An experimental test of the geodesic rule proposition for the non-cyclic geometric phase

  Or Dobkowski  ,  Zhifan Zhou  ,  Yair Margalit  ,   Samuel Moukouri  ,  Yigal Meir  ,  Ron Folman  
1Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel

The geometric phase due to the evolution of the Hamiltonian is a central concept in quantum physics, and may become advantageous for quantum technology. In non-cyclic evolutions, a proposition relates the geometric phase to the area bounded by the phase-space trajectory and the shortest geodesic connecting its end points. The experimental verification of this geodesic rule proposition has remained elusive for more than three decades. Here, we report an unambiguous experimental confirmation of the geodesic rule for a non-cyclic geometric phase by means of a spatial SU(2) matter-wave interferometer, demonstrating, with high precision, the predicted phase sign change and π jumps.
We show the connection between our results and the Pancharatnam phase. Finally, we point out that the geodesic rule can be applied to obtain the red-shift in general relativity, enabling a completely new quantum tool to measure gravity.