Quantum Fluctuations of the Order Parameter in Superconductors

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This grant supports theoretical research in fundamental condensed matter physics. In the past decade a strong experimental effort was devoted to mesoscopic superconductivity. Currently, the interest in this field has increased even more because of the search for viable schemes in quantum computing. The parallel work in theory until recently was concentrated mostly on equilibrium characteristics and linear response properties of superconducting and hybrid structures. However, there is a clear need, dictated by experiments, to understand the properties of hybrid structures far from equilibrium. This research will explore these properties.The first project deals with dynamic properties of circuits of small Josephson junctions subject to parametric excitation. The driven junctions system may be brought to the regime of classical or quantum dynamic chaos. Quantum effects become important if the junctions are small enough to allow for charge quantization. We will explore the chaos in a system of two junctions. It appears that investigation of such a simple model may be intellectually challenging and technically involved, in part because it requires understanding of the system properties far from equilibrium.The second project is devoted to the study of non-equilibrium properties of a junction consisting of superconducting leads connected by a mesoscopic normal metal bridge. In such SNS junctions, deviations from equilibrium arise inevitably, even in the limit of the smallest applied biases; developing an adequate theory is important for many applications. At the same time, it presents a serious challenge , as currently there are no convenient theoretical tools for predicting the behavior of strongly non-equilibrium states of SNS structures.The third project aims at obtaining estimates of the decoherence rate for a superconducting qubit coupled to a quantized radiation field. We will concentrate on mechanisms associated with the quasiparticle excitations in the superconducting grains forming the qubit.The research is relevant to experiment and may resolve several existing puzzles. Advances will aid further development of several analytical techniques. Graduate students will be trained. Results of the research will affect a number of fields including mesoscopic superconductivity, cold atomic gases and quantum chaos.%%%This theoretical research explores a number of topics related to non-equilibrium properties of superconducting junctions and their relation to chaos, structures of involving superconductors and their potential use in quantum computers. Students will be trained and connections made to experiment.***