Study On The Dynamic Spectroscopy Of Optical Lattice Clock System Under Periodic Frequency Modulation

The optical lattice clock system based on alkaline-earth metal atoms,as the most accurate measurement platform,not only lays the foundation for the next generation of time standards,but also can be used in the measurement of physical constants,the detection of dark matter,the verification of general relativity and other basic physics.At the same time,Fermi alkaline-earth metal atoms themselves have rich physical properties,among which the most remarkable is the existence of SU（N）symmetry,which comes from the decoupling of the nuclear spin and the electron angular momentum of Fermi atoms.SU（N）symmetry of alkaline earth metal atoms in optical lattices has been confirmed by various experiments.On the other hand,quantum systems with periodic frequency modulation have many interesting physical phenomena,such as Landau-Zener-Stuckelberg-Majorana（LZSM）interference and side-band spectral effect.At the same time,it also shows great potential in various quantum systems in the simulation of quantum coherence phenomena,universal quantum state manipulation,suppressing specific noise to prolong the quantum coherence time and so on.Therefore,if the transition frequency of optical lattice clock is modulated,it will certainly have more application prospects.Recently,a periodic modulation of the bell transition frequency has been achieved in an optical lattice clock system,and a very stable modulation spectrum of the order of Hz has been observed.Although SU（N）symmetry of alkaline earth metal atoms has been experimentally verified many times,whether SU（N）symmetry is maintained under periodic drive is still an open question.In this paper,we use high-resolution ultra-narrow spectra of an ⁸⁷Sr atomic optical lattice clock to verify SU（N）symmetry under periodic modulation.The SU（N）symmetry of the Fermi-alkali earth metal atoms is reflected by some physical quantities related to electronic degrees of freedom such as the confinement potential in the lattice,collisions between atoms independent of the nuclear spin.Here we modulate the ten nuclear levels of an ⁸⁷Sr atom simultaneously in a near-zero magnetic field environment.Because each nuclear level corresponds to a different Rabi frequency,the Rabi spectrum we detect is the result of the interaction of all nuclear levels,so the Rabi spectrum will reflect the behavior at all nuclear levels.Through degenerate Rabi spectra under periodic modulation,we mainly verify the following two aspects:first,whether the nuclear energy level follows the same driving function under the modulated optical lattice potential;second,whether the number of particles at the nuclear level is conserved during the whole modulation process,so as to verify the symmetry of SU（N）.We also theoretically discuss and simulate how to implement LZSM interference in optical lattice clock system based on practical experimental conditions.Especially considering the coherence of optical lattice clock length,LZSM interferon-LZ Rabi oscillations（LZROs）in time domain are simulated in the system.LZROs are difficult to observe experimentally due to the limitation of coherence time in quantum systems.The first experimental implementation of LZROs was in NV color center system,but it has not been observed in atomic system.Here our theoretical simulations show that we can not only implement LZROs in optical lattice clock systems,but also find that LZSM interference can eliminate dephasing effects due to system temperature in specific parameter regions.Then we discuss how to calculate the geometric phase using the LZSM interferometry and how to calculate the geometric phase based on a model that has been implemented experimentally.