Cavity Attenuators for Superconducting Qubits

Dephasing induced by residual thermal photons in the readout resonator is a leading factor limiting the coherence times of qubits in the circuit quantum electrodynamics architecture. This residual thermal photon, on the order of ${10}^{-1}$–${10}^{-3}$, is suspected to arise from noise impinging on the resonator from its input and output ports. To address this problem, we designed and tested a new type of band-pass microwave attenuator that consists of a dissipative cavity well thermalized to the mixing chamber stage of a dilution refrigerator. By adding such a cavity attenuator in-line with a three-dimensional superconducting cavity housing a transmon qubit, we have reproducibly measured increased qubit coherence times. At base temperature, through a Hahn echo experiment, we measured $T_{2e}/2T_1=1.0\begin{array}{c}+0.0\\ -0.1\end{array}$ for two qubits over multiple cooldowns. Through noise-induced dephasing measurement, we obtained an upper bound of $2\times {10}^{-4}$ on the residual photon population in the fundamental mode of the readout cavity, which to our knowledge is the lowest value reported so far. These results validate an effective method for protecting qubits against photon noise, which can be developed into a standard technology for quantum circuit experiments.

Figure 1

Comparison of the electromagnetic fields outside and currents inside (a) a lumped-element resistor and (b) a dissipative waveguide section (TE mode). Blue and green arrows indicate electric and magnetic field lines, while yellow and red arrows indicate electric current ${\mathbf{j}}_e$ and heat current ${\mathbf{j}}_h$, respectively.

Figure 2

Brass cavity attenuator. (a) Photograph of the device. (b) Cross-section drawing of the thin seamless cavity. (c) Enlarged optical micrograph. (d) Cavity transmission at room temperature.

Figure 3

Test of an attenuator with a transmon-cavity system. (a) Measurement setup anchored to the base stage of a dilution refrigerator. A transmon qubit (green) is dispersively coupled to the fundamental mode of an aluminum readout cavity (blue), which is itself coupled to a cavity attenuator (orange) through an aperture. Between the two hybridized modes, the one with greater participation in the aluminum cavity is used to measure the qubit in reflection through the standard circuit QED dispersive readout. See Fig. 8 for a detailed wiring diagram of the cryostat. (b) Photograph of the coupled cavities. The transmon is held inside the aluminum cavity (left). The cavity attenuator (middle) is coupled to the microwave lines through a coaxial cable coupler (right). See Fig. 7 for a 3D interior drawing of this assembly. (c) Cavity reflection at 13 mK showing the hybridized modes. The color bar indicates the participation of the mode in the aluminum (blue) and brass (orange) cavities.

Figure 4

Qubit coherence data. (a) $T_1$, (b) Hahn echo $T_{2e}$, and (c) $T_{2e}/2T_1$ versus temperature with and without cavity attenuators. All the data are collected on transmon A. Error bars include both the measurement imprecision and the fluctuation of $T_1$ over the 1 h data acquisition time. Red circles represent the data without attenuator. Yellow circles represent the data with a 75-$\mu$m-gap aluminum cavity attenuator. Blue circles represent the data with a 300-$\mu$m-gap brass cavity attenuator. Green circles represent the data with a 75-$\mu \mathrm{m}$-gap copper cavity attenuator.

Figure 5

Consistency of $T_{2e}/2T_1$ across multiple samples and cooldowns when the qubits are protected by 300-$\mu \mathrm{m}$-gap brass cavity attenuators. For transmon B, $T_1\approx 50\pm 10\mu \mathrm{s}$ below 100 mK.

Figure 6

Noise-induced dephasing measurement of ${\overline{n}}_{\mathrm{th}}$ in the readout mode. (a) Transmon A protected by a 75-$\mu \mathrm{m}$-gap copper cavity attenuator. (b) Transmon B protected by a 125-$\mu \mathrm{m}$-gap copper cavity attenuator. $T_1$ (blue squares) and $T_{2e}$ (green diamonds) are plotted versus added thermal photon number $n_{\mathrm{add}}$. The extracted $T_{\varphi }$ values (red circles) are shown together with a fit (solid curve). Purple shading represents the fitting error within one standard deviation.

Figure 7

Interior drawing of the readout cavity (blue)–cavity attenuator (orange)–waveguide coupler–coaxial cable assembly. The transmon qubit is on the sapphire chip (green). The enlargement is a cross-section view of the cavity attenuator and the coupling aperture between the two cavities.

Figure 8

Cryogenic wiring diagram with simplified room-temperature microwave electronics. The bottommost segment of the leftmost input line is dashed since it is only connected in the second control experiment reported in Sec. 3.