Flux Noise Probed with Real Time Qubit Tomography in a Josephson Phase Qubit

We measure the dependence of qubit phase coherence and flux noise on inductor loop geometry. While wider inductor traces change neither the flux noise power spectrum nor the qubit dephasing time, increased inductance leads to a simultaneous increase in both. Using our new tomographic protocol for measuring low frequency flux noise, we make a direct comparison between the flux noise spectrum and qubit phase decay, finding agreement within 10% of theory.

Figure 1

Phase qubit devices used in the experiments. Panel (a) shows the readout SQUID, inductor coils, bias coils, and shunt capacitor; panels (b), (c), and (d) show close-ups of the inductors and SQUIDs. Panel (b) shows the standard qubit coils, (c) the wide trace coils, and (d) the high inductance coils. Horizontal image lengths are (b) $117\mu \mathrm{m}$, (c) $173\mu \mathrm{m}$, and (d) $123\mu \mathrm{m}$. Device parameters are given in Table .

Figure 2

The Ramsey tomography oscilloscope protocol. (a) Four Ramsey sequences are performed: two with the final $\pi /2$ pulse about the $\pm X$ axes and two with the final $\pi /2$ pulse about the $\pm Y$ axes. The precession time for both sequences is fixed at $\tau =100\mathrm{ns}$. (b) The combined $X$ axis and $Y$ axis sequences constitute tomography of the state in the $x,y$ plane after precession by $\tau$, thereby measuring the angle $\phi$ traversed by the state. (c) Several hundred subsequent $X$ and $Y$ measurements are grouped together to get an average value for $\phi$. The entire process is repeated once per second for several hours to build up a time series $\delta f(t)=\delta \phi (t)/2\pi \tau$.

Figure 3

Power spectra for each inductor design. (a) Typical spectra for each type of device. (b) Spectral power integrated over the range 0.001 to 0.1 Hz. In (a) we plot only one spectrum for each device design for clarity in the plot. In (b) we show several curves, measured at several bias points, in