Fig. 3: Anisotropy of the hole spin coherence and sweet-spot operation.
From: A single hole spin with enhanced coherence in natural silicon
a, Normalized Hahn-echo amplitude versus free evolution time τwait at fL = 17 GHz. The top-right inset sketches the pulse sequence. The bottom-left inset displays P↑ (τwait = 31.4 μs) versus the phase ϕ of the last π/2 pulse for 100 repetitions. For each τwait, we extract the average amplitude of the P↑(ϕ) oscillations and normalize it to the average amplitude in the zero-delay limit. The resulting normalized echo amplitudes are reported on the main plot. The dashed curve is a fit to \(\exp (-{({\tau }_{{{{\rm{wait}}}}}/{T}_{2}^{\mathrm{E}})}^{\beta })\) with β = 1.5 ± 0.1. b, Measured \({T}_{2}^{{{{\rm{E}}}}}\) versus magnetic field angle θzx (symbols). The solid line is a fit to equation (1), using the experimental LSESG1 and LSESG2 from Fig. 2a–d. c, Normalized CPMG amplitude as a function of free evolution time τwait for different numbers Nπ of π pulses (curves are offset for clarity). The solid lines are fits to the same exponential decay function as in a with β = 1.5. d, Extracted \({T}_{2}^{{{{\rm{CPMG}}}}}\) as a function of Nπ. The dashed line is a linear fit with slope γ = 0.34. The inset sketches the CPMG pulse sequence: Nπ equally spaced πy pulses between two πx/2 pulses. For the Hahn-echo, we detune the phase of the last pulse.
