Geometric Ramsey interferometry with a tripod scheme

Ramsey interferometry is a key technique for precision spectroscopy and for probing the coherence of quantum systems. Typically, an interferometer is constructed using two quantum states and involves a time-dependent interaction with two short resonant electromagnetic pulses. Here, we explore a different type of Ramsey interferometer where we perform quantum state manipulations by geometrical means, eliminating the temporal dependence of the interaction. We use a resonant tripod scheme in ultracold strontium atoms where the interferometric operation is restricted to a two-dimensional dark-state subspace in the dressed-state picture. The observed interferometric phase accumulation is due to an effective geometric scalar term in the dark-state subspace, which remarkably does not vanish during the free evolution time when the light-matter interaction is turned off. This study opens the door for more robust interferometers operating on multiple input-output ports.