Figure 2: Coherence of the qubit.

Measured normalized coherences as a function of solid angle with fluctuations in the effective magnetic field. Each data point is the average of 400 realizations of noise. If not stated otherwise, the precession period of the field is T=100 ns. Solid lines indicate fits to the data. The error bars indicate the s.d. (a) Coherence measured in a complete spin echo experiment (‘protocol P’, see Fig. 3) with noise during the first window of the spin echo only. The direction of precession is preserved in the second window of the echo, leading to pulse sequences C⁺⁺ and C⁻⁻. The exponents denote sgn(n), the direction of precession of the field. ‘dynamic phase (D. P.) only’ denotes a magnetic field which does not precess (ω_B=0), so that the qubit acquires only dynamic phase. (b) As in a but with uncorrelated noise. (c) Coherence measured in a spin echo in which the direction of precession of the magnetic field is reversed in the second half (‘protocol R’), giving C⁺⁻ and C⁻⁺. (d) As in c but with uncorrelated noise. (e) As in c but with precession period T=160 ns. (f) Dynamic (solid line), geometric (dashed line) and non-geometric non-adiabatic (dotted line) contributions to dephasing, as they appear in the exponent of ν in equation (1), as a function of precession period T. The curves are computed with the parameters used for recording the data shown in c and e for A=π/2. The values for dynamic and geometric dephasing extracted from fits to these measurements are indicated by black dots. The vertical lines indicate the periods T=0.1, 0.16 μs used in our experiments.