Photonic crystals provide an extremely powerful toolset for manipulation of optical dispersion and density of states, and have thus been employed for applications from photon generation to quantum sensing with NVs and atoms [1, 2]. The unique control afforded by these media make them a beautiful, if unexplored, playground for strong coupling quantum electrodynamics, where a single, highly nonlinear emitter hybridizes with the bandstructure of the crystal. In this work we demonstrate that such hybridization can create localized cavity modes that live within the photonic bandgap, whose localization and spectral properties we explore in detail. We then demonstrate that the coloured vacuum of the photonic crystal can be employed for efficient dissipative state preparation. This work opens exciting prospects for engineering long-range spin models [3, 4] in the circuit QED architecture, as well as new opportunities for dissipative quantum state engineering.The perturbative effect of a structured vacuum is the renowned Purcell effect which states that the lifetime of an atom in such space will be proportional to the local photonic density of states (DOS) near the atomic transition frequency. In practice, the birth of the photonic crystal, which greatly modifies the vaccuum fluctuations, has enabled the control of spontaneous emission of various emitters such as quantum dots [5,6], magnons [7] and superconducting qubits [8]. However, when an atom is strongly coupled to a photonic crystal, non-perturbative effects become important and significantly enrich the physics. For instance, a single photon bound state has been predicted to emerge within the gap [9], and spontaneous emission of the atom will thus exhibit Rabi oscillation and light trapping behavior. In contrast to electronic band-gap systems, even multiple photons can be simultaneously localized by a single atom, and the coherent photonic transport within the otherwise forbidden band-gap can have a strongly correlated nature [10, 2,12]. In contrast to a system with discrete cavity modes, which is well described by the single mode or multimode Jaynes-Cummings Hamiltonian [16,17,18], a continuous density of states enables the formation of a localized state in the band gap. While other spin-boson problems with continuous DOS have also been studied experimentally [19,20] or theoretically [21,22] with superconducting circuits, this work explores physics near the band edge, where localized states emerge and reservoir engineering becomes possible.Light-matter interactions are being actively pursued using cold atoms coupled to optical photonic crystals [23,24], where the study of photonic band edge effects requires a combination of challenging nanostructure fabrication and optical laser trapping. Though impressive progress has been made, atoms are only weakly coupled to photonic crystal waveguides [24], potentially limiting the physics to the the perturbative regime. In this letter, using a microwave photonic crystal and a superconducting transmon qubit, we are able to r...

Here, we report an experimental realization of multimode strong coupling in cavity quantum electrodynamics. This novel regime is achieved when a single artificial atom is simultaneously strongly coupled to a large, but discrete, number of nondegenerate photonic modes of a cavity with coupling strengths comparable to the free spectral range. Our experiment reveals complex quantum multimode dynamics and spontaneous generation of quantum coherence, as evidenced by resonance fluorescence spanning many modes and ultranarrow linewidth emission. This work opens a new avenue for future experiments in light-matter interactions and poses a challenge to current theoretical approaches to its study. DOI: 10.1103/PhysRevX.5.021035 Subject Areas: Condensed Matter Physics, Photonics, Quantum PhysicsThe study of light-matter interaction has seen a resurgence in recent years, stimulated by highly controllable, precise, and modular experiments in cavity quantum electrodynamics (QED) [1]. The achievement of strong coupling [2][3][4], where the coupling between a single atom and fundamental cavity mode exceeds the decay rates, was a major milestone that opened the doors to a multitude of new investigations [5,6].Here, we investigate multimode strong coupling (MMSC) [7,8], where the coupling is comparable to the free spectral range (FSR) of the cavity; i.e., the rate at which a qubit can absorb a photon from the cavity is comparable to the roundtrip transit rate of a photon in the cavity. We realize, via the circuit QED architecture, an experiment accessing the MMSC regime and report remarkably widespread and highly structured resonance fluorescence. The observed drive dependence of the width, height, and position of the fluorescence peaks cannot be explained by cavity enhancement of sidebands observed in the single-mode regime [9]. As expounded below, our observations reveal a generation of coherence across multiple frequencies mediated by a single qubit and necessitate a multimode analysis. Beyond the novel phenomena presented here, the access to the MMSC regime opens up a new direction of exploration that is of interest both theoretically and experimentally.Interest in going beyond strong coupling has focused on the ultrastrong-coupling limit, where the breakdown of the rotating-wave approximation for the light-matter interaction results in excitation nonconserving terms [10][11][12][13]. In contrast, the direction which we pursue is the simultaneous strong coupling of the qubit to numerous modes, leading to qubit-mediated mode-mode interactions and nonlinear quantum dynamics not present in the single-mode problem. Thus, MMSC demonstrates a qualitatively new domain, intermediate between the quantum mechanics of systems with a small number of degrees of freedom and full continuum quantum field theory in free space. Unlike the traditional spin-boson problem that involves a bosonic continuum with an algebraic bath spectral function of the type JðωÞ ¼ αω s , the MMSC regime is described by a structured spectral function with an infi...

