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IEEE Transactions on Terahertz Science and Technology

Experiments With Tunable Superconducting Metamaterials

Alexey Vladimirovich Ustinov

Published Jan 1, 2014• 11 citations
Publisher

Abstract

The paper reviews experiments with networks of compact thin-film superconducting microwave resonators. Superconducting circuits offer low loss properties, well-controlled nonlinearity, and frequency tunability in the microwave and mm-wave frequency ranges. An interesting spin-off of superconducting metamaterials is going to be quantum metamaterials comprised of arrays of superconducting qubits. This direction is an emerging new field for fundamental studies in quantum optics using microwaves.

DOI
10.1109/tthz.2014.2379433

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The paper reviews experiments with networks of compact thin-film superconducting microwave resonators. Superconducting circuits offer low loss properties, well-controlled nonlinearity, and frequency tunability in the microwave and mm-wave frequency ranges. An interesting spin-off of superconducting metamaterials is going to be quantum metamaterials comprised of arrays of superconducting qubits. This direction is an emerging new field for fundamental studies in quantum optics using microwaves.
We report on experiments with superconducting Josephson metamaterials. In such a material, conventional split ring resonators are replaced by superconducting loops that are interrupted by Josephson junctions, so called rf-SQUIDs. Like the split ring resonators, they can be seen as LCresonators that couple to the magnetic component of the incoming wave. The advantage of superconducting thin-film metamaterials is that due to the tunable intrinsic inductance of the Josephson junction, the resonance frequency of the rf-SQUID can be changed by applying an external dc magnetic field. We present experimental results that show the tunability of the resonance frequency of these devices.
Superconducting circuits operated at low temperatures have led to rapid advances in quantum information processing as well as quantum optics in the microwave regime. Engineered quantum systems with a dense spectrum of modes coupled to artificial atoms, or qubits, formed from superconducting circuits offer an opportunity to explore large-scale entanglement or perform quantum simulations of many-body phenomena. Recent research efforts into artificial metamaterials have yielded microwave and optical systems with numerous counterintuitive properties, including left-handed transmission, where the group velocity and phase velocity for a wave point in opposite directions. Metamaterial resonators implemented with superconducting thin-film circuits provide a route to generating dense mode spectra in the microwave regime for coupling to qubits. In this thesis, we discuss the implementation of such superconducting metamaterial resonators. First, we derive the dispersion relation for one-dimensional metamaterial transmission lines and we describe the formation of resonators from such lines and their quality factors. Next, we describe the design and fabrication of transmission-line metamaterial resonators using superconducting thin films. We characterize the metamaterials through low-temperature microwave measurements as well as Laser Scanning Microscope (LSM) images of the microwave field distributions in the circuit. We compare these various measurements with numerical simulations of the microwave properties of the circuits, including simulated current density and charge density distributions for the excitation of different resonance modes. Following the successful realization of dense mode spectra in these circuits, we have initiated the first experiments with a superconducting transmon qubit coupled to a metamaterial resonator and we describe our progress in this direction.
Superconducting thin-film metamaterial resonators can provide a dense microwave mode spectrum with potential applications in quantum information science. We report on the fabrication and low-temperature measurement of metamaterial transmission-line resonators patterned from Al thin films. We also describe multiple approaches for numerical simulations of the microwave properties of these structures, along with comparisons with the measured transmission spectra. The ability to predict the mode spectrum based on the chip layout provides a path towards future designs integrating metamaterial resonators with superconducting qubits.
Superconducting metamaterials show the promise of low loss, compact size and extreme tunability and nonlinearity, allowing for new applications. Most demonstrations of these metamaterials have been conducted in waveguide geometries, either in co-planar form or three-dimensional single-conductor structures. Here we demonstrate for the first time a widely tunable superconducting metamaterial operating under the free-space illumination of a quasi-optical beam in the 100 GHz regime. The meta-atoms are Radio Frequency Superconducting QUantum Interference Devices (RF SQUIDs) that form compact self-resonant objects endowed with the nonlinearity of the Josephson effect. The metamaterial is tuned with dc magnetic flux, temperature and mm-wave power, and holds promise for a new generation of mm-wave agile devices. This work is supported by the NSF-GOALI and OISE programs through grant #ECCS-1158644, and CNAM.
Metamaterial resonant structures made from arrays of superconducting lumped-circuit elements can exhibit microwave-mode spectra with left-handed dispersion for the standing-wave resonances, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this regime for multimode circuit quantum electrodynamics, we perform a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we observe the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we probe the qubit dispersively and characterize the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we investigate the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. Through numerical simulations, we explore designs based on this scheme with enhanced coupling so that the coupling energy between the qubit and the metamaterial modes can exceed the intermode spacing in future devices with achievable circuit parameters. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation with microwave photons and quantum memories.
Multimode microwave resonators that can be strongly coupled to superconducting qubits allow exploration of large-scale entanglement, or quantum simulations of many-body phenomena. Typically, long superconducting transmission lines or large arrays of transmission-line resonators are required. This work demonstrates superconducting metamaterial resonators with a dense mode spectrum above a low-frequency band gap. Imaging of the microwave fields shows that these devices exhibit a left-handed dispersion relation, consistent with modeling and simulations. This compact design is compatible with superconducting-qubit integration for applications in quantum information and communication.