Raising the Cavity Frequency in cQED

TL;DR

This work demonstrates the feasibility of raising the cavity frequency in cQED to the 21 GHz range while preserving a strong dispersive interaction with a fixed-frequency transmon and maintaining state-of-the-art coherence. By combining CKP spectroscopy with repeated-readout tests, the authors show MHz-scale dispersive shifts, readout efficiencies up to ~8%, and T1 values exceeding 100 μs across multiple devices, with some devices reaching >350 μs. The results argue for transformative advantages of high-frequency cavities, including reduced thermal photon populations and potential resilience to higher operating temperatures, while outlining paths to further suppress leakage and push toward ultra-dispersive regimes. This paves the way for exploring high-frequency cavity QED in the microwave K-band and motivates further development of packaging and readout strategies to harness these benefits in scalable quantum architectures.

Abstract

The basic element of circuit quantum electrodynamics (cQED) is a cavity resonator strongly coupled to a superconducting qubit. Since the inception of the field, the choice of the cavity frequency was, with a few exceptions, been limited to a narrow range around 7 GHz due to a variety of fundamental and practical considerations. Here we report the first cQED implementation, where the qubit remains a regular transmon at about 5 GHz frequency, but the cavity's fundamental mode raises to 21 GHz. We demonstrate that (i) the dispersive shift remains in the conventional MHz range despite the large qubit-cavity detuning, (ii) the quantum efficiency of the qubit readout reaches 8%, (iii) the qubit's energy relaxation quality factor exceeds $10^7$, (iv) the qubit coherence time reproducibly exceeds $100~μ\rm{s}$ and can reach above $300~μ\rm{s}$ with a single echoing $π$-pulse correction. The readout error is currently limited by an accidental resonant excitation of a non-computational state, the elimination of which requires minor adjustments to the device parameters. Nevertheless, we were able to initialize the qubit in a repeated measurement by post-selection with $2\times 10^{-3}$ error and achieve $4\times 10^{-3}$ state assignment error. These results encourage in-depth explorations of potentially transformative advantages of high-frequency cavities without compromising existing qubit functionality.

Figures (8)

• Figure 1: (a) Scanning electron micrographs of the transmon device, showing the AlOx Josephson junction and the Nb capacitor electrodes. (b) Photograph of a rectangular aluminum cavity (made of two pieces) in the two-port transmission measurement configuration. (c) Schematic of Si chip containing a transmon circuit placed inside a 3D rectangular cavity. The electric dipole of the transmon is oriented along the z-dimension. (d) Measured room-temperature transmission $S_{21}$ of the cavity containing a qubit chip. (e) Transmon energy levels and wavefunctions inside the Josephson potential. The parameters used in the simulation are from device C. The magenta dashed line indicates the cavity frequency $\omega_r/2\pi$. (f) Theoretical scaling of the qubit-cavity coupling constant $g$ as the cavity dimensions are scaled down. (g) Estimation of the dependence of the dispersive shift $2\chi$ on the cavity frequency (Eqn. \ref{['eq:chi']}) as the cavity's dimensions are scaled down. The transmon parameters remain fixed.
• Figure 2: (a) The pulsed ac Stark shift calibration of cavity drive power. The qubit frequency shift, $\delta \omega_{01}$, is linear with cavity photon number and can be used less ambiguously to indicate the relative readout power. (b) The measurement-induced dephasing rate ($\Gamma_m$) for low cavity photon numbers. The dependence of $\Gamma_m$ on $\bar{n}$ is linear, with the fit values of $\chi$ and $\kappa$ within 10 percent of the values extracted from CKP measurement. (c) The simultaneous fits of the spectroscopy drive, $\omega_{01,d}^*$, with the qubit initially prepared in $|g\rangle$ or $|e\rangle$. The fits are performed simultaneously using Eqn.\ref{['eq:CKP']} with $\chi$, $\kappa$, and $\omega_r/2\pi$ as the free parameters.
• Figure 3: (a) Single-shot-histogram of Device C starting in equilibrium for two values of mean photon number $\bar{n}$ and integration time $\tau$. (b) Same as (a) but with a $\pi_{ge}$-pulse applied prior to the measurement. Note the angle $\theta_{eg}$ is independent on the choice of $\bar{n}$. (c) The $\mathrm{SNR}$ per photon vs $\tau$ extracted from the single-shot data. Note the data respects linear dependence of $\mathrm{SNR}$ on both $\tau$ and $\bar{n}$ in a broad range of values. Furthermore, the efficiency is independent of mean photon number.
• Figure 4: Results of 4 repeated measurement protocols corresponding to initializing the qubit in states $|g\rangle$ (a); $|e\rangle$ (b); $|f\rangle$ (c); and $|h\rangle$ (d); and observing the measurement outcome. The colored "x" represents the center of each states blob extracted from a calibration measurement. (d) A histogram of the three data sets above versus angle from the negative x-axis. We use the threshold shown by the black dashed line to separate the outcomes corresponding to $|g\rangle$ state from outcomes corresponding to non-$|g\rangle$ state (in this case $|f\rangle$-state) to define both the initialization error and the assignment error. Notice the suppressed leakage tail in the $|g\rangle$-state histogram in comparison to the higher states.
• Figure 5: (a) Coherence of device C. The fitted data are from an interleaved measurement with the energy relaxation $T_1 = 250 \pm 3 ~\mu$s, $T_2^E = 307 \pm 11 ~\mu$s. The Ramsey fringe is fit with $T_2^* = 112 \pm 4 ~\mu$s. (b) Indexed interleaved $T_1$ and $T_2^E$ results for all devices. When $T_1$ increases so does $T_2^E$ indicating the same mechanism limiting energy relaxation could also limit the coherence. The indexed time domain measurements include 200 points per device; fluctuates are seen simulataneously for the interleaved $T_1$ and $T_2^E$ values where the ratio $T_2^E/2T_1<1$. (c) A spin locking measurement shows residual cavity photons $\bar{n} < 10^{-3}$ (purple data). A coherent cavity tone was applied for the other data sets to demonstrate the validity of the experiment. (d) From the attenuation of the drive line starting at 4 K, there is no significant change to the residual cavity photon number for a 21 GHz cavity if the last attenuator is at 10 mK (gray line) or at 100 mK (blue line). Likewise if the readout line (circulators) were thermalized to 100 mK this would not be the limit of measuring with a 21 GHz cavity (yellow star).