Figure 1

(a) Schematic circuit diagram of inductively-coupled charge qubits. Rectangles with an X inside denote Josephson junctions with corresponding Josephson energy $E_{Ji}$ and junction capacitance $C_i$. The arrow near each junction denotes the chosen direction for the positive phase drop across the corresponding junction. (b) A scanning electron micrograph of a sample. A rectangular-shape electrode indicated by the dotted rectangles is connected to the reservoir and forms a shunt capacitance with the large island in the middle of the picture. The Josephson junction for the qubit coupling, inside the dotted circle, links the reservoir and the large island. Two probe electrodes and a pulse-gate electrode are shown in (b), but not in (a).Reuse & Permissions

Figure 2

(a) Magnetic field dependence of the Josephson quasiparticle current through the two probe electrodes in sample A. The currents become maximum not at zero field because of the constant background field. (b) Coherent oscillations of sample A at the flux bias $f=0.00$. Two probe currents are plotted as a function of the duration time of a nonadiabatic voltage pulse applied to the gate electrode. For clarity, the trace for qubit 1 is offset by $-0.6\mathrm{pA}$.Reuse & Permissions

Figure 3

An example of the spectroscopic measurements. The current through probe electrode 2 is plotted as a function of $n_{g2}$, the normalized gate-induced charge on the gate electrode 2. The dotted curve is the data when no microwave is applied, while the solid curve is the one when a $20\mathrm{GHz}$ microwave is applied. The inset shows the direction of the gate sweep in the $(n_{g1},n_{g2})$ plane.Reuse & Permissions

Figure 4

Results of the spectroscopic measurement for qubit 2 of sample A under the flux biases (a) $f=0.00$, (b) $f=0.25$, and (c) $f=0.37$. The black dots represent the positions of the photon-assisted Josephson quasiparticle peaks at the corresponding frequencies of the applied microwave.Reuse & Permissions

Figure 5

(Color online) (a) Energy spectrum of the coupled-qubit system for $f=0$ and $n_{g2}=(1.0n_{g1}-0.11)$. (b) Energy spectrum of the coupled-qubit system for $f=0.37$ and $n_{g2}=(1.0n_{g1}-0.21)$. The energy bands with zero-photon state for the plasma mode of the coupling junction are shown in thin (red) lines. Four arrows indicate the positions where anticrossings, due to the coupling between one of the two qubits and the plasma mode of the coupling junction, are observed. Two of them shown in dotted (red) lines correspond to the anticrossings observed in the experiment. A small dotted circle shows the anticrossing due to the coupling between the qubits via the coupling junction.Reuse & Permissions

Figure 6

(Color online) Comparison between the theory and the experimental data from the spectroscopic measurements. Black dots are the experimentally obtained positions of photon-assisted Josephson quasiparticle peaks and the (red) solid lines are the results of energy-band calculations.Reuse & Permissions

Figure 7

Observed “center frequency” and minimum energy gap of the anticrossing as a function of the reduced flux bias $f$. Only the data for qubit 2 is used. The dotted lines show the theoretical predictions from energy-band calculations.Reuse & Permissions