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We have investigated decoherence in Josephson-junction flux qubits. Based onthe measurements of decoherence at various bias conditions, we discriminatecontributions of different noise sources. In particular, we present a Gaussiandecay function of the echo signal as evidence of dephasing due to $1/f$ fluxnoise whose spectral density is evaluated to be about $(10^{-6} \Phi_0)^2$/Hzat 1 Hz. We also demonstrate that at an optimal bias condition where the noisesources are well decoupled the coherence observed in the echo measurement ismainly limited by energy relaxation of the qubit.Comment: 4 pages, error in Fig.4 corrected, to appear in PR

physical review letters

Decoherence of Flux Qubits due to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>f</mml:mi></mml:math>Flux Noise

Decoherence of Flux Qubits due to1/fFlux Noise