Autler-Townes splitting in a three-dimensional transmon superconducting qubit

We have observed the Autler-Townes doublet in a superconducting Al/AlO${}_X$/Al transmon qubit that acts as an artificial atom embedded in a three-dimensional Cu microwave cavity at a temperature of 22 mK. Using pulsed microwave spectroscopy, the three lowest transmon levels are isolated, eliminating unwanted effects of higher qubit modes and cavity modes. The long coherence time ($\sim$$40\mu \text{s}$) of the transmon enables us to observe a clear Autler-Townes splitting at drive amplitudes much smaller than the transmon level anharmonicity (177 MHz). Three-level density matrix simulations with no free parameters provide excellent fits to the data. At maximum separation, the fidelity of a dark state achieved in this experiment is estimated to be $99.6\%–99.9\%$.

Figure 1

(a) Energy level diagram for the transmon indicating the levels and microwave drives. (Inset) Optical micrograph of transmon showing Al pads (light gray) on sapphire (dark gray). (b) Cavity transmission at ${\omega }_{\mathrm{cav}}/2\pi =7.1585\text{GHz}$ after the transmon is prepared in state $|0\rangle$ (black line), $|1\rangle$ (blue dash) or $|2\rangle$ (magenta dots). Vertical dashed lines indicate drive powers $P_a$ used in the AT experiment to achieve the readout proportional to ${\rho }_{11}+{\rho }_{22}$, and $P_b$ to readout ${\rho }_{22}$ for ${\omega }_{12}$ calibration. (c) Spectroscopic measurements (black dots) and fit (red line) of ${\omega }_{01}$. Note small shoulder at $4.292$ GHz near the 0-to-1 transition peak at $4.294$ GHz. (d) Spectroscopic measurements (black dots) and fit (red line) of ${\omega }_{12}$.

Figure 2

(a)–(c) Data and (d)–(f) simulations of the AT splitting for several coupler powers. Coupler strengths are (a), (d) 0.177 MHz; (b), (e) 0.707 MHz; (c), (f) 2.82 MHz. To account for larger peak separation, the scale is increased on the bottom row of plots.

Figure 3

Data (black dots) and simulation (red line) of the AT doublet at ${\Delta }_c=0$. Coupler strengths are (a) 0.354 MHz, (b) 0.707 MHz, (c) 1.41 MHz, (d) 2.82 MHz, (e) 5.63 MHz, (f) 11.2 MHz.

Figure 4

Dark-state fidelity inferred from simulations versus coupler power (black dots), and theoretical fidelity (colored lines) for a system with ${\Gamma }_{21}^{\prime }={\Gamma }_{21}/2^n$, $n=0,1,...,9$ (red to violet). A crossover to ${\Gamma }_{21}\ll {\Gamma }_{10}$ regime where EIT is possible manifests in the increased fidelity even at small ${\Omega }_c/{\Omega }_p$.