Noise correlations in a flux qubit with tunable tunnel coupling

We have measured flux-noise correlations in a tunable superconducting flux qubit. The device consists of two loops that independently control the qubit’s energy splitting and tunnel coupling. Low-frequency flux noise in the loops causes fluctuations of the qubit frequency and leads to dephasing. Since the noises in the two loops couple to different terms of the qubit Hamiltonian, a measurement of the dephasing rate at different bias points provides a way to extract both the amplitude and the sign of the noise correlations. We find that the flux fluctuations in the two loops are anticorrelated, consistent with a model where the flux noise is generated by randomly oriented unpaired spins on the metal surface.

Figure 1

(a) A standard flux qubit. The two diabatic states correspond to clockwise and counterclockwise circulating currents. (b) A tunable flux qubit. The smallest junction has been replaced by an additional loop. (c) The actual sample design. The qubit is embedded in a SQUID used for readout of the qubit state. The line widths are not drawn to scale; a detailed drawing can be found in Appendix pp1.

Figure 2

(a) Qubit spectra, measured for two values of $f_x$. The features at 3.2 GHz are due to the SQUID plasma frequency. Note that the scale for $f_z$ is magnified by a factor of 1000. (b) Qubit tunnel coupling $\Delta$ measured as a function of $f_x$. The dashed line is the result of a numerical simulation. (c) Numerical derivative $\partial \Delta /\partial f_x$ of the data in (b).

Figure 3

(a) Energy decay time $T_1$. The decay does not depend strongly on the flux detuning. (b) Echo and free-induction decay times versus flux detuning. The position of the longest decay times is shifted to positive flux detuning. (c) Free-induction decay measured at $f_x=\pm 0.39$. Depending on the sign of $f_x$, the position of the longest decay time shifts in different directions. All measurements were done by sweeping $f_z$ while keeping $f_x$ constant.

Figure 4

(a) Phase decay rate ${\Gamma }_{\varphi F}$ expected from the sensitivities shown in (b), with $A_z=A_x=\left(3\mu {\Phi }_0^2\right)$. (b) Sensitivity of the qubit energy to flux fluctuations. For perfectly correlated noise ($c_{zx}=\pm 1$), the fluctuations cancel out when $\partial E_{01}/\partial f_x=\mp \partial E_{01}/\partial f_z$. (c) Measured decay rate ${\Gamma }_{\varphi F}$. The fit gives a correlation factor of $c_{zx}=-0.25$. (d) Schematic picture of the surface-spin model. Spins located on the shared line labeled $d_c$ induce fields pointing in opposite directions in the two loops.

Figure 5

(a) Drawing of the device, showing the location of metal from the two evaporation stages. (b) SEM picture of a device with the same geometry as the one used in the experiments.