Probing Noise in Flux Qubits via Macroscopic Resonant Tunneling

Macroscopic resonant tunneling between the two lowest lying states of a bistable rf SQUID is used to characterize noise in a flux qubit. Measurements of the incoherent decay rate as a function of flux bias revealed a Gaussian-shaped profile that is not peaked at the resonance point but is shifted to a bias at which the initial well is higher than the target well. The rms amplitude of the noise, which is proportional to the dephasing rate $1/{\tau }_{\phi }$, was observed to be weakly dependent on temperature below 70 mK. Analysis of these results indicates that the dominant source of low energy flux noise in this device is a quantum mechanical environment in thermal equilibrium.

Figure 1

(a) MRT flux control bias sequence as a function of time. The inset depicts a CJJ rf SQUID subjected to the external biases ${\Phi }_x^{\mathrm{cjj}}$ and ${\Phi }_x^q$. The sense of the macroscopic persistent current states $|0⟩$ (counterclockwise) and $|1⟩$ (clockwise) is noted. (b) Evolution of the qubit potential $U(\Phi )$.

Figure 2

(a) MRT from the initial state $|0⟩$ versus $t$ at $T_{\mathrm{th}}=28\mathrm{mK}$. Results are shown for ${\Phi }_f^q=-0.488\mathrm{m}{\Phi }_0$ (solid squares), $-0.014\mathrm{m}{\Phi }_0$ (hollow circles), and $0.554\mathrm{m}{\Phi }_0$ (solid circles). Slopes of the linear fits yield $-{\Gamma }_{01}({\Phi }_f^q)$. (b) ${\Gamma }_{01}$ (hollow symbols) and ${\Gamma }_{10}$ (solid symbols) versus ${\Phi }_f^q$ at $T_{\mathrm{th}}=28\mathrm{mK}$. The peaks nearest ${\Phi }_f^q=0$ have been fit to Eq. (2).

Figure 3

(a) ${ϵ}_p$ (solid symbols, upper plot), $W$ (hollow symbols, upper plot), and $\Delta$ (solid symbols, lower plot) versus $T_{\mathrm{th}}$. $W$ and $\Delta$ have been fit to lines (dashed) and ${ϵ}_p$ to $C/T_{\mathrm{th}}^{\alpha }$ (solid). (b) $T_{\mathrm{eff}}=W^2/2{ϵ}_p$ versus $T_{\mathrm{th}}$. The dashed line indicates $T_{\mathrm{eff}}=T_{\mathrm{th}}$.