with the increase of two-photon detuning,the average Rydberg excitation number appears two stable occupying platforms,which are 1/3-and 2/3-filling states,respectively.Accordingly,the results of order parameters and static structure factors show that the system is a stable(?)triangular antiferromagnetic(TAF)phase in the two platform regions.The specific locations of the phase transition point between the TAF and disordered phases on both sides are given by Binder ratio and correlation length ratio under finite-size scale analysis.Moreover,there is a special position in the average Rydberg occupation,that is,the 1/2-filling,where the atoms of the system are still arranged in a triangular pattern,and the additional"particle-hole" symmetry of the system leads to six-fold ground state degeneracy.At finite temperature,unlike the transition from TAF phase to disordered phase at 1/3-and 2/3-filling,there is a Kosterlitz-Thouless(KT)phase with an emergent U(1)symmetry at 1/2-filling.The existence of this KT phase is demonstrated by calculating the mean value of six-fold anisotropy,the distribution histogram of the order parameters,and the fitting of the susceptibility collapse,and it exists only strictly at the 1/2-filling.These rich physical phenomena may be observed in the Rydberg experiment using fluorescence imaging techniques.