Flux-tunable heat sink for quantum electric circuits

Abstract

Superconducting microwave circuits show great potential for practical quantum technological applications such as quantum information processing. However, fast and on-demand initialization of the quantum degrees of freedom in these devices remains a challenge. Here, we experimentally implement a tunable heat sink that is potentially suitable for the initialization of superconducting qubits. Our device consists of two coupled resonators. The first resonator has a high quality factor and a fixed frequency whereas the second resonator is designed to have a low quality factor and a tunable resonance frequency. We engineer the low quality factor using an on-chip resistor and the frequency tunability using a superconducting quantum interference device. When the two resonators are in resonance, the photons in the high-quality resonator can be efficiently dissipated. We show that the corresponding loaded quality factor can be tuned from above 10⁵ down to a few thousand at 10 GHz in good quantitative agreement with our theoretical model.

Figure 1

Sample structure. (a) Optical top image of the measured sample. (b) False-colour scanning electron microscope image of the coupling capacitor between the two resonators, and (c) between Resonator 1 (light blue) and the port to the external transmission line (dark blue). (d) Two micrographs of the SQUID loop highlighted in blue and the junctions highlighted in red. (e) Two micrographs of the termination Cu resistor (red). (f) Electrical circuit diagram of the sample. Resonators 1 and 2 with characteristic impedances Z₀ are coupled to each other by a coupling capacitance C_T and to external transmission lines with characteristic impedance Z_L by capacitances C_C. The inductance of the SQUID is denoted by L, and the termination resistance by R. The SQUID is connected to the centre conductor of Resonator 2 line with capacitances C_L, and the resistor to centre conductor and ground with C_R1 and C_R2, respectively. The lengths of the resonator sections are denoted by x_1/2. The image in panel (a) is from Sample A, and those in panels (b)–(e) from Sample B.

Figure 2

Resonances of Sample A. (a,b) Experimental and (c,d) computational (a,c) amplitude and (b,d) phase of the scattering parameter S₂₁ for the first four modes of Resonator 1 as functions of frequency and magnetic flux. The amplitude of S₂₁ in each subpanel is normalized independently by dividing with the corresponding maximum amplitude. The power in the measurements is approximately −90 dBm at Port 1. The resonance frequencies at half flux quantum are given above the panels, and the simulation parameters are given in Table 1. The measured mode 1 has a lower signal-to-noise ratio compared to the other modes due to unintentional loss near 2.5 GHz in the measurement setup.

Figure 3

Quality factors of Resonator 1 and resonances of Resonator 2 for Sample A. (a) Measured loaded quality factor, Q_L, for mode 2 (blue circles) and for mode 4 (red squares) as functions of the magnetic flux through the SQUID together with the simulated values (dashed line and dash-dotted line, respectively). (b) Absolute value of the simulated scattering parameter S₂₁ of Sample A with only Resonator 2, i.e., at the limit C_C → ∞. The colour bar is truncated at 0.999 for clarity. (c) Measured loaded quality factor, Q_L, of Sample A (markers) for the first four modes as functions of power at Port 1. (d) Measured Q_L of Sample A (circles), predicted external quality factor, Q_ext, (squares) and calculated internal quality factor, Q_int, (triangles) as functions of the mode number. The simulation parameters are given in Table 1. In (a), the power at Port 1 is approximately −90 dBm, and in (d) −85 dBm. In (c) and (d), the magnetic flux through the SQUID is Φ/Φ₀ = 0.5.

Figure 4

Effect of the termination resistance. Simulated (a) amplitude, and (b) phase of mode 4 in Sample A as functions of frequency and magnetic flux with different resistance values, R, as indicated above the panels. The resonance frequency is f₄ = 9.9 GHz, and the other parameters are given in Table 1.