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arXiv:1203.5363 · Physical Review A

Low-disorder microwave cavity lattices for quantum simulation with photons

Devin Underwood, Will Shanks, Jens Koch, Andrew Houck

Published Aug 20, 2012• 206 citations
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Abstract

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 $t/2\ensuremath{\pi}=0.8$ 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 $t/2\ensuremath{\pi}=31$ MHz shows little effect of disorder, rendering resonator arrays a good backbone for the study of condensed-matter physics with photons.

DOI
10.1103/physreva.86.023837

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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/2\ensuremathπ=0.8t/2\ensuremath{\pi}=0.8t/2\ensuremathπ=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 104{10}^{4}104. The normal-mode spectrum of devices with a high photon hopping rate t/2\ensuremathπ=31t/2\ensuremath{\pi}=31t/2\ensuremathπ=31 MHz shows little effect of disorder, rendering resonator arrays a good backbone for the study of condensed-matter physics with photons.
Historically our understanding of the microscopic world has been impeded by limitations in systems that behave classically. Even today, understanding simple problems in quantum mechanics remains a difficult task both computationally and experimentally. As a means of overcoming these classical limitations, the idea of using a controllable quantum system to simulate a less controllable quantum system has been proposed. This concept is known as quantum simulation and is the origin of the ideas behind quantum computing. In this thesis, experiments have been conducted that address the feasibility of using devices with a circuit quantum electrodynamics (cQED) architecture as a quantum simulator. In a cQED device, a superconducting qubit is capacitively coupled to a superconducting resonator resulting in coherent quantum behavior of the qubit when it interacts with photons inside the resonator. It has been shown theoretically that by forming a lattice of cQED elements, different quantum phases of photons will exist for dierent system parameters. In order to realize such a quantum simulator, the necessary experimental foundation must rst be developed. Here experimental eorts were focused on addressing two primary issues: 1) designing and fabricating low disorder lattices that are readily available to incorporate superconducting qubits, and 2) developing new measurement tools and techniques that can be used to characterize large lattices, and probe the predicted quantum phases within the lattice. Three experiments addressing these issues were performed. In the rst experiment a Kagome lattice of transmission line resonators was designed and fabricated, and a comprehensive study on the effects of random disorder in the lattice demonstrated that disorder was dependent on the resonator geometry. Subsequently a cryogenic 3-axis scanning stage was developed and the operation of the scanning stage was demonstrated in the final two experiments. The rst scanning experiment was conducted on a 49 site Kagome lattice, where a sapphire defect was used to locally perturb each lattice site. This perturbative scanning probe microscopy provided a means to measure the distribution of photon modes throughout the entire lattice. The second scanning experiment was performed on a single transmission line resonator where a transmon qubit was fabricated on a separate substrate, mounted to the tip of the scanning stage and coupled to the resonator. Here the coupling strength of the qubit to the resonator was mapped out demonstrating strong coupling over a wide scanning range, thus indicating the potential for a scanning qubit to be used as a local quantum probe.
We give a concrete experimental scheme for engineering the insulator-superfluid transition of light in a one-dimensional (1D) array of coupled superconducting stripline resonators. In our proposed architecture, the on-site interaction and the photon-hopping rate can be tuned independently by adjusting the transition frequencies of the charge qubits inside the resonators and at the resonator junctions, respectively, which permits us to systematically study the quantum phase transition of light in a complete parameter space. By combining the techniques of photon-number-dependent qubit transition and fast readout of the qubit state using a separate low-QQQ resonator mode, the statistical property of the excitations in each resonator can be obtained with a high efficiency. An analysis of the various decoherence sources and disorders shows that our scheme can serve as a guide to upcoming experiments involving a small number of coupled resonators.
We explore experimentally a quantum metamaterial based on a superconducting chip with 25 frequency-tunable transmon qubits coupled to a common coplanar resonator. The collective bright and dark modes are probed via the microwave response, i.e., by measuring the transmission amplitude of an external microwave signal. All qubits have individual control and readout lines. Their frequency tunability allows the number NNN of resonantly coupled qubits to change and a disorder in their excitation frequencies to be introduced with preassigned distributions. While increasing NNN, we demonstrate the expected N1/2{N}^{1/2}N1/2 scaling law for the energy gap (Rabi splitting) between bright modes around the cavity frequency. By introducing a controllable disorder and averaging the transmission amplitude over a large number of realizations, we demonstrate a decay of mesoscopic fluctuations which mimics an approach towards the thermodynamic limit. The collective bright states survive in the presence of disorder when the strength of individual qubit coupling to the cavity dominates over the disorder strength.
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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.
Abstract Integrated photonics has been a promising platform for analog quantum simulation of condensed matter phenomena in strongly correlated systems. To that end, we explore the implementation of all-photonic quantum simulators in coupled cavity arrays with integrated ensembles of spectrally disordered emitters. Our model is reflective of color center ensembles integrated into photonic crystal cavity arrays. Using the Quantum Master equation and the Effective Hamiltonian approaches, we study energy band formation and wavefunction properties in the open quantum Tavis–Cummings–Hubbard framework. We find conditions for polariton creation and (de)localization under experimentally relevant values of disorder in emitter frequencies, cavity resonance frequencies, and emitter-cavity coupling rates. To quantify these properties, we introduce two metrics, the polaritonic and nodal participation ratios, that characterize the light-matter hybridization and the node delocalization of the wavefunction, respectively. These new metrics combined with the Effective Hamiltonian approach prove to be a powerful toolbox for cavity quantum electrodynamical engineering of solid-state systems.