V. I. Kuznetsov, A. A. Firsov
We measured unusual quantum oscillations of a rectified direct voltage V_{rec}(B) biased with an alternating current (without a dc component) and dc voltage V_{dc}(B) biased with a direct current (without an ac component) as a function of magnetic field $B$ in a thin-film aluminum structure consisting of two different serial circular asymmetric at temperatures slightly below the superconducting critical temperature T_{c}. The distance between the loop centers is many times longer than the superconducting coherence length of pure aluminum at zero temperature. Fourier analysis of these V_{rec}(B) and V_{dc}(B) oscillations gives two fundamental frequencies, attributable to periodic responses of each loop to the changing magnetic field, and the sum and difference of these fundamental frequencies. Moreover, the Fourier spectrum contains two low frequencies characterizing the oscillation envelopes as well as a variety of linear combinations consisting of fundamental and/or low frequencies. We found the coupling between the quantum states of these serial loops persists if the loops are moving apart to a considerable distance equal to the penetration depth of an electric field into the superconductor. In low fields, V_{rec}(B) and V_{dc}(B) oscillations are of unusual character and cannot be described in terms of the simple Ginsburg-Landau quasi-one-dimensional model.
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http://arxiv.org/abs/1210.1678
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