We develop a formalism to incorporate exchange symmetry considerations into the calculation of collisional frequency shifts and blackbody radiation effects for atomic clock transitions using a density matrix formalism. The formalism is developed for both fermionic and bosonic atomic clocks. Results for a finite temperature ${ }^{ 87}$Sr ${ }^1S_0$ ($F = 9/2$) atomic clock in a magic wavelength optical lattice are presented.
Categories: quant-ph cond-mat.quant-gas