The loss and noise mechanisms of superconducting resonators are useful tools for understanding decoherence in superconducting circuits. While the loss mechanisms have been heavily studied,noise in superconducting resonators has only recently been investigated. In particular, there is an absence of literature on noise in the single photon limit. Here, we measure the loss and noise of an aluminium on silicon quarter-wavelength (λ/4) resonator in the single photon regime.
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.
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.
Dynamical error suppression techniques are commonly used to improve coherence in quantum systems. They reduce dephasing errors by applying control pulses designed to reverse erroneouscoherent evolution driven by environmental noise. However, such methods cannot correct for irreversible processes such as energy relaxation. In this work, we investigate a complementary, stochastic approach to reducing errors: instead of deterministically reversing the unwanted qubit evolution, we use control pulses to shape the noise environment dynamically. In the context of superconducting qubits, we implement a pumping sequence to reduce the number of unpaired electrons (quasiparticles) in close proximity to the device. We report a 70% reduction in the quasiparticle density, resulting in a threefold enhancement in qubit relaxation times, and a comparable reduction in coherence variability.
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 infer the high-frequency flux noise spectrum in a superconducting flux qubit by studying the decay of Rabi oscillations under strong driving conditions. The large anharmonicity ofthe qubit and its strong inductive coupling to a microwave line enabled high-amplitude driving without causing significant additional decoherence. Rabi frequencies up to 1.7 GHz were achieved, approaching the qubit’s level splitting of 4.8 GHz, a regime where the rotating-wave approximation breaks down as a model for the driven dynamics. The spectral density of flux noise observed in the wide frequency range decreases with increasing frequency up to 300 MHz, where the spectral density is not very far from the extrapolation of the 1/f spectrum obtained from the free-induction-decay measurements. We discuss a possible origin of the flux noise due to surface electron spins.
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.
We present a new method for determining pulse imperfections and improving the
single-gate fidelity in a superconducting qubit. By applying consecutive
positive and negative $pi$ pulses,we amplify the qubit evolution due to
microwave pulse distortion, which causes the qubit state to rotate around an
axis perpendicular to the intended rotation axis. Measuring these rotations as
a function of pulse period allows us to reconstruct the shape of the microwave
pulse arriving at the sample. Using the extracted response to predistort the
input signal, we are able to improve the pulse shapes and to reach an average
single-qubit gate fidelity higher than 99.8%.
In the presence of time-reversal symmetry, quantum interference gives strong
corrections to the electric conductivity of disordered systems. The
self-interference of an electron wavefunctiontraveling time-reversed paths
leads to effects such as weak localization and universal conductance
fluctuations. Here, we investigate the effects of broken time-reversal symmetry
in a driven artificial two-level system. Using a superconducting flux qubit, we
implement scattering events as multiple Landau-Zener transitions by driving the
qubit periodically back and forth through an avoided crossing. Interference
between different qubit trajectories give rise to a speckle pattern in the
qubit transition rate, similar to the interference patterns created when
coherent light is scattered off a disordered potential. Since the scattering
events are imposed by the driving protocol, we can control the time-reversal
symmetry of the system by making the drive waveform symmetric or asymmetric in
time. We find that the fluctuations of the transition rate exhibit a sharp peak
when the drive is time-symmetric, similar to universal conductance fluctuations
in electronic transport through mesoscopic systems.
We implement dynamical decoupling techniques to mitigate noise and enhance
the lifetime of an entangled state that is formed in a superconducting flux
qubit coupled to a microscopictwo-level system. By rapidly changing the
qubit’s transition frequency relative to the two-level system, we realize a
refocusing pulse that reduces dephasing due to fluctuations in the transition
frequencies, thereby improving the coherence time of the entangled state. The
coupling coherence is further enhanced when applying multiple refocusing
pulses, in agreement with our $1/f$ noise model. The results are applicable to
any two-qubit system with transverse coupling, and they highlight the potential
of decoupling techniques for improving two-qubit gate fidelities, an essential
prerequisite for implementing fault-tolerant quantum computing.