We investigate nondegenerate parametric oscillations in a multimode superconducting microwave resonator that is terminated by a SQUID. The parametric effect is achieved by modulatingmagnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonance tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.
In the cavity-QED architecture, photon number fluctuations from residual cavity photons cause qubit dephasing due to the AC Stark effect. These unwanted photons originate from a varietyof sources, such as thermal radiation, leftover measurement photons, and crosstalk. Using a capacitively-shunted flux qubit coupled to a transmission line cavity, we demonstrate a method that identifies and distinguishes coherent and thermal photons based on noise-spectral reconstruction from time-domain spin-locking relaxometry. Using these measurements, we attribute the limiting dephasing source in our system to thermal photons, rather than coherent photons. By improving the cryogenic attenuation on lines leading to the cavity, we successfully suppress residual thermal photons and achieve T1-limited spin-echo decay time. The spin-locking noise spectroscopy technique can readily be applied to other qubit modalities for identifying general asymmetric non-classical noise spectra.
We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated in the quantum regime, kBT≪ℏω. The resonator is terminatedby a tunable inductance that provides a Kerr-type nonlinearity. We detected the output field quadratures at frequencies near the fundamental mode, ω/2π∼5GHz, when the resonator was driven by a current at 3ω with an amplitude exceeding an instability threshold. The output radiation was red-detuned from the fundamental mode. We observed three stable radiative states with equal amplitudes and phase-shifted by 120∘. The downconversion from 3ω to ω is strongly enhanced by resonant excitation of the second mode of the resonator, and the cross-Kerr effect. Our experimental results are in quantitative agreement with a model for the driven dynamics of two coupled modes.
We present a new read-out technique for a superconducting qubit dispersively coupled to a Josephson parametric oscillator. We perform degenerate parametric flux pumping of the Josephsoninductance with a pump amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillations: one oscillating state, with on average 180 photons in the resonator, and one with zero oscillation amplitude. We demonstrate single-shot readout performance, with a total state discrimination of 81.5%. When accounting for qubit errors, this gives a corrected fidelity of 98.7%, obviating the need for a following quantum-limited amplifier. An error budget indicates that the readout fidelity is currently limited by spurious switching events between two bistable states of the resonator.
We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on a superconducting lambda /4 resonator, and is terminated by a flux-tunable SQUID.We extract parameters for two devices. In particular, we study the effect of the nonlinearities in the system and compare to theory. The Duffing nonlinearity, \alpha, is determined from the probe-power dependent frequency shift of the oscillator, and the nonlinearity, \beta, related to the parametric flux pumping, is determined from the pump amplitude for the onset of parametric oscillations. Both nonlinearities depend on the parameters of the device and can be tuned in-situ by the applied dc flux. We also suggest how to cancel the effect of \beta by adding a small dc flux and a pump tone at twice the pump frequency.