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The recent experimental realization of a three-dimensional (3D) opticallattice clock not only reduces the influence of collisional interactions on theclock's accuracy but also provides a promising platform for studying dipolarmany-body quantum physics. Here, by solving the governing master equation, weinvestigate the role of both elastic and dissipative long-range interactions inthe clock's dynamics and study its dependence on lattice spacing,dimensionality, and dipolar orientation. For small lattice spacing, i.e.,$k_0a\ll 1$, where $a$ is the lattice constant and $k_0$ is the transitionwavenumber, a sizable spin squeezing appears in the transient state which isfavored in a head-to-tail dipolar configuration in 1D systems and aside-by-side configuration in 2D systems, respectively. For large latticespacing, i.e., $k_0a\gg 1$, the single atomic decay rate can be effectivelysuppressed due to the destructive dissipative emission of neighboring atoms inboth 1D and 2D. Our results will not only aid in the design of the futuregeneration of ultraprecise atomic clocks but also illuminates the richmany-body physics exhibited by radiating dipolar system.

Spin squeezing and many-body dipolar dynamics in optical lattice clocks