Generalized hyper-Ramsey-Bord\'e matter-wave interferometry: quantum engineering of robust atomic sensors with composite pulses

A new class of atomic interferences using ultra-narrow optical transitions are pushing quantum engineering control to a very high level of precision for a next generation of sensors and quantum gate operations. In such context, we propose a new quantum engineering approach to Ramsey-Bord\'e interferometry introducing multiple composite laser pulses with tailored pulse duration, Rabi field amplitude, frequency detuning and laser phase-step. We explore quantum metrology with hyper-Ramsey and hyper-Hahn-Ramsey clocks below the $10^-18$ level of fractional accuracy by a fine tuning control of light excitation parameters leading to spinor interferences protected against light-shift coupled to laser-probe field variation. We review cooperative composite pulse protocols to generate robust Ramsey-Bord\'e, Mach-Zehnder and double-loop atomic sensors shielded against measurement distortion related to Doppler-shifts and light-shifts coupled to pulse area errors. Fault-tolerant auto-balanced hyper-interferometers are introduced eliminating several technical laser pulse defects that can occur during the entire probing interrogation protocol. Quantum sensors with composite pulses and ultra-cold atomic sources should offer a new level of high accuracy in detection of acceleration and rotation inducing phase-shifts, a strong improvement in tests of fundamental physics with hyper-clocks while paving the way to a new conception of atomic interferometers tracking space-time gravitational waves with a very high sensitivity.