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    Measurement of the Current-Phase Relation in Josephson Junctions Rhombi Chains

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    We present low temperature transport measurements in one dimensional Josephson junctions rhombi chains. We have measured the current phase relation of a chain of 8 rhombi. The junctions are either in the classical phase regime with the Josephson energy much larger than the charging energy, EJ≫ECE_{J}\gg E_{C}, or in the quantum phase regime where EJ/EC≈2E_{J}/E_{C}\approx 2. In the strong Josephson coupling regime (EJ≫EC≫kBTE_{J}\gg E_{C} \gg k_{B}T) we observe a sawtooth-like supercurrent as a function of the phase difference over the chain. The period of the supercurrent oscillations changes abruptly from one flux quantum Φ0\Phi_{0} to half the flux quantum Φ0/2\Phi_{0}/2 as the rhombi are tuned in the vicinity of full frustration. The main observed features can be understood from the complex energy ground state of the chain. For EJ/EC≈2E_{J}/E_{C}\approx 2 we do observe a dramatic suppression and rounding of the switching current dependence which we found to be consistent with the model developed by Matveev et al.(Phys. Rev. Lett. {\bf 89}, 096802(2002)) for long Josephson junctions chains.Comment: to appear in Phys. Rev.