Quantum Simulation About Artificial Gauge Field Based On Ultracold Atoms

In particle physics,the Standard Model has been by far the most successful theory for illustrating elementary particles and their interactions.In the framework of the Standard Model,fermions are the fundamental building blocks of matter,and gauge bosons mediate the interactions between fermions.Lattice quantum field theory is a discrete version of continuous quantum field theory.Gauge invariance,which ensures that the Lagrangian remains unchanged under a local transformation,constrains the dynamics of matter and gauge fields by imposing local symmetries at each point in spacetime,which has fundamentally shaped our understanding of interacting elementary particles in quantum electrodynamics and quantum chromodynamics.The lattice gauge theory was introduced by Wilson in 1974 when he studied the interaction between quarks and gluons.It has now become one of the most accurate and efficient methods of calculation in particle physics.It is an extremely arduous task to address lattice gauge theory using classical computers,since computing large-scale quantum systems is beyond their performance,and the sign problem arises when dealing with fermions by quantum Monte Carlo,which leads to an urgent need for dedicated quantum simulators for lattice gauge theory.The optical lattice ultracold atoms becomes an ideal platform for such a quantum simulator due to its highly controllability.Though a number of breakthroughs in synthesizing gauge fields in cold atoms have been made over several years,including the experimental realization of artificial electric and magnetic fields,spin-orbit coupling,and the density-dependent gauge field,none of them is essentially endowed with gauge invariance.It is well known that（1+1）-dimensional lattice Schwinger model is typical for simulating U（1）lattice gauge theory in quantum electrodynamics.Two cold-atom groups experimentally realized spin-1/2 lattice Schwinger model until 2020.Inspired by such progress,in this thesis,we simulate artificial gauge fields based on ultracold atoms in one-dimensional optical lattice.The specific contents are as follows:1.Long-range order induced by spin-orbit coupling in one-dimensional repulsive Fermi gasWe investigate quantum phase transitions of one-dimensional fermi gas with spin-orbit coupling induced by two-photon Raman transition under strong repulsive interaction.The phase diagram of the system including two trivial phases apart from the nontrivial topological state is mapped out according to the numerical results of matrix product state and the effective spin model.In topological regime the magnetic correlation manifests exponential decay and spin-orbit coupling is key for the gapped spin excitation.The antiferromagnetic Mott insulator with the spin correlation exhibiting power-law decay in the case of both weak-and strong-spin-orbit coupling is identified under strong repulsive interaction.In the intermediate-spin-orbit-coupling regime the long-range order of Ising Néel Mott insulator with gapless excitation is discovered and the phase region eventually shrinks into a line in the strong-coupling limit.2.Synthetic U（1）gauge invariance in spin-1 Bose gasRecent experimental realizations of the U（1）gauge invariance open a door for quantum simulation of elementary particles and their interactions using ultracold atoms.Stimulated by such exciting progress,we propose a platform—a spin-1 Bose-Einstein condensate—to simulate the deconfined lattice Schwinger model.Unlike previous platforms,it is shown that the atomic interactions in the spin-1 condensate naturally lead to a matter-field interaction term which respects the U（1）gauge symmetry.As a result,a newZ₃-ordered phase with threefold ground-state degeneracy emerges in the phase diagram.TheZ₃ phase connects to the disordered phase by a three-state Potts criticality,which is in contrast to the conventional Coleman’s transition with Ising criticality.Furthermore,the ordered state is constructed by a set of weak quantum scars,which is responsible for the anomalously slow dynamics as it is quenched to a special point in the phase diagram.Our proposal provides a platform for extracting emergent physics in synthetic gauge systems with matter-field interactions.3.Nonthermal dynamics in a spin-1/2 lattice Schwinger modelLocal gauge symmetry is intriguing for the study of quantum thermalization breaking.For example,in the high-spin lattice Schwinger model（LSM）,the local U（1）gauge symmetry underlies the disorder-free many-body localization（MBL）dynamics of matter fields.This mechanism,however,would not work in a spin-1/2 LSM due to the absence of electric energy in the Hamiltonian.In this paper,we show that the spin-1/2 LSM can also exhibit disorder-free MBL dynamics,as well as entropy prethermalization,by introducing a four-fermion interaction into the system.The interplay between the fermion interaction and U（1）gauge symmetry endows the gauge fields with an effectively disordered potential which is responsible for the thermalization breaking.It induces anomalous（i.e.,non-thermal）behaviors in the long-time evolution of such quantities as local observables,entanglement entropy,and correlation functions.Our work offers a new platform to explore emergent non-thermal dynamics in state-of-the-art quantum simulators with gauge symmetries.