Multi-state interferometric measurement of nonlinear AC Stark shift

In spin measurement using Faraday rotation of near-resonant probe light, the probe can change the atomic spin state. Nonlinear spin evolution due to quadratic AC Stark shift causes spin change harmful in precise measurements and quantitative evaluation of this change is important.

We demonstrate measurement of quadratic AC Stark shifts between Zeeman sublevels using a multi-state atomic interferometer. The interferometer can detect a quadratic shift without being affected by relatively large state-independent shifts, thereby improving the measurement precision. We measure quadratic shifts in the total spin $F = 2$ state of an $^{87}$Rb Bose--Einstein condensate due to the light near-resonant to the D$_1$ line. The agreement between the measured and theoretical detuning dependences of the quadratic shifts confirm the validity of the measurement. We also present results on the suppression of nonlinear spin evolution using near resonant dual color light pulses with opposite quadratic shifts. Finally, we discuss quanum nondemolition (QND) Faraday spin measurement with dual color pulses.