Noise in a dynamical open quantum system: coupling a resonator to an artificial atom
Harvey, Thomas (2009) Noise in a dynamical open quantum system: coupling a resonator to an artificial atom. PhD thesis, University of Nottingham.
The subject of this thesis is the study of a particular open quantum system consisting of a resonator coupled to a superconducting single electron transistor (SSET). The theoretical model we use is applicable to both mechanical and superconducting stripline resonators leading to a large parameter regime that can be explored. The SSET is tuned to the Josephson quasi-particle resonance, in which the transport occurs via Cooper pairs coherently tunnelling across one junction followed by the incoherent tunnelling of quasi-particles across the other. The SSET can be thought of as an artificial atom since it has a similar energy level structure and transitions to an atom. We investigate to what extent the current and current noise through the SSET can be used to infer the state of the resonator. In order to carry out these investigations we describe the system with a Born-Markov master equation, which we solve numerically. The evolution of the density matrix of the system is described by a Liouvillian superoperator. In order to better understand the results we perform an eigenfunction expansion of the Liouvillian, which is useful in connecting the behaviour of the resonator to the current noise. The mixture of coherent and incoherent processes in the SSET leads to interesting back action effects on the resonator. For weak coupling the SSET acts as an effective thermal bath on the resonator. Depending on the operating point the resonator can be either heated or cooled in comparison to its surroundings. In this regime we can use a set of mean field equations to describe the system and also capture certain aspects of the behaviour with some simple models. For sufficient coupling the SSET can drive the resonator into states of self-sustained oscillations. At the transition between stable and oscillating states of the resonator we also find regions of co-existence between oscillating and fixed point states of the resonator. The current noise provides a way to identify these transitions and the state of the resonator. The system also shows analogies with quantum optical systems such as the micromaser. We calculate the linewidth of the resonator and find deviations from the expected behaviour.
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