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arXiv:1802.01708 · Nature Communications

Superconducting metamaterials for waveguide quantum electrodynamics

Mohammad Mirhosseini, Eunjong Kim, Vinicius S. Ferreira, Mahmoud Kalaee, Alp Sipahigil, Andrew J. Keller, Oskar J. Painter

Published Sep 6, 2018• 130 citations
arXivHTMLPDF

Abstract

Abstract Embedding tunable quantum emitters in a photonic bandgap structure enables control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite-range emitter–emitter interactions via bound photonic states. Here, we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant (λ/60). The metamaterial is formed by periodically loading a transmission line with compact, low-loss, low-disorder lumped-element microwave resonators. Tuning the qubit frequency in the vicinity of a band-edge with a group index of ng = 450, we observe an anomalous Lamb shift of −28 MHz accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions, which provide simultaneous access to short-lived radiatively damped and long-lived metastable qubit states.

DOI
10.1038/s41467-018-06142-z

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Abstract Embedding tunable quantum emitters in a photonic bandgap structure enables control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite-range emitter–emitter interactions via bound photonic states. Here, we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant (λ/60). The metamaterial is formed by periodically loading a transmission line with compact, low-loss, low-disorder lumped-element microwave resonators. Tuning the qubit frequency in the vicinity of a band-edge with a group index of ng = 450, we observe an anomalous Lamb shift of −28 MHz accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions, which provide simultaneous access to short-lived radiatively damped and long-lived metastable qubit states.
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 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.
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.
Atom-photon bound states arise from the coupling of quantum emitters to the band edge of dispersion-engineered waveguides. Thanks to their tunable-range interactions, they are promising building blocks for quantum simulators. Here, we study the dynamics of an atom-photon bound state emerging from coupling a frequency-tunable quantum emitter-a transmon-type superconducting circuit-to the band edge of a microwave metamaterial. Employing precise temporal control over the frequency detuning of the emitter from the band edge, we examine the transition from adiabatic to nonadiabatic behavior in the formation of the bound state and its melting into the propagating modes of the metamaterial. Moreover, we experimentally observe multimode emission from the bound state, triggered by a fast change of the emitter's frequency. Our Letter offers insight into the dynamic preparation of APBS and provides a method to characterize their photonic content, with implications in quantum optics and quantum simulation.
Superconducting quantum metamaterials extend the idea of their classical counterpart to a regime where their constituent meta-atoms are quantum objects, which can hold their quantum coherence for longer than the propagation time of light through the medium. In this work, we have realized a quantum metamaterial consisting of eight individually controllable superconducting transmon qubits, which are coupled to the mode continuum of a one-dimensional coplanar waveguide. This system can be described within the framework of waveguide-quantum electrodynamics, which predicates that the mutual interaction of the qubits with the waveguide gives rise to long-range interactions of the qubits. In spectroscopic measurements we observe the formation of super- and subradiant collective metamaterial excitations, as well as the emergence of a polaritonic band gap and study their dependence on the number of participating resonant qubits. We utilize the collective Autler-Townes splitting of the metamaterial to demonstrate control over its band gap. Furthermore, we exploit the control over the band structure for a first realization of slowly propagating light in the metamaterial. Our findings show that superconducting quantum metamaterials are a suitable platform to study fundamental excitations in solids and pave way to applications in quantum information processing like quantum memories.
The rapid progress in quantum information processing leads to a rising demand for devices to control the propagation of electromagnetic wave pulses and to ultimately realize universal and efficient quantum memory. While in recent years, significant progress has been made to realize slow light and quantum memories with atoms at optical frequencies, superconducting circuits in the microwave domain still lack such devices. Here, we demonstrate slowing down electromagnetic waves in a superconducting metamaterial composed of eight qubits coupled to a common waveguide, forming a waveguide quantum electrodynamics system. We analyze two complementary approaches, one relying on dressed states of the Autler–Townes splitting and the other based on a tailored dispersion profile using the qubits tunability. Our time-resolved experiments show reduced group velocities of down to a factor of about 1500 smaller than in vacuum. Depending on the method used, the speed of light can be controlled with an additional microwave tone or an effective qubit detuning. Our findings demonstrate high flexibility of superconducting circuits to realize custom band structures and open the door to microwave dispersion engineering in the quantum regime.