Classical rhombi chain
The measured current-phase relation for a classical rhombi chain (EJ/EC 20) is plotted in Figure 2a and b for two different frustration parameters f = 0 and f = 0.5, zero and full frustration respectively. In both cases they follow a sawtooth dependence as expected, since in the classical regime E(g) is a series of shifted parabolas as a function of g. Interestingly, the period of the supercurrent oscillations as a function of the phase difference changes abruptly from 2p to p as the rhombi are tuned to the vicinity of full frustration. This double periodicity can be explained by the existence of two different persistent current configuration states (circulating clockwise and counterclockwise) in each rhombus for frustration close to f=0.5 (see reference 6).
Fig. 2 : Measured current-phase relation I(g) at T = 26mK. a) Dependence near rhombus frustration f = 0. b) Dependence near full rhombi frustration f = 0.5.
The measurement of the current-phase relation obtained for a quantum chain with EJ/EC 2 close to zero frustration is shown in figure 3. The main feature here is the smearing of the sawtooth dependence to a smooth sinusoidal one by keeping a periodicity of 2p. This measured current-phase relation can be explained by the presence of quantum fluctuations, that grow with decreasing ratio EJ/Ec and increasing number of Josephson junction rhombi. Quantum fluctuations lift the degeneracy at the crossing points of the parabolas in the classical energy spectrum. They produce therefore phase slip events on individual rhombi that smear the sawtooth function obtained in the classical regime. The measured current-phase relation could be fitted by a tight binding model initially proposed by Matveev et al.7 for single junction chains and extended to rhombi chains. This is the first time that this model has been verified experimentally.
Figure 3 : Current-phase relation of a quantum rhombi chain at frustration f=0. The dots show the measured switching current versus external magnetic field. The line represents the theoretical fit.