Relativistic Effects in Optical Lattice Clocks

Optical lattice clocks based on $^{87}$Sr fermionic atoms have achieved fractional frequency uncertainties at the $10^{-19}$ level, where leading-order relativistic effects—namely the gravitational redshift and the second-order Doppler shift—become measurable within a single experimental system. While the gravitational redshift has recently been observed across a millimeter-scale atomic cloud in a 1D lattice, the second-order Doppler shift remains unresolved. In this talk, I present a proposal that enables the detection of this elusive effect by engineering spin–motion entanglement within the optical lattice clock. This approach amplifies both relativistic shifts and opens a path toward probing fundamental aspects of time dilation in many-body quantum systems.