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IEEE Transactions on Applied Superconductivity

Experimental Demonstration of Superconducting Metamaterial Nonlinear Resonators With Well-Isolated Modes

Qing Tang, P. Ouyang, Y. Q. Chai, J. X. He, L. F. Wei

Published Apr 8, 2024• 0 citations
Publisher

Abstract

The usual linear superconducting resonators (with equal frequency intervals between nearest-neighbor modes) are right-handed electromagnetic devices, wherein cross talks between the nearest-neighbor modes are practically unavoidable. Here, we demonstrate the nonlinear superconducting metamaterial resonators, wherein frequency intervals between the nearest-neighbor modes are unequal, by using the composite right/left-handed transmission lines. The microwave transport properties are analyzed by the developed real-space approach, instead of the usual equivalent circuit method. The devices are fabricated by using the usual electron beam evaporation technique, and their microwave transport parameters are measured at 50 mK temperature. The observations are basically consistent with the relevant theoretical predictions and also numerical simulations. Hopefully, the demonstrated nonlinear devices, with well-isolated modes, could be used to encode the superconducting qubits for microwave quantum information processing.

DOI
10.1109/tasc.2024.3385416

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The usual linear superconducting resonators (with equal frequency intervals between nearest-neighbor modes) are right-handed electromagnetic devices, wherein cross talks between the nearest-neighbor modes are practically unavoidable. Here, we demonstrate the nonlinear superconducting metamaterial resonators, wherein frequency intervals between the nearest-neighbor modes are unequal, by using the composite right/left-handed transmission lines. The microwave transport properties are analyzed by the developed real-space approach, instead of the usual equivalent circuit method. The devices are fabricated by using the usual electron beam evaporation technique, and their microwave transport parameters are measured at 50 mK temperature. The observations are basically consistent with the relevant theoretical predictions and also numerical simulations. Hopefully, the demonstrated nonlinear devices, with well-isolated modes, could be used to encode the superconducting qubits for microwave quantum information processing.
Superconducting transmission line resonators (TLRs) have been widely applied to circuit quantum electrodynamical systems for superconducting quantum computation and single-photon detections. Recently, such a right-handed TLR has been generalized to electromagnetic metamaterials (MTMs), and its unconventional mode structure has been experimentally characterized (Wang et al. in Phys Rev Appl 11:054062, 2019). Here, we demonstrate another kind of MTM TLR, i.e., the superconducting quarter-wavelength composite right/left-handed (CRLH) TLRs composed of lumped elements. We design the devices and analyze their transport properties by developing a real-space approach, wherein the physical parameters at the device boundaries are utilized conveniently. Superconducting MTM TLRs with typical three unit cells were experimentally prepared by etching a superconducting aluminum film on a SiO[Formula: see text] substrate, and their microwave transport properties were measured at low temperatures of 50 mK. The results show that the modes spacing in such a quarter-wavelength CRLH-TLR is non-uniform, due to the nonlinear dispersion relation. This implies that it could be utilized to encode the superconducting qubits, analogously to the usual ones encoded by using the Josephson devices.
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.
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.
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.
Abstract We present a theoretical and experimental study of superconducting ring resonators as an initial step toward their implementation in superconducting electronics and quantum technologies, with promising applications including superconducting parametric amplifiers with pump-signal isolation, flux-controlled quantum circuits, ultra-sensitive measurements in quantum sensing, and THz instrumentations. These devices have the potentially valuable property of supporting two orthogonal electromagnetic modes that couple to a common Cooper pair, quasiparticle, and phonon system. We present here a comprehensive theoretical and experimental analysis of the superconducting ring resonator system. We have developed superconducting ring resonator models that describe the key features of microwave behaviour to first order, providing insights into how transmission line inhomogeneities give rise to frequency splitting and mode rotation. Furthermore, we constructed signal flow graphs for a four-port ring resonator to numerically validate the behaviour predicted by our theoretical analysis. Superconducting ring resonators were fabricated in both coplanar waveguide and microstrip geometries using Al and Nb thin films. Microwave characterisation of these devices demonstrates close agreement with theoretical predictions. Our study reveals that frequency splitting and mode rotation are prevalent in ring systems with coupled degenerate modes, and these phenomena become distinctly resolved in high quality factor superconducting ring resonators.
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.