Ramsey Spectroscopy and Geometric Operations on Sodium Bose–Einstein Condensates Using Two-Photon Stimulated Raman Transitions

Abstract

Ramsey spectroscopy and geometric operations on the released sodium Bose–Einstein condensates consisting of 10 7 atoms were demonstrated using copropagating two-photon stimulated Raman pulses, which were resonant to the clock transition between the F =1, m F =0 and F =2, m F =0 states of sodium atoms. The Ramsey fringes with a visibility close to 1 were obtained for two Raman pulses separated by 10 ms. A relative frequency resolution of Ramsey resonance was 6×10 -10 and a phase uncertainty of fringes was 0.06 rad for single measurement. Using resonant laser-controlled Raman pulses, geometric operations for rotations of the two-level Bose–Einstein condensates around axes 2 and 3 on the Bloch sphere were also demonstrated with a relative phase uncertainty of 4%.