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Density shift plays one of the major roles in the uncertainty of opticallattice clock, thus has attracted lots of theoretical and experimental studies.However, most of the theoretical research considered the single-band andcollective approximation, so the density shift of the system at highertemperatures can not be analyzed accurately. Here, we design a numericalalgorithm that combines Monte Carlo sampling and exact diagonalization and nameit as Multi-Band Sampling Exact Diagonalization (MBSED). The MBSED methodconsiders the collision of atoms between multi-bands, so it can provide thedensity shift of an optical lattice clock with higher precision. Such analgorithm will benefit the numerical simulation of an optical lattice clock,and may also be used in other platforms of quantum metrology. In addition,through our numerical simulation, we also found that the density shift of Rabispectrum is slightly non-linear with atom number.

Density Shift of Optical Lattice Clock via Multi-Bands Sampling Exact Diagonalization Method