We assess experimentally the suitability of coupled transmission line resonators for studies of quantum phase transitions of light. We have measured devices with low photon hopping rates t/2π = 0.8 MHz to quantify disorder in individual cavity frequencies. The observed disorder is consistent with small imperfections in fabrication. We studied the dependence of the disorder on transmission line geometry and used our results to fabricate devices with disorder less than two parts in 10 4 . The normal mode spectrum of devices with a high photon hopping rate t/2π = 31 MHz shows little effect of disorder, rendering resonator arrays a good backbone for the study of condensed matter physics with photons.PACS numbers: 03.67. Ac, 42.50.Ct, 71.36.+c Solving seemingly simple problems in quantum mechanics is a formidable task for even the most sophisticated classical computers. For this reason Feynman proposed using controlled quantum systems to simulate and study other quantum systems [1]. The development of such quantum simulators [2] has since been an active area of research in a number of physical systems, including ultracold atoms in traps and optical lattices [3,4], trapped ions [5], and Josephson junction arrays [6].An idea of growing interest is to use photons as particles in a quantum simulator for non-equilibrium systems [7][8][9][10][11][12][13]. According to this idea, a photon lattice is created with an array of cavity quantum electrodynamics (cQED) elements, each consisting of a photonic cavity coupled strongly to a two level system, or qubit. Systems consisting of up to three coupled cavities have been realized for quantum information processing [14][15][16], and early proposals consider using larger arrays as a possible quantum computing architecture [17][18][19], but a latticebased quantum simulator of this type has yet to be realized.In these lattices, photons can hop between neighboring cavities and experience an effective photon-photon interaction within each cavity, mediated by the qubit. The superconducting circuit architecture is an attractive candidate for realizing such lattices due to the flexibility afforded by lithographic fabrication and the relative ease of attaining strong coupling [20]. Such cQED lattices have been predicted to exhibit a wide variety of phenomena, including a superfluid-Mott insulator transition [7][8][9][10], macroscopic quantum self trapping [21], and fractional quantum Hall physics [11].In order to jump-start the implementation of these lattice-based simulators, we have fabricated and characterized 25 arrays of cavities, with each cavity designed to be identical.(Devices discussed here do not include qubits yet.) In this letter, we focus on understanding and reducing uncontrolled disorder in arrays of resonators in a kagome geometry, the most natural two-dimensional lattice for such transmission line resonators. We find that disorder in the individual resonator frequencies mainly originates from variations in the kinetic inductance due to small changes in the transverse ...
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...
Like a quantum computer designed for a particular class of problems, a quantum simulator enables quantitative modelling of quantum systems that is computationally intractable with a classical computer. Superconducting circuits have recently been investigated as an alternative system in which microwave photons confined to a lattice of coupled resonators act as the particles under study, with qubits coupled to the resonators producing effective photon-photon interactions. Such a system promises insight into the non-equilibrium physics of interacting bosons, but new tools are needed to understand this complex behaviour. Here we demonstrate the operation of a scanning transmon qubit and propose its use as a local probe of photon number within a superconducting resonator lattice. We map the coupling strength of the qubit to a resonator on a separate chip and show that the system reaches the strong coupling regime over a wide scanning area.
Microwave photons inside lattices of coupled resonators and superconducting qubits can exhibit surprising matterlike behavior. Realizing such open-system quantum simulators presents an experimental challenge and requires new tools and measurement techniques. Here, we introduce scanning defect microscopy as one such tool and illustrate its use in mapping the normal-mode structure of microwave photons inside a 49-site kagome lattice of coplanar waveguide resonators. Scanning is accomplished by moving a probe equipped with a sapphire tip across the lattice. This locally perturbs resonator frequencies and induces shifts of the lattice resonance frequencies, which we determine by measuring the transmission spectrum. From the magnitude of mode shifts, we can reconstruct photon field amplitudes at each lattice site and thus create spatial images of the photon-lattice normal modes.
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