Density shift of optical lattice clocks via the multiband sampling exact diagonalization method

Density shift plays an important role in the uncertainty of an optical lattice clock and thus has attracted a great deal of theoretical and experimental studies. However, most of the theoretical research has considered the single-band model and collective approximation, so the density shift of the system at higher temperatures cannot be analyzed accurately. Here we design a numerical algorithm that combines Monte Carlo sampling and exact diagonalization and name it multiband sampling exact diagonalization (MBSED). The MBSED method considers the collision of atoms between multiple bands, so it can provide the density shift of an optical lattice clock with higher precision. Such an algorithm will benefit the numerical simulation of an optical lattice clock and may also be used in other platforms of quantum metrology.