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expectations.

One of our main research topics on current fluctuations has been their measurement, and especially that of non-Gaussian noise. In 2007 we showed how the relaxation rate of quantum bits can be employed to “measure” the frequency dependent third cumulant of current fluctuations. It turns out from the full quantum theory of these fluctuations that the detailed description of these effects is very sensitive to the proper ordering of the current operators employed in the theory. In this work we showed that depending on how the fluctuations are connected, a quantum bit can act both as a “quantum observer” for the fluctuations, in which case it detects a non-classical ordering of the current fluctuations, or as a “classical observer” in which case it is only sensitive to the fluctuations that correspond to the “classical” ordering. Connected to this work, we also participated in the analyzing of the experimental results from the PICO group on the third-cumulant effects on the supercurrent escape process.

#### OPEN QUANTUM CIRCUITS

Tero Heikkilä, Matti Laakso, and Teemu Ojanen

Collaborators: V. Bergholm and J. Salo (Laboratory of Physics, TKK), P. Helistö, A. Luukanen and A.O. Niskanen (VTT), and A. A. Abdumalikov and Y. Nakamura (NEC, Tsukuba, Japan)

Large part of our research on open quantum circuits is summarized in the doctoral thesis of Teemu Ojanen. During the year 2007 our group studied for example effects related to relaxation and decoherence in quantum bits. The effects of quantum and classical noise on qubit dynamics were compared and it was shown how pairs of qubits coupled to the same fluctuating bath can be efficiently decoupled from the noise. Our group also studied the squeezing of quantum states with on-chip elements, an effect which allows measuring position or momentum coordinates more accurately than what is predicted by the Heisenberg’s uncertainty principle. These works were done in collaboration with the Laboratory of Physics of TKK and with the NEC Fundamental and Environmental Research Laboratories, Japan.

Recently, we studied the reactive response of single-electron transistors (SET) and showed that the correlations induced by the Coulomb energy in the system can make rise to a gate-dependent capacitance contribution in the SET response (see Fig. 2).

Annual Report 2007