| Summary: | Ramsey interferometry is a key technique for precision spectroscopy and to
probe 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.
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