Figure 1

(a) Circuit diagram for the phase qubit, coupler, and resonator. The qubit parameters are $L_{Jq}\simeq 550\mathrm{pH}$, $I_{q0}\simeq 0.6\mu \mathrm{A}$, $L_q\simeq 1000\mathrm{pH}$, $C_s\simeq 0.6\mathrm{pF}$, $C_{Jq}\simeq 0.3\mathrm{pF}$, and $M_{qc}\simeq 60\mathrm{pH}$. The coupler parameters are $L_{Jc}\simeq 370\mathrm{pH}$, $I_{c0}\simeq 0.9\mu \mathrm{A}$, $L_c\simeq 200\mathrm{pH}$, and $C_{Jc}\simeq 0.3\mathrm{pF}$. The resonator parameters are $L_r\simeq 1000\mathrm{pH}$, $C_r\simeq 0.4\mathrm{pF}$, and $M_{cr}\simeq 60\mathrm{pH}$. (b) Optical micrograph of the circuit.Reuse & Permissions

Figure 2

Measured dependence of $I_c$, ${\omega }_r$, and $g_c$ on applied coupler flux, ${\Phi }_x/{\Phi }_0$. The vertical dashed lines bracket the applied flux ranges for the waterfall data shown in Fig. 3. (a) The measured circulating coupler current as a function of applied coupler flux along with the theoretical fit giving ${\beta }_c=0.51$. (b) Measured resonator frequency as a function of applied coupler flux, along with theoretical fit using ${\beta }_c$ extracted from (a). The fit yields ${\omega }_{r0}/2\pi =7.710\mathrm{GHz}$. (c) Measured coupling strength as a function of applied coupler flux along with the theoretical fit using parameters extracted from the theory fits in (a) and (b). Note that the position of zero coupling does not coincide with the coupler biased at its critical current. This is due to a cancelable direct coupling ($g_0\sim 50\mathrm{MHz}$) between the qubit and resonator resulting from their close proximity.Reuse & Permissions

Figure 3

Spectroscopic and time-domain data over the range ${\Phi }_x/{\Phi }_0=-0.462$ to $-0.366$. (a) Waterfall plot of the spectroscopic measurements showing the splitting transition from $g_c(-0.462)/\pi \simeq 50\mathrm{MHz}$ through $g_c(-0.421)/\pi =0$ to $g_c(-0.366)/\pi \simeq 40\mathrm{MHz}$. The inset to the left is a 3D plot of the qubit spectroscopy for applied coupler flux values close to ${\Phi }_x=-0.421$. (b) The corresponding vacuum Rabi measurements demonstrating coherent modulation in the coupling strength $g_c({\Phi }_x)$.Reuse & Permissions

Figure 4

A higher resolution trace of the occupation probability of the qubit excited state $P_e$ when ${\Phi }_x/{\Phi }_0=-0.421$ along with other time-domain measurements that show nonexponential and exponential ($T_1$ decay) behavior when taken at qubit frequencies largely detuned from the resonator. The nonexponential trace shows no evidence of a TLS interaction in the corresponding spectroscopy (not shown).Reuse & Permissions