Quantum engineering of atomic phase shifts in optical clocks

Quantum engineering of time-separated Raman laser pulses in three-level systems is presented to produce an ultranarrow optical transition in bosonic alkali-earth clocks free from light shifts and with a significantly reduced sensitivity to laser parameter fluctuations. Based on a quantum artificial complex wave-function analytical model and supported by a full density-matrix simulation including a possible residual effect of spontaneous emission from the intermediate state, atomic phase shifts associated with Ramsey and hyper-Ramsey two-photon spectroscopy in optical clocks are derived. Various common-mode Raman frequency detunings are found in which the frequency shifts from off-resonant states are canceled, while their uncertainties at the ${10}^{\ensuremath{-}18}$ level of accuracy are strongly reduced.