Figure 1: Measurement of quantum oscillations between three quantum states of three electrons in two quantum dots.

(a) Scanning electron micrograph of a device identical to the one used in the experiment. The scale bar is 200 nm in length. The current I_QPC through the quantum point contact (QPC) is used for charge sensing through a measurement of its transconductance G_L=∂ I_QPC/∂ V_L, where V_L is the voltage on gate L. (b) A typical pulse trace from the output of the Agilent 81134A pulse generator, with pulse width t_p. (c) Diagram of energy levels of the system versus detuning ε. The (2,1) state |0 anticrosses with the (1,2) states |2 and |3 with tunnel couplings Δ₁ and Δ₂. The two anticrossings are separated by an energy of δE_R, which is the singlet-triplet energy splitting in the right dot. Colours correspond to features in the data described in (e). (d) Measurement of the transconductance through the QPC, which reflects changes in the charge occupation of the double dot, as a function of pulse duration t_p and detuning of the pulse tip ε_p. (e) Data from (d) in which different oscillation frequencies are highlighted in colour. The orange features at small detuning with frequency ~5 GHz are charge qubit oscillations^8,9,10,17,18 between the states |0 and |2. The pink features with frequency ~9 GHz that occur at larger values of the detuning reflect phase winding between states |2 and |3. (f) Results of the calculated quantum dynamics (see Methods for details) of a system with energy separation between |2 and |3 of δE_R=9.2 GHz and tunnel couplings Δ₁=2.62 GHz and Δ₂=3.5 GHz, including low-frequency noise in detuning as in Petersson et al.⁸ (g) Left: Bloch sphere of the projection of the wavefunction onto the |2, |3 subspace with the trajectory of the state vector during the ε_p-portion of the pulse mapped out for the case of ε_p=100 μeV. Right: the relative position of the pulse and the energy diagram for the data point labelled with pink pentagon (ε_p=100 μeV, t_p=800 ps) in (f). (h) Top: computed time evolution of the diagonal elements of the density matrix during the pulse for the data point labelled with pink pentagon in (f). The rising edge of the pulse increases the population of states |2 and |3 to 70 and 23%, respectively. Bottom: Time evolution of off-diagonal terms in the density matrix for the data point labelled with pink pentagon in (f). Relative phase oscillations between the two states during the ε_p-portion of the pulse are clearly visible. (i) The relative phase θ₂₃ of states |2 and |3, taken at the half point of the falling edge of the pulse, as a function of pulse width and the probability of measuring (1,2) charge occupation as a function of pulse width. The two curves are well correlated with each other, indicating the phase oscillation information during the pulse is mapped to charge probability by the falling edge of the pulse.