Fig. 4. Time domain measurements of the qubit transition.

a Measurement sequence, plotted in gate voltage–B_|| plane (top) and in gate-voltage time diagram (bottom). The state is initialized on the $∣N⟩$ ↔ $∣B⟩$ Coulomb blockade (CB) line (red, star marks initialization point). Voltage on the center three gates is rapidly ramped to a value V_probe, dwelling a time τ_probe, and then ramped back to the original point on the CB line, dwelling a time τ_read,init. The sequence is repeated periodically. b Conductance averaged over the above sequence, $⟨G⟩$, measured as a function of V_probe (blue) and the quasi-DC conductance, G(red), measured at the same point in V_G. c Bright state return probability, $⟨P_B⟩$ as a function of V_probe, determined from $⟨G⟩$ and G in panel b (see text). d Similar measurement of $⟨G⟩$ but now as a function of V_probe and B_||. A red peak is visible at the location of the Coulomb blockade peak and a much narrower blue dip appears along a line that corresponds to the $∣D⟩$ ↔ $∣B⟩$ crossing. Both a fast traverse to a point before this line (marked 1) or after this line (marked 3) do not alter the state of the system from its initialized $∣B⟩$ state, however, a fast traverse to a point on the line (marked 2) results in occupation of the $∣D⟩$ state with a significant probability. The corresponding traverses in energy are shown in the side panels. e Left: The change in spatial charge distribution at the $∣D⟩$ ↔ $∣B⟩$ transition, ρ_BD(x), imaged using gate resolved capacitance shift imaging of this line (as outlined in Fig. 3a). Right: The difference between the the spatial charge distributions measured at the $∣N⟩$ ↔ $∣B⟩$ and $∣N⟩$ ↔ $∣D⟩$ transitions, ρ_NB(x) − ρ_ND(x), taken from Fig. 3c and d, strongly resembling the directly imaged ρ_BD(x) in the left panel, further confirming that the narrow line corresponds to the $∣D⟩$ ↔ $∣B⟩$ transition.