SUMMARYExploiting the coupling between microwave waveguides and nanosystems is emerging as a new, powerful method of probing nanoscale devices. Such 'on-chip spectroscopy' was already demonstrated on superconducting quantum circuits (qubits) and nanoscale magnets. In this paper, we present an equivalent-circuit approach for the simulation and design of the coupled system. The waveguide structure is modelled by finite-element method and a 'modes to nodes' conversion yields to the circuit representation of the electromagnetic field problem. The nanosystem dynamics is modelled by equivalent circuits which are derived from the Landau-Lifshitz equations for nanomagnetic systems and by the Bloch equations for simple two-state quantum-mechanical problems. Interconnection of the two 'circuit modules' gives the model of the entire measurement set-up in a semiclassical approximation. Such 'field coupling' between nanosystems and microwave resonators can provide a novel, practical way for accessing nanoelectronic information processing devices.
We present an equivalent circuit approach to understand, simulate and design experimental setups, where superconducting coplanar resonators are applied to probe quantum systems. We employ finite-element electromagnetic simulations to construct an equivalent lumped circuit representation of the microwave cavity and we use a circuit model based on the Bloch equations to simulate the behavior of a two-state model quantum system. Interconnection of the two circuit modules gives a semiclassical description of the coupled quantum/classical dynamics and yields predictions that are directly comparable with measurements on realized circuits.
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