Quantum Magnetism And Many-body Stability In Low-dimensional Strongly Interacting Ultracold Atoms

As a highly tunable quantum system,today's ultra-cold atomic system is an ideal platform for simulating novel quantum effects.Strongly interacting system is always significant research topic in condensed matter physics even in the whole physics.By means of Feshbach resonance or optical lattice technology,people can adjust interaction strength between ultracold atoms which makes the interaction dominates in the system and then implements a series of physical systems with strong interaction,such as TG gas,Bose-Hubbard model,Fermi Hubbard model and so on.The questions of non-equilibrium dynamics in quantum system permeate the whole areas of physics: from creation and expansion of the universe to the high-energy collisions of microscopic particles.As nearly isolated quantum systems,ultracold atoms have great advantages in simulating non-equilibrium systems.In recent years,more and more experiments on non-equilibrium dynamics have provided us with great opportunities to understand non-equilibrium physics.Moreover,recent ultra-cold atomic experiment on controlling atoms loss by laser field,has been realized the quantum dynamics system with dissipation and observed the novel dynamics behavior of Parity-Time(PT)symmetry and its PT symmetry breaking.Based on the stimulation and inspiration of the current cold atom experiments,we will carry out the theoretical research in the following aspects in this paper:1.Quantum magnetism in one-dimensional strongly s-wave interacting Fermi systems.A two-component Fermi subsystem with finite force equation s-wave interaction is studied.The low-energy effective Hamiltonian of the system under the limit of strong interaction is obtained by adiabatic elimination technique.We find that the range will greatly affect the magnetism properties in harmonically trapped systems.In particular,in addition to the complete ferromagnetic and anti-ferromagnetic correlation,there is another mixed magnetic correlation in which ferromagnetic and anti-ferromagnetic coexist.We obtain the parameter region of the mixed magnetic correlation by using the Thomas-Fermi approximation of local density.Futhermore,we propose to detect the range-induced magnetic order in the tunneling experiment.Our results can be directly tested in1 D Fermi gases across narrow resonance,and suggest a convenient route towards the local manipulation of quantum magnetism in cold atoms.2.Many-body stabilization of a p-wave interacting Fermi gas in one dimension with finite range.Using the asymptotic Bethe ansatz,we study the stabilization problem of the one-dimensional spin-polarized Fermi gas confined in a hard-wall potential with tunable p-wave scattering length and finite effective range.We find that the interplay of two factors,i.e.,the finite interaction range and the hard-wall potential,will help to stabilize the system near resonance.The stabilization occurs even in the positive scattering length side,where the system undergoes a many-body collapse if any of the factors is absent.In particular,at p-wave resonance,the system is stabilized if the finite range is above twice the mean particle distance.Slightly away from resonance,we extract the lowest-order correction to the stability condition in terms of the inverse scattering length.Finally,we present a global picture for the energetics and the stability property of fermions from weakly attractive to deep bound state regime.Our results suggest a many-body stable p-wave Fermi gas is within the reach of current cold atoms techniques and new physics of breaking ing Bose-Fermi duality in 1D system is also revealed.3.The high order exceptional point in interacting quantum gas and ultra-sensitive spectrum response.We show that arbitrarily high-order exceptional points(EP)can be achieved in a repulsively interacting two-species Bose gas in one dimension.By exactly solving the non-Hermitian two-boson problem,we demonstrate the existence of third-order EPs when the system is driven across the parity-time symmetry breaking transition.We further address the fourth-order EPs with three bosons and generalize the results to N-body system,where the EP order can be as high as N + 1.Moreover,we show how to create ultra-sensitive spectral response around EPs via an interaction anisotropy in different spin channels and general rule of energy spectrum splitting is given.We further extend these results to 3D system with high spin system.Our work puts forward the possibility of atomic sensors made from highly controllable ultracold gases.4.Nonequilibrium and non-Hermite dynamics in one-dimensional dissipative Fermi-hubbard model.We study the nonequilibrium dynamics of a one-dimensional Fermi-Hubbard model with dissipations.By solving Lindblad master equations numerically,it is found that under a given dissipation intensity,the dynamic instability appears in the system when the interaction strength of the system is large enough.Using the adiabatic elimination technique,we derive the non-Hermition effective Hamiltonian of the system,and find that the dynamic instability is related to the spontaneous breaking of the PT symmetry.By studying the two-site model,we obtain the analytical solutions of the problem,and find that the low-energy Mott state of the system is also unstable and give the lifetime of the Mott state,although its energy level has no imaginary part.The numerical results of the multi-lattice system show that these dynamical phenomena still exist.These results will benefit to deepen the understanding of the dynamic properties of the dissipative systems with strong interactions,and also have directive significance for the experimental preparation of stable Mott states.