The circuit quantum electrodynamical Josephson interferometer
Physik Department, Technische Universitaet Muenchen, James Franck Str, Garching, 85748, Germany
4 Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT, United Kingdom
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Accepted: 5 December 2013
Published online: 29 January 2014
Arrays of circuit cavities offer fascinating perspectives for exploring quantum many-body systems in a driven dissipative regime where excitation losses are continuously compensated by coherent input drives. Here we investigate a system consisting of three transmission line resonators, where the two outer ones are driven by coherent input sources and the central resonator interacts with a superconducting qubit. Whereas a low excitation number regime of such a device has been considered previously with a numerical integration, we here specifically address the high excitation density regime. We present analytical approximations to these regimes in the form of two methods. The first method is a Bogoliubov or linear expansion in quantum fluctuations which can be understood as an approximation for weak nonlinearities. As the second method we introduce a combination of mean-field decoupling for the photon tunneling with an exact approach to a driven Kerr nonlinearity which can be understood as an approximation for low tunneling rates. In contrast to the low excitation regime we find that for high excitation numbers the anti-bunching of output photons from the central cavity does not monotonously disappear as the tunnel coupling between the resonators is increased.
© The Author(s), 2014