Figure 1

Experimental device: a transmon qubit coupled to a nonlinear superconducting cavity. (a) Circuit diagram of the device; the anharmonic resonator is formed from a meander inductor embedded with a Josephson junction and an interdigitated capacitor. The resonator is isolated from the 50 $\Omega$ environment by coupling capacitors $C_{\mathrm{c}}$ and coupled to a transmon qubit characterized by Josephson and charging energy scales $E_{\mathrm{J}}$ and $E_{\mathrm{C}}$ respectively. The coupling rate is $g$. (b) False color scanning electron micrograph of the device with the resonator and qubit junctions (lower and upper insets).Reuse & Permissions

Figure 2

Energy levels and the effective nonlinearity $\lambda$ of the strongly coupled system. (a) The measured coefficient of nonlinear response for a strongly coupled system versus qubit-cavity detuning for the qubit prepared in the ground state in the low excitation regime. Theory curves for Eq. (1) with $N_l=2$ (blue), $N_l=3$ (gray), and for a model of coupled nonlinear classical oscillators (red) are shown. The arrows indicate the locations of avoided crossings of the level pairs $|1,3\rangle \leftrightarrow |0,4\rangle$ and $|1,4\rangle \leftrightarrow |0,5\rangle$. (Inset) The transmission of the resonator when driven with tone at ${\omega }_{\mathrm{d}}$ that populated the resonator with $\overline{n}=0.4$ (black) and $\overline{n}=10$ (gray) off-resonant photons. (b) Energy levels of the qubit-oscillator model with $N_l=7$ show the avoided crossings in the 4 and 5 excitation manifold. (c) Quantum trajectory simulation of the system exhibits a general trend of increasing effective nonlinearity $\lambda$ with diminishing qubit-cavity detuning ($\Delta$) with abrupt reductions associated with avoided crossings in the 4 and 5 excitation manifold. For these simulations, the qubit energy levels were modeled as a Duffing nonlinearity.Reuse & Permissions

Figure 3

(a) The transmitted magnitude for chirp sequences with drive voltages that were above (black), near (dashed), and below (gray) the AR threshold. (Inset) Pulse sequence: the qubit manipulation pulse was applied immediately before the start of the chirp sequence. (b) The average transmitted magnitude near 400 ns vs drive voltage shows $S_{|0\rangle }$ (black) and $S_{|1\rangle }$ (red) for $\Delta /2\pi =0.59$ GHz.Reuse & Permissions

Figure 4

Measured autoresonance threshold sensitivity on the level structure and initial qubit state. (a) Color plot shows $S_{|1\rangle }$ versus qubit detuning. The dashed line indicates the AR threshold $V_{|1\rangle }$. AR measurements were not taken for small values of the detuning as indicated by the hatched region. (b) Color plot of $S_{|0\rangle }$ with $V_{|0\rangle }$ indicated as a solid black line. The AR threshold $V_{|1\rangle }$ is also plotted for comparison as a dashed black line. The two arrows indicate the location of avoided crossings in the 4 and 5 excitation manifold.Reuse & Permissions