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Geometry and characterization of the tunable resonator. (a) Optical micrograph of the circuit. The SQUID tuner (detailed in the bottom-right panel) is inserted in the middle of the CPW transmission line. The size of the SQUID loop is approximately . (b) Simplified schematic circuit diagram for the device. (c) Measured resonator frequency as a function of magnetic flux coupled to the SQUID loop (dots) and fit according to theory (line). Inset is the pulse sequence. We excited the resonator with a 1 μs-long microwave tone (the red sinusoidal) at various frequencies in the 6–7 GHz range while the resonator SQUID was at a fixed flux value (the blue line), and then swapped the excitation into the qubit for readout (the black line). The excitation in the resonator was swapped into the qubit by tuning the two into resonance for a fixed amount of time. The trapezoid pulse at the end of the pulse sequence was to readout the qubit probability. The microwave frequency value corresponding to the maximum qubit response was chosen as the resonator resonance frequency at this SQUID flux. (d) Resonator and as a function of applied magnetic flux in SQUID.
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(a) Swap spectroscopy for a qubit capacitively coupled to a non-tunable CPW resonator. Pulse sequence at top: we excited the qubit with a π pulse (red), tuned the qubit frequency close to the resonator by changing the qubit bias, then after a delay, measured the qubit excited state. Main plot shows probability (color scale) versus delay and qubit bias. Inset displays same data for a qubit-resonator swap spectrum in the absence of a TLS, with a Lorentzian-shaped chevron with clear and continuous swap dependence on qubit frequency; main panel shows the perturbation of the chevron due to the TLS. (b) Single-photon energy dissipation of tunable resonator in Fig. 1 . Pulse sequence at top: we excited the qubit and immediately swapped the excitation into the resonator, then tuned the resonator frequency by changing the flux applied to the embedded SQUID. After a delay time, we swapped the residue excitation from resonator to qubit for measurement. Main panel: measured excited state probability typically decays exponentially with time, with decay time . Arrows indicate chevron-like features consistent with the resonator swapping energy with a defect TLS.
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Benchmark test of the tunable resonator using the n = 1 and n = 2 photon Fock states. The resonator Fock state was generated and probed by (a) and (d) biasing the qubit to the resonator frequency, (b) and (e) biasing the resonator to the qubit frequency, or (c) and (f) biasing both to a sweet frequency point. Shown are the qubit probabilities versus the interaction time for reading out the Fock state (lines are guides to the eye). Schematics of the measurement sequences are shown on top. Red sine waves are π pulses to excite the qubit. Black and blue lines are the qubit flux bias and the resonator SQUID bias used to change their frequencies, respectively. It is seen that biasing both the qubit and the resonator (c) and (f) gives the best result.
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Coherent control of a microscopic TLS via the tunable resonator. (a) Resonator real-time swap spectroscopy showing its interaction with a TLS through the partial Lorentzian pattern. The TLS generates a resonance at 6.85 GHz, as estimated from the resonator frequency at its SQUID bias . The same feature is also observable in Fig. 2(b) (indicated by the green arrow). Its coupling strength to the resonator is 5.49 MHz using a 182 ns 2π-swaptime estimated from the figure. (b) Qubit real-time swap spectroscopy. The Lorentzian feature represents its interaction with the resonator. The qubit is also very weakly coupled to a TLS (indicated by the white arrow) via the resonator-TLS coupling shown in (a). (c) Measurement of the TLS lifetime via the resonator. Inset: Pulse sequence. (d) Measurement of the TLS dephasing time.
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