Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms

We report a superconducting artificial atom with a coherence time of $T_2^{*}=92$ $\mu$s and energy relaxation time $T_1=70$ $\mu$s. The system consists of a single Josephson junction transmon qubit on a sapphire substrate embedded in an otherwise empty copper waveguide cavity whose lowest eigenmode is dispersively coupled to the qubit transition. We attribute the factor of four increase in the coherence quality factor relative to previous reports to device modifications aimed at reducing qubit dephasing from residual cavity photons. This simple device holds promise as a robust and easily produced artificial quantum system whose intrinsic coherence properties are sufficient to allow tests of quantum error correction.

Figure 1

Transmon qubit in three-dimensional copper waveguide cavity with long coherence. (a) Device model (HFSS) showing interior volume of the waveguide enclosure housing a sapphire chip and transmon qubit, with two symmetric coaxial connectors for coupling signals in and out. (b) Eigenmodes of the enclosure with sapphire chip (obtained with HFSS eigenmode solver) illustrating the robustness of the single-mode-cavity approximation. The qubit is positioned at a cavity symmetry point where the electric field of the fundamental mode (TE101) is maximal. Device dimensions and symmetries imply that the next mode interacting with the qubit (TE301) is $>$20 GHz detuned from the qubit. (c) Equivalent circuit diagram of our device. The interior walls of the normal-metal cavity provide an ideal cold resistor (light blue) that is expected to sink the residual cavity photon population to the lowest available temperature. (d) Optical image of the transmon qubit, consisting of two capacitor pads, each 350 $\mu$m $\times$ 700 $\mu$m (outlined in yellow), and separated by a $50\mu$m wire interrupted by a shadow-evaporated Al/AlOx/Al Josephson junction (yellow overlay). Pads are formed of mesh with $5\mu$m wires and 20 $\mu$m $\times$ 20 $\mu$m holes to suppress vortex trapping and motion. (c) Cryogenic microwave measurement setup. Experiments are performed at 10 mK in a BlueFors cryogen-free dilution refrigerator.

Figure 2

Typical quantum state lifetimes. Top: Energy relaxation time with exponential fit (red line); typical obtained times range $T_1=50$–70 $\mu$s. Bottom: Ramsey fringe experiment to determine coherence time with exponentially damped sinusoidal fit (red line); typical obtained times range $T_2^{*}=75$–105 $\mu$s. The range of observed times is much greater than statistical fit errors.