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arXiv:1508.06758 · EPJ Quantum Technology

Tunable coupling of transmission-line microwave resonators mediated by an rf SQUID

F. Wulschner, Jan Goetz, Fabian R Koessel, Elisabeth Hoffmann, A. Baust, Peter Eder, Michael Fischer, M. Haeberlein, M. J. Schwarz, Matthias Pernpeintner, Edwar Xie, L. Zhong, Christoph W. Zollitsch, Borja Peropadre, Juan José García‐Ripoll, E. Solano, Kirill G. Fedorov, E. P. Menzel, Frank Deppe, Achim Marx, Rudolf Groß

Published Jul 27, 2016• 58 citations
arXivHTMLPDF

Abstract

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 $g/2\pi$ ranging between −320 MHz and 37 MHz. In the case of $g \simeq 0$ , 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.

DOI
10.1140/epjqt/s40507-016-0048-2

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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 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 propose a frequency-tunable source to emit entangled microwave photons on the platform of a superconducting circuit, in which two superconducting transmission-line resonators are coupled via a capacitor and one resonator is inserted with a superconducting quantum interference device (SQUID) in the center. By pumping the circuit appropriately with an external coherent microwave signal through the SQUID, microwave photons are emitted in pairs out of the circuit. The entanglement between the two modes is demonstrated by numerically calculating the second-order coherence function and the logarithmic negativity of the output microwave signals. Due to the tunability of SQUID’s equivalent inductance, the frequencies of the entangled microwave photons can be tuned by an external flux bias in situ. Our proposal paves a new way for obtaining entangled frequency-tunable two-mode microwave photons.
In this licentiate thesis design, fabrication, and measurements of tunable superconducting microwave transmission line resonators are described. The resonators are of quarter wavelength type were the tuning is achieved by changing one of the boundary conditions of the resonator through a tunable impedance. As tunable impedance the Josephson inductance in form of SQUIDs is used. The Josephson inductance can then be tuned by applying a magnetic field to the SQUID loop. A tuning range of 750 MHz for a 5 GHz resonator is achieved, and as a figure of merit it can be tuned over 200 line widths. The purpose of the tunable resonators is to use them for dynamic coupling of superconducting quantum bits, this requires that the resonators can be tuned fast on the timescale of the resonator-qubit coupling. To measure tuning speeds faster then the ring up time of the resonators a method that measures the leakage of energy out of a detuned resonator was developed. With this method a frequency shift of the energy stored in the resonator can be measured. A detuning of 330 MHz in less than 10 ns is demonstrated for a 4.5 GHz resonator with a quality factor of 104^44. Working in the few photon limit indicates that the devices can be used to change the frequency of individual photons, this is however still to be demonstrated. As a part of this work the dressed states of a superconducting charge qubit was also studied.
We have created a doubly tunable resonator, with the intention to simulate relativistic motion of the resonator boundaries in real space. Our device is a superconducting coplanar-waveguide microwave resonator, with fundamental resonant frequency ω 1 / (2 π ) ~ 5 GHz. Both of its ends are terminated to ground via dc-SQUIDs, which serve as magnetic-flux-controlled inductances. Applying a flux to either SQUID allows the tuning of ω 1 / (2 π ) by approximately 700 MHz. Using two separate on-chip magnetic-flux lines, we modulate the SQUIDs with two tones of equal frequency, close to 2 ω 1 . We observe photon generation, at ω 1 , above a certain pump amplitude threshold. By varying the relative phase of the two pumps we are able to control this threshold, in good agreement with a theoretical model. At the same time, some of our observations deviate from the theoretical predictions, which we attribute to parasitic couplings resulting in current driving of the SQUIDs.
We present a system which allows to tune the coupling between a superconducting resonator and a transmission line. This storage resonator is addressed through a second, coupling resonator, which is frequency-tunable and controlled by a magnetic flux applied to a superconducting quantum interference device. We experimentally demonstrate that the lifetime of the storage resonator can be tuned by more than three orders of magnitude. A field can be stored for 18 μs when the coupling resonator is tuned off resonance and it can be released in 14 ns when the coupling resonator is tuned on resonance. The device allows capture, storage, and on-demand release of microwaves at a tunable rate.
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.