Modeling of the lossy Josephson parametric amplifier

Union Radio-Scientifique Internationale International Union of Radio Science U.R.S.I. Landesausschuss in der Bundesrepublik Deutschland e.V. Kleinheubacher Tagung 2013 Miltenberg • Germany • 23. - 25. Septembe r U.R.S.I. Landesausschuss in der Bundesrepublik Deutschland e.V. Kleinheubacher Tagung 2016 Miltenberg • Germany • 26. – 28. September 2016 14:10 – 14:30 Uhr: KH2016-D-10 Waldemar Kaiser, Michael Haider, Johannes Russer, Peter H. Russer, Christian Jirauschek (Technische Universität München, Germany) Modeling of the lossy Josephson parametric amplifier Recent advances in superconducting nanoelectr onic circuits exhibit the potential for future electronic applications. Experimental and theoretical research on superconducting quantum circuits based on the Josephson effect have recently gained more and more attention due to developments in quantum information theory and quantum metrology (Russe r and Russer, 2011). The Josephson effect is observed, if two superconducting materials ar e weakly coupled across a tunnel barrier or a narrow conducting bridge. Electronic devices based on the Josephson effect allow the generation, detection, mixing and parametric amplification of hi gh-frequency signals. Mor eover, Josephson devices are nanometre-sized low power devices and show hi gh sensitivity. So far, Josephson parametric amplifiers have been treated classically as well as quantum mechanically. The existing quantum mechanical models do not include loss contributions (Russer and Russer, 2012). In this work the lossy negative- resistance Josephson parametric am plifier is analyzed. Losses are considered using the quantum Langevin method. Hereby , the resonator circuits, i.e. the signal and the idler circuit, are coupled to a heat bath, represented by a photon gas in thermal equilibrium. In this way, also temperature dependencies are taken into account. In our model, the heat bath consists of harmonic oscillators, inducing fluctuations in the resonators a nd causing damping of the signal energy (Jirauschek and Russer, 2012). The DC biased Josephson junction is causing a strong interaction between the idler and the signal modes. Thus, power exchange occurs between the signal and the idler mode, as well as between the DC power supply and the resonator ci rcuits. The energy conversion in the DC-pumped Josephson parametric amplifier follows the Manley-Row e equations, with an additional DC term (Russer, 1971). The time evolution of the signal e nergy and the noise contributions ar e derived based on the Heisenberg equations of motion. The rotating wave approximati on is applied in order to simplify the Josephson coupling Hamiltonian.We assume the heat bath noise cont ributions to follow the statistics of a Markovian process. We have explicitly computed the time evolut ion of the various energy contributions for different initial settings. The signal photon number in therma l equilibrium is determined by the photon occupation number of the heat bath, given by Boltzmann statistics, and the damping constants. Our analytic results show, that this model is capable of including th ermal noise into the description of the Josephson parametric amplifier. For low damping constants, the signal energy is amplified exponentially as shown in previous publications without loss considerations (Russer and Russer, 2012).      «

Union Radio-Scientifique Internationale International Union of Radio Science U.R.S.I. Landesausschuss in der Bundesrepublik Deutschland e.V. Kleinheubacher Tagung 2013 Miltenberg • Germany • 23. - 25. Septembe r U.R.S.I. Landesausschuss in der Bundesrepublik Deutschland e.V. Kleinheubacher Tagung 2016 Miltenberg • Germany • 26. – 28. September 2016 14:10 – 14:30 Uhr: KH2016-D-10 Waldemar Kaiser, Michael Haider, Johannes Russer, Peter H. Russer, Christian Jirau...     »