We develop a formalism to incorporate exchange symmetry considerations into the calculation of collisional frequency shifts for atomic clocks using a density-matrix formalism. The formalism is developed for both fermionic and bosonic atomic clocks. Numerical results for a finite-temperature ${}^{87}$Sr ${}^1{S}_0$ ($F=9/2$) atomic clock in a magic wavelength optical lattice are presented.

• Received 16 November 2010

DOI:https://doi.org/10.1103/PhysRevA.84.013822