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arXiv:1606.04222 · Physical Review Letters

Observation of Collective Coupling between an Engineered Ensemble of Macroscopic Artificial Atoms and a Superconducting Resonator

Kosuke Kakuyanagi, Yuichiro Matsuzaki, Corentin Déprez, Hiraku Toida, Kouichi Semba, Hiroshi Yamaguchi, William J. Munro, Shiro Saito

Published Nov 16, 2016• 70 citations
arXivHTMLPDF

Abstract

The hybridization of distinct quantum systems is now seen as an effective way to engineer the properties of an entire system leading to applications in quantum metamaterials, quantum simulation, and quantum metrology. Recent improvements in both fabrication techniques and qubit design have allowed the community to consider coupling large ensembles of artificial atoms, such as superconducting qubits, to a resonator. Here, we demonstrate the coherent coupling between a microwave resonator and a macroscopic ensemble composed of several thousand superconducting flux qubits, where we observe a large dispersive frequency shift in the spectrum of 250 MHz. We achieve the large dispersive shift with a collective enhancement of the coupling strength between the resonator and qubits. These results represent the largest number of coupled superconducting qubits realized so far.

DOI
10.1103/physrevlett.117.210503

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The hybridization of distinct quantum systems is now seen as an effective way to engineer the properties of an entire system leading to applications in quantum metamaterials, quantum simulation, and quantum metrology. Recent improvements in both fabrication techniques and qubit design have allowed the community to consider coupling large ensembles of artificial atoms, such as superconducting qubits, to a resonator. Here, we demonstrate the coherent coupling between a microwave resonator and a macroscopic ensemble composed of several thousand superconducting flux qubits, where we observe a large dispersive frequency shift in the spectrum of 250 MHz. We achieve the large dispersive shift with a collective enhancement of the coupling strength between the resonator and qubits. These results represent the largest number of coupled superconducting qubits realized so far.
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.
In recent years the interest in studying interactions of Rydberg atoms or ensembles thereof with optical and microwave frequency fields has steadily increased, both in the context of basic research and for potential applications in quantum information processing. We present measurements of the dispersive interaction between an ensemble of helium atoms in the 37s37s37s Rydberg state and a single resonator mode by extracting the amplitude and phase change of a weak microwave probe tone transmitted through the cavity. The results are in quantitative agreement with predictions made on the basis of the dispersive Tavis-Cummings Hamiltonian. We study this system with the goal of realizing a hybrid between superconducting circuits and Rydberg atoms. We measure maximal collective coupling strengths of 1 MHz, corresponding to $3\ifmmode\times\else\texttimes\fi{}{10}^{3}$ Rydberg atoms coupled to the cavity. As expected, the dispersive shift is found to be inversely proportional to the atom-cavity detuning and proportional to the number of Rydberg atoms. This possibility of measuring the number of Rydberg atoms in a nondestructive manner is relevant for quantitatively evaluating scattering cross sections in experiments with Rydberg atoms.
By coupling a collection of two-level artificial atoms simultaneously to two superconducting resonators, we propose a quantum switch that can tune the resonator-resonator coupling strength from zero to a large value proportional to the qubit number. This process is realized by preparing the qubits in different pairwise subradiant states, where the microwave photons released by different qubits interfere destructively such that the coupling strength can be stabilized in an open environment. The resulting two-step control scheme tunes the coupling strength between different values in nanoseconds without changing the transition frequency of the qubits. We also use the quantum switch to network multiple resonators with programmable couplings, and we demonstrate its potential applications in quantum simulation and quantum information storage and processing.
Abstract Waveguide quantum electrodynamics offers a wide range of possibilities to effectively engineer interactions between artificial atoms via a one-dimensional open waveguide. While these interactions have been experimentally studied in the few qubit limit, the collective properties of such systems for larger arrays of qubits in a metamaterial configuration has so far not been addressed. Here, we experimentally study a metamaterial made of eight superconducting transmon qubits with local frequency control coupled to the mode continuum of a waveguide. By consecutively tuning the qubits to a common resonance frequency we observe the formation of super- and subradiant states, as well as the emergence of a polaritonic bandgap. Making use of the qubits quantum nonlinearity, we demonstrate control over the latter by inducing a transparency window in the bandgap region of the ensemble. The circuit of this work extends experiments with one and two qubits toward a full-blown quantum metamaterial, thus paving the way for large-scale applications in superconducting waveguide quantum electrodynamics.
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.
Waveguide quantum electrodynamics offers a wide range of possibilities to effectively engineer interactions between artificial atoms via a one-dimensional open waveguide. While these interactions have been experimentally studied in the few qubit limit, the collective properties of such systems for larger arrays of qubits in a metamaterial configuration has so far not been addressed. Here, we experimentally study a metamaterial made of eight superconducting transmon qubits with local frequency control coupled to the mode continuum of a waveguide. By consecutively tuning the qubits to a common resonance frequency we observe the formation of super- and subradiant states, as well as the emergence of a polaritonic bandgap. Making use of the qubits quantum nonlinearity, we demonstrate control over the latter by inducing a transparency window in the bandgap region of the ensemble. The circuit of this work extends experiments with one and two qubits toward a full-blown quantum metamaterial, thus paving the way for large-scale applications in superconducting waveguide quantum electrodynamics.