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arXiv:1001.0816 · Physical Review Letters

rf-SQUID-Mediated Coherent Tunable Coupling between a Superconducting Phase Qubit and a Lumped-Element Resonator

Michael S. Allman, Fabio Altomare, Jed D. Whittaker, Katarina Cicak, Dale Li, Adam J. Sirois, Joshua Strong, John D. Teufel, Raymond W. Simmonds

Published Apr 29, 2010• 89 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.104.177004

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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.
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.
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 realize tunable coupling between two superconducting transmission line resonators. The coupling is mediated by a non-hysteretic rf SQUID acting as a flux-tunable mutual inductance between the resonators. We present a spectroscopic characterization of the device. In particular, we observe couplings g/2πg/2\pig/2π ranging between −320 MHz and 37 MHz. In the case of g≃0g \simeq 0g≃0 , the microwave power cross transmission between the two resonators is reduced by almost four orders of magnitude as compared to the case where the coupling is switched on.
We report on two different manipulation procedures of a tunable rf SQUID. First, we operate this system as a flux qubit, where the coherent evolution between the two flux states is induced by a rapid change of the energy potential, turning it from a double well into a single well. The measured coherent Larmor-like oscillation of the retrapping probability in one of the wells has a frequency ranging from 6 to 20 GHz, with a theoretically expected upper limit of 40 GHz. Furthermore, here we also report a manipulation of the same device as a phase qubit. In the phase regime, the manipulation of the energy states is realized by applying a resonant microwave drive. In spite of the conceptual difference between these two manipulation procedures, the measured decay times of Larmor oscillation and microwave-driven Rabi oscillation are rather similar. Due to the higher frequency of the Larmor oscillations, the microwave-free qubit manipulation allows for much faster coherent operations.
An improved tunable coupling element for building networks of coupled rf-superconducting quantum interference device (rf-SQUID) flux qubits has been experimentally demonstrated. This new form of coupler, based on the compound Josephson-junction rf-SQUID, provides a sign and magnitude tunable mutual inductance between qubits with minimal nonlinear crosstalk from the coupler tuning parameter into the qubits. Quantitative agreement is shown between an effective one-dimensional model of the coupler's potential and measurements of the coupler persistent current and susceptibility.
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.