Frequency-Tunable Josephson Junction Resonator for Quantum Computing

We have fabricated and measured a high-Q Josephson junction resonator with a tunable resonance frequency. A dc magnetic flux allows the resonance frequency to be changed by over 10 %. Weak coupling to the environment allows a quality factor of $\thicksim$7000 when on average less than one photon is stored in the resonator. At large photon numbers, the nonlinearity of the Josephson junction creates two stable oscillation states. This resonator can be used as a tool for investigating the quality of Josephson junctions in qubits below the single photon limit, and can be used as a microwave qubit readout at high photon numbers.Comment: 3 pages, 5 figure

Improving broadband displacement detection with quantum correlations

Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the tradeoff between the probe's shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work we investigate how quantum correlations accessed by modifying the readout of the interferometer can access physics beyond the SQL and improve displacement sensitivity. Specifically, we use an optical cavity to probe the motion of a silicon nitride membrane off mechanical resonance, as one would do in a broadband displacement or force measurement, and observe sensitivity better than the SQL dictates for our quantum efficiency. Our measurement illustrates the core idea behind a technique known as \textit{variational readout}, in which the optical readout quadrature is changed as a function of frequency to improve broadband displacement detection. And more generally our result is a salient example of how correlations can aid sensing in the presence of backaction.Comment: 17 pages, 5 figure

Quantum nondemolition measurement of a nonclassical state of a massive object

While quantum mechanics exquisitely describes the behavior of microscopic systems, one ongoing challenge is to explore its applicability to systems of larger size and mass. Unfortunately, quantum states of increasingly macroscopic objects are more easily corrupted by unintentional measurements from the classical environment. Additionally, even the intentional measurements from the observer can further perturb the system. In optomechanics, coherent light fields serve as the intermediary between the fragile mechanical states and our inherently classical world by exerting radiation pressure forces and extracting mechanical information. Here we engineer a microwave cavity optomechanical system to stabilize a nonclassical steady-state of motion while independently, continuously, and nondestructively monitoring it. By coupling the motion of an aluminum membrane to two microwave cavities, we separately prepare and measure a squeezed state of motion. We demonstrate a quantum nondemolition (QND) measurement of sub-vacuum mechanical quadrature fluctuations. The techniques developed here have direct applications in the areas of quantum-enhanced sensing and quantum information processing, and could be further extended to more complex quantum states.Comment: 9 pages, 6 figure

The integrated dynamic land use and transport model MARS

Cities worldwide face problems like congestion or outward migration of businesses. The involved transport and land use interactions require innovative tools. The dynamic Land Use and Transport Interaction model MARS (Metropolitan Activity Relocation Simulator) is part of a structured decision making process. Cities are seen as self organizing systems. MARS uses Causal Loop Diagrams from Systems Dynamics to explain cause and effect relations. MARS has been benchmarked against other published models. A user friendly interface has been developed to support decision makers. Its usefulness was tested through workshops in Asia. This paper describes the basis, capabilities and uses of MARS

Parametric coupling between macroscopic quantum resonators

Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediated tunable coupler. By calculating the logarithmic negativity of the partially transposed density matrix, we quantitatively study the entanglement generated at finite temperatures. We also show that characterization of the nanomechanical resonator state after the quantum operations can be achieved by detecting the electrical resonator only. Thus, one of the electrical resonator modes can act as a probe to measure the entanglement of the coupled systems and the degree of squeezing for the other resonator mode.Comment: 15 pages, 4 figures, submitte