Flux Noise in a Superconducting Transmission Line

Abstract

We study a superconducting transmission line (TL) formed by distributed LC oscillators and excited by external magnetic fluxes which are aroused from random magnetization (A) placed in substrate or (B) distributed at interfaces of a two-wire TL. Low-frequency dynamics of a random magnetic field is described based on the diffusion Langevin equation with a short-range source caused by (a) random amplitude or (b) gradient of magnetization. For a TL modeled as a two-port network with open and shorted ends, the effective magnetic flux at the open end has non-local dependency on noise distribution along the TL. The flux-flux correlation function is evaluated and analyzed for the regimes (Aa), (Ab). (Ba), and (Bb). Essential frequency dispersion takes place around the inverse diffusion time of random flux along the TL. Typically, noise effect increases with size faster than the area of TL. The flux-flux correlator can be verified both via the population relaxation rate of the qubit, which is formed by the Josephson junction shunted by the TL with flux noises, and via random voltage at the open end of the TL.

Effect of 1/f noise on the dissipative dynamics of an LC-shunted qubit

“…A possible deviation from 1/f spectrum, e.g. due to the size effect in the transmission line [23], may be described similarly after choosing a specific parameters of device. (d) The qubit-noise interaction is studied by adding random fluxes to the tilt and control fluxes and by taking into account correlations between these sources.…”

“…Due to softness of the barrier, there is no the dependency ν 1 ∝ ω −1 10 for the 1/f noise under consideration. This disagreement with [16] may be compensated by the frequency dispersion of noise caused by the size effect in transmission line [23]. (4) There is a dip of decoherence : the rate ν 2 and the renormalization of the gap frequency are increased sharply around ϕ = 0 and are saturated with increasing of ϕ.…”