Unusual quantum magnetic-resistive oscillations in a superconducting structure of two circular asymmetric loops in series

We measured both quantum oscillations of a rectified time-averaged direct voltage Vrec(B) and a dc voltage Vdc(B) as a function of normal magnetic field B, in a thin-film aluminum structure of two asymmetric circular loops in series at temperatures below the superconducting critical temperature Tc. The Vrec(B) and Vdc(B) voltages were observed in the structure biased only with an alternating current (without a dc component) and only with a direct current (without an ac component), respectively. The aim of the measurements was to find whether interaction (nonlinear coupling) exists between quantum magnetic-resistive states of two loops at a large distance from each other. The distance between the loop centers was by an order of magnitude longer than the Ginzburg-Landau coherence length ξ(T). At such distance, one would not expect to detect any interaction between the quantum states of the loops. But we did find such an interaction. Moreover, we found that Vdc(B) functions (like Vrec(B) ones) can be used to describe the quantum states of the loops.