The ability to perform fast, high-fidelity readout of quantum bits (qubits) is essential to the goal of building a quantum computer. However, coupling a fast measurement channel to a superconducting qubit typically also speeds up its relaxation via spontaneous emission. Here we use impedance engineering to design a filter by which photons may easily leave the resonator at the cavity frequency but not at the qubit frequency. We implement this broadband filter in both an on-chip and off-chip configuration.Superconducting qubits have become strong candidates for implementing fault-tolerant quantum computing 1-3 and digital quantum simulations 4,5 . Recent progress has been driven by improved coherence times 6,7 , gate fidelities 8,9 , and readout fidelities 10-12 . The demonstration of a fault-tolerant logical qubit will require both further improvements in these areas and also the engineering of architectures for inter-connected networks of superconducting qubits 13 .One critical area of exploration for larger networks of superconducting devices is the complementary pursuit of fast, high-fidelity readout and suppression of qubit decay. Currently, low qubit decay rates are made possible by coupling the superconducting qubit to a microwave resonator in the circuit quantum electrodynamics (cQED) architecture 14,15 . The microwave resonators protect the qubits from spontaneous emission into the environment. With the appropriate coupling, they also permit a quantum non-demolition readout of the qubit state. However, suppression of the qubit decay rate comes at a cost of the readout rate. To speed up the readout, a number of methods have been proposed for dispersive filtering, where radiation at the qubit frequency is filtered and that at the resonator frequency is passed 2,16-18 . Among these proposals, large bandwidth filters with the possibility of off-device integration have been absent. In this Letter we demonstrate the suppression of qubit decay rates with a broadband stepped impedance Purcell filter (SIPF) in both on-and off-chip configurations, while maintaining the ability to perform fast, high-fidelity readout.A qubit coupled to the environment suffers relaxation based on the admittance (reciprocal impedance) Y (ω q ) at its transition frequency ω q . This dependence of spontaneous emission on the coupled electromagnetic environment is known as the Purcell effect 19 , and is a key factor used to either enhance or abate qubit relaxation. Approximating a transmon qubit as a harmonic oscillator, its lifetime isa) Electronic mail: ntbronn@us.ibm.com where C Σ is the sum of the shunting and Josephson capacitances 20 . Initial experiments coupling superconducting qubits to the external environment (i.e. measurement and control instruments) through coupling capacitors and tunnel junctions 21 did not provide sufficient protection and thus yielded large decay rates γ 1 = T −1 1 . Placing the qubit inside a resonator modifies the available decay channels and hence Y (ω q ), which forms the basis of cQED 14,15 . In parti...

We demonstrate the suppression of photon shot noise dephasing in a superconducting qubit by eliminating its dispersive coupling to the readout cavity. This is achieved in a tunable coupling qubit, where the qubit frequency and coupling rate can be controlled independently. We observe that the coherence time approaches twice the relaxation time and becomes less sensitive to thermal photon noise when the dispersive coupling rate is tuned from several MHz to 22 kHz. This work provides a promising building block in circuit quantum electrodynamics that can hold high coherence and be integrated into larger systems.npj Quantum Information (2017) 3:1 ; doi:10.1038/s41534-016-0002-2 INTRODUCTIONSuperconducting quantum circuits are a strong candidate for quantum computing, 1-3 and a convenient platform for quantum optics 4-6 and quantum simulation. 7,8 Extensive efforts have been made in the last decade to isolate these quantum systems from various decay channels and noise sources in the environment, leading to an increase of several orders of magnitude in energy relaxation time T 1 and phase coherence time T 2 .9 State-of-the-art devices have achieved T 1 and T 2 in the millisecond regime 10,11 and pushed gate fidelity close to the threshold for fault-tolerant quantum computing.12 However, the progress in T 2 is slower than that in T 1 and T 2 /T 1 ratios in these devices fall in the range between 0.5 and 1.5. 10,13,14 Deviation from the theoretical limit of T 2 = 2T 1 indicates dephasing mechanisms that need to be understood and circumvented.In circuit quantum electrodynamics (cQED), 15,16 manipulation and readout of a superconducting qubit are mediated by its coupling to a transmission line cavity. When the coupling is dispersive, photons in the cavity can be utilized to measure the qubit if their phase is shifted by a distinguishable amount depending on the qubit state. On the other hand, changes in cavity photon number will shift the qubit frequency due to the same coupling mechanism. When the amount of the frequency shift is large enough, thermal or quantum fluctuations of cavity photons lead to dephasing of the qubit. This photon shot noise dephasing mechanism has been studied theoretically 17 and experimentally 14 and has become a dominant factor that limits the coherence time of superconducting qubits. The qualitative discussion above indicates that the dephasing can be suppressed by reducing (1) the photon number fluctuation, characterized by cavity decay rate κ, (2) the thermal photon population n th , and (3) the frequency shift caused by each photon, characterized by the dispersive coupling rate χ. Most work in the past has adopted the first two strategies and used high-Q (>10 6 ) 3D cavities 10,18 and careful filtering and thermal anchoring to reduce κ and n th .

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