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We show that charge noise $S_Q$ in Josephson qubits can be produced byfluctuating two level systems (TLS) with electric dipole moments in thesubstrate using a flat density of states. At high frequencies the frequency andtemperature dependence of the charge noise depends on the ratio $J/J_c$ of theelectromagnetic flux $J$ to the critical flux $J_c$. It is not widelyappreciated that TLS in small qubits can easily be strongly saturated with$J/J_c\gg 1$. Our results are consistent with experimental conclusions that$S_Q\sim 1/f$ at low frequencies and $S_Q\sim f$ at high frequencies.

Effect of Two Level System Saturation on Charge Noise in Josephson Junction Qubits