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Physical Review Letters

Tunable Resonant and Nonresonant Interactions between a Phase Qubit and L C Resonator

Michael S. Allman, Jed D. Whittaker, Manuel A. Castellanos-Beltran, Katarina Cicak, Fabio Teixeira Ferreira da Silva, M. P. DeFeo, Florent Lecocq, Adam J. Sirois, John D. Teufel, José Aumentado, Raymond W. Simmonds

Published Mar 26, 2014• 74 citations
Publisher

Abstract

We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.

DOI
10.1103/physrevlett.112.123601

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We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.
We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. The coupling strength is mediated by a flux-biased rf SQUID operated in the nonhysteretic regime. By tuning the applied flux bias to the rf SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator. We verify the modulation of coupling strength from 0 to 100 MHz by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillation frequency when on resonance. The measured spectroscopic splittings and vacuum Rabi oscillations agree well with theoretical predictions.
Abstract Here we consider a tunable superconducting cavity that can be used either as a tunable coupler to a qubit inside the cavity or as a tunable low noise, low temperature, RF filter. Our design consists of an array of radio-frequency superconducting quantum interference devices (rf SQUIDs) inside a superconducting cavity. This forms a tunable metamaterial structure which couples to the cavity through its magnetic plasma frequency. By tuning the resonant frequency of the metamaterial through an applied magnetic flux, one can tune the cavity mode profile. This allows us to detune the cavity initially centered at 5.593 GHz by over 200 MHz. The maximum quality factor approaches that of the empty cavity, which is 4.5 × 106. The metamaterial electromagnetic response is controlled via a low-frequency or dc magnetic flux bias, and we present a control line architecture that is capable of applying sufficient magnetic flux bias with minimal parasitic coupling. Together this design allows for an in-situ tunable cavity which enables low-temperature quantum control applications.
We have prepared meta-atoms based on radio-frequency superconducting quantum-interference devices (rf SQUIDs) and examined their tunability with dc magnetic field, rf current, and temperature. rf SQUIDs are superconducting split-ring resonators in which the usual capacitance is supplemented with a Josephson junction, which introduces strong nonlinearity in the rf properties. We find excellent agreement between the data and a model that regards the Josephson junction as the resistively and capacitively shunted junction. A magnetic field tunability of 80 THz=G at 12 GHz is observed, a total tunability of 56% is achieved, and a unique electromagnetically induced transparency feature at intermediate excitation powers is demonstrated for the first time. An rf SQUID metamaterial is shown to have qualitatively the same behavior as a single rf SQUID with regard to dc flux and temperature tuning.
This thesis presents a detailed investigation of coherent tunable coupling between two coupled quantum circuits. Quantum circuits have the potential to be used as the fundamental building blocks in quantum processors. Any large scale quantum processor will be composed of a large number of these coupled circuits. The efficient implementation of quantum algorithms will be difficult without a reliable mechanism for controlling the interaction strength between coupled systems, while preserving the delicate quantum information stored in the coherent superpositions of quantum states. We show that a flux-biased rf-SQUID can be used to coherently mediate the interaction between two coupled quantum circuits, a phase qubit and LC resonator. This interaction results from an effective mutual inductance between the qubit and resonator as a result of their direct coupling to the rf-SQUID. The sign and magnitude of this effective mutual inductance can be tuned with applied flux to the rf-SQUID, thus controlling the coupled interactions over a large range. We observe the modulation in coupling strength using measurements in both the frequency and time domains. The measurements are shown to agree well with theoretical predictions. This thesis discusses all aspects of the experiments from a theoretical description of each component to the design, fabrication, experimental setup and measurements.
We present a design and implementation of a frequency-tunable superconducting resonator. The resonance frequency tunability is achieved by flux-coupling a superconducting LC loop to a current-biased feedline; the resulting screening current leads to a change of the kinetic inductance and shift in the resonance frequency. The thin-film aluminum resonator consists of an interdigitated capacitor and thin line inductors forming a closed superconducting loop. The magnetic flux from the nearby niobium current feedline induces Meissner shielding currents in the resonator loop leading to a change in the kinetic part of the total inductance of the resonator. We demonstrate continuous frequency tuning within 160 MHz around the resonant frequency of 2.7 GHz. We show that: (1) frequency up-conversion is achieved when a kilohertz ac modulation signal is superimposed onto the dc bias resulting in sidebands to the resonator tone; (2) three-wave mixing is attained by parametrically pumping the nonlinear kinetic inductance using a strong rf pump signal in the feedline. The simple architecture is amenable to large-array multiplexing and on-chip integration with other circuit components. The concept could be applied in flux magnetometers, up-converters, and parametric amplifiers operating above 4 K when alternative high-critical-temperature material with high kinetic inductance is used.
We investigate the ultrastrong tunable coupler for coupling of superconducting resonators. The obtained coupling constant exceeds 1 GHz, and the wide-range tunability is achieved for both antiferromagnetics and ferromagnetics from $\ensuremath{-}1086$ to 604 MHz. The ultrastrong coupler is composed of a rf superconducting quantum interference device (SQUID) and dc SQUID as tunable junctions, which connect to resonators via shared aluminum thin-film meander lines enabling such a huge coupling constant. The spectrum of the coupler obviously shows the breaking of the rotating-wave approximation, and our circuit model treating the Josephson junction as a tunable inductance reproduces the experimental results well. The ultrastrong coupler is expected to be utilized in quantum annealing circuits and/or noisy intermediate-scale quantum devices with dense connections between qubits.