Ultrastrong Coupling and Coherent Dynamics in a Gate-Tunable Transmon Qubit

Abstract

Ultrastrong light-matter coupling (USC) gives access to exotic quantum phenomena and promises faster quantum gates, yet coherent time-domain control in this regime remains largely unexplored. Here, we realize USC in a hybrid system consisting of an InAs nanowire-based gatemon qubit coupled to a superconducting resonator. Spectroscopy reveals an avoided crossing that cannot be captured by the Jaynes-Cummings (JC) model, as well as photon-number-dependent transitions whose energies deviate markedly from the JC ladder expected in the strong coupling regime. Beyond demonstrating USC, we achieve time-resolved coherent control of the qubit and measure coherence times comparable to gatemons operating outside the USC regime. These results establish that hybrid semiconductor-superconductor qubits can retain coherent control in USC and provide a platform for exploring quantum dynamics and device concepts in this regime.

Figures (6)

• Figure 1: False-color optical and SEM micrographs of the gatemon–resonator device. Zoomed views highlight the superconducting island (red) and the coplanar waveguide resonator (green). The SEM image shows an InAs/Al nanowire junction with a side gate (dark blue), taken from a device similar to the one discussed in the main text; the junction length of the device studied here is approximately 200--250 nm. The circuit schematic defines the variables used in the model.
• Figure 2: (a) Single-tone spectroscopy as a function of $V_g$. The colormap shows the normalized transmission magnitude, $|S_{21}|$ after background noise subtraction. The inset shows the extracted resonances $f_+$ (blue) and $f_-$ (orange). (b)$f_+$ and $f_-$ ordered as a function of $f_+ + f_- -f_r$. The red rectangle correspond to data from panel (a). The remaining data are obtained from combined two-tone and single-tone spectroscopy measurements (see Supplementary Material). The green (black) line represents $f_r$ ($f_q$ predicted by the JC model). (c) Discrepancy between the $f+-f-$ experimental (black dots) data and the JC fit, $\delta$. The curves correspond to fits using different theoretical models: the quantum Rabi model (dashed gold), the three-level transmon model (solid green), and the full model given by Eq. \ref{['eq:full_coupled_hamiltonian']} with $U(\hat{\varphi}) = -E_J\cos{\hat{\varphi}}$ (dotted pink). The $E_J/E_C$ ratio is shown for reference and is calculated using the full model.
• Figure 3: (a) Two-tone spectroscopy as a function of $V_g$. The inset shows the extracted peak positions (orange dots, green triangles, red squares and purple diamonds), which heuristically correspond to initial states with $m = 0, 1, 2, 3$ photons in the resonator. (b) Energy-level diagram of the uncoupled (dotted grey) and coupled (solid black) resonator-qubit system for different photon numbers. The colored arrows depict the qubit $|0\rangle \rightarrow |1\rangle$ transition, whose frequency decreases as $m$ increases. (c) Schematic comparison of the dispersive shifts in the strong and ultrastrong coupling regimes. The transition spacing in the latter depends on the resonator photon number. (d) Transition frequencies extracted from (a) compared to the two-tone spectra (dotted-black) calculated using the potential in Eq. \ref{['eq:abs_potential']}.
• Figure 4: Coherent Rabi oscillations as a function of (a) the drive pulse duration and amplitude ($f_q = 2.598$ GHz and $V_g=3.184$ V), and (b) the drive frequency and pulse duration ($V_g = 3.174$ V). (c)$T_1$ relaxation measurement taken at same $V_g$ and $f_q$ as (a). (d) Ramsey oscillations as a function of drive frequency and delay between two consecutive $\pi/2$ pulses. Lower panel displays a line cut at a drive frequency of 2.607 GHz. Measurement taken at the same $V_g$ as (b). All measurements were taken around the same sweet spot with small variations in $V_g$ and $f_q$ arising from gate hysteresis and frequency drift.
• Figure 5: Phase of the resonator $S_{21}$ signal measured while applying a tone at $f_r - 2~MHz$ and as a function of the frequency of a drive tone applied near the qubit transition frequency. Panels (a)-(h) correspond to increasing input power of the first tone in 3 dB steps. Dotted red lines in (c) indicate the expected position of the photon-number–resolved transitions.