Dynamical Topological Phenomone In Peoridically Driven Quantum Systems

The concept of quantum simulation was proposed by the famous physicist Feynman in 1982,in order to solve the complex quantum many-body problems that are difficult to solve by classical computers and that cannot be directly observed experimentally.The idea used in quantum simulation is to simulate these complex quantum many-body systems by designing a quantum system that is easy to control experimentally.The experimental realization of the Bose-Einstein condensation in 1995 opened up the possibility for quantum simulation in ultracold atomic gases,which possess remarkable quantum properties,high purity and controllable experimental parameters.Ultracold atomic gas subject to a standing wave field can form an optical lattice that simulates quantum properties of solid materials such as band topology.More importantly,many-body strongly correlated systems such as the Bose-Hubbard model and the Fermi-Hubbard model can also be simulated by tuning the interaction between atoms in the optical lattice.In 2011,spin-orbit coupling was realized in ultracold atomic gas,hence all properties of charged particles in electromagnetic fields can be simulated by neutral atoms and ultracold atomic systems become an ideal quantum simulator.In recent years,people have used ultracold atomic systems to simulate not only static topological systems but also topological phenomena in non-equilibrium dynamic processes,where the quantum quench is currently the most popular method in experiments.In 2017,the dynamical quantum phase transition based on quantum quench process in ultracold atom systems was experimentally realized by K.Sengstock’s group.After that,quantum quench of ultracold atomic gas in the Raman lattice has also been studied in Liu’s group from Peking University and Pan’s group from University of Science and Technology of China.In addition to the quantum quench,time-periodically driving technique is also an important method for the realization of dynamical processes.For example,two experimental groups achieved Thouless pumping in ultracold bosonic and ultracold fermionic systems under the adiabatic conditions by periodically driving method in 2016.Away from adiabatic conditions,the current experiments about Floquet dynamical quantum phase transitions in time-periodically driven systems have only been realized in solid spin systems.Floquet dynamical quantum phase transitions in lattice systems also requires further study.Based on experimental progresses in simulating dynamic topological phenomena in ultracold atomic systems,we theoretically propose a zero-dimensional system that is driven periodically to simulate 1D topological lattices.Furthermore,we also design a periodically driven 1D Raman lattice to simulate Floquet dynamical quantum phase transitions and other dynamical topological phenomena in lattice systems.More specific research contents are as follows:1.Geometric phase of Wannier-Stark ladders in alkaline-earth(-like)atomsBased on the current experimental progress where the atomic Bloch oscillations and Ramsey interference are combined to measure geometric phases in one-dimensional optical superlattice systems,we propose a theoretical model which can be used to extract the accumulated geometry phase by making use of the periodically driven alkalineearth(-like)atomic clock states.We discuss the scheme by taking the clock transition of 171Yb atoms as an example.Two sets of lasers are used to couple two groups of clock transitions that are decoupled from each other,in which the single-photon detuning of these two sets of lasers is the same,while the two-photon detuning has the same magnitude and opposite sign.Each group of the two-level system can be mapped onto a two-band Wannier-Stark ladder,and the driving dynamics is equivalent to Bloch oscillations in opposite directions for two different groups of 1D tilted lattices.When the adiabatic condition is satisfied,the quantization of the geometric phases accumulated in one period of dynamic evolution is discussed.Due to the special cross-coupling mechanism,the two groups of ladders have the same band structure but different topological properties,so the dynamical phase accumulated by the two groups are equal while the geometric phase are not.We further study the conditions for the occurrence of topological phase transition in the system,as well as the variation trend at away from the adiabatic limit.Finally,we propose a corresponding experimental detection scheme,where the difference in geometric phase between different ladders is extracted through interference between different nuclear spin states.Our study sheds light on the engineering of exotic band structures in Floquet dynamics.2.Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman latticeStimulated by the recent progress in engineering topological band structures in ultracold atomic gases and dynamical quantum phase transition in other quantum simulators,we study the dynamic topological phenomena for atoms loaded in a periodically driven optical lattice.When the frequency of the periodic modulation is low,the time-dependent Hamiltonian can be mapped to a 2D topological insulator,with the discretized frequency components playing the role of an additional,synthetic dimension.In the high-frequency limit,we derive the effective Floquet Hamiltonian of the system,and reveal the occurrence of Floquet dynamic quantum phase transitions—an emergent topological phenomenon in the micromotion of the Floquet dynamics.Addressing the relation between the topology of the effective Floquet Hamiltonian and the presence of dynamic topological phenomena,we demonstrate that the topologically non-trivial nature of the Floquet Hamiltonian is a sufficient but not necessary condition for the onset of the Floquet dynamic quantum phase transition.We further discuss the relation of the topology of the Floquet Hamiltonian with the existence of dynamic skyrmion structures in the emergent momentum-time manifold of the micromotion,as well as the fate of these dynamic topological phenomena when the modulation frequency decreases away from the high-frequency limit.We also study another periodically driven Raman lattice system that can be solved exactly,and we obtain the conditions for the emergence of dynamical quantum phase transitions and dynamical skyrmion structures at arbitrary modulation frequencies.Since the current experimental realization of the Floquet dynamical quantum phase transition is based on the zero-dimensional solid spins,and there is no experimental progress on the lattice system,our scheme is of great significance for promoting the development of experiments related to dynamical topological phenomena.