Fig. 3
From: Non-Abelian adiabatic geometric transformations in a cold strontium gas
Geometric gate operation. a Phase loop in parameter space (ϕ2, ϕ1). ϕi (i = 1, 2) are the two independent offset phases tuned by the EOMs shown in Fig. 1a. We have performed two counterclockwise cycles: the first one is \(a \to b \to c\) and starts from the origin, the second one is \(c \to a \to b\) and starts from the upper corner. The loop is completed in 12 μs and its excursion is ϕ0. b Measured bare-state populations \(\bar P_1\) (blue circles), \(\bar P_2\) (green squares), and \(\bar P_3\) (red stars) as a function of ϕ0 for the first cycle. The Rabi frequencies are \(\Omega = 2\pi \times 450{\kern 1pt}\) kHz and T = 0.5 μK. Dark-state reconstruction as a function of ϕ0. c Population of \(|D_1\rangle\) (blue circles) and \(|D_2\rangle\) (red squares). d Azimuthal phase φ. The solid and dashed curves in b, c, and d are the theoretical predictions for a pinned atom and for a gas at temperature T, respectively. The error bars correspond to a 95% confidence interval
