  Clock interferometry refers to the coherent splitting of a clock into two
different paths and recombining in a way that reveals the proper time
difference between them. Unlike the comparison of two separate clocks, this
approach allows testing how non-flat spacetime influences quantum coherence.
Atomic clocks are currently the most accurate time keeping devices. Here we
propose using optical tweezers to implement clock interferometry. Our proposed
clock interferometer employs an alkaline-earth-like atom held in an optical
trap at the magic wavelength. Through a combination of adiabatic,
tweezer-based, splitting and recombining schemes and a modified Ramsey sequence
on the clock states, we achieve a linear sensitivity to the gravitational time
dilation. Moreover, the measurement of the time dilation is insensitive to
relative fluctuations in the intensity of the tweezer beams. We analyze the
tweezer clock interferometer and show that it is feasible with current
technological capabilities. The proposed interferometer could test the effect
of gravitational redshift on quantum coherence, and implement the quantum twin
paradox.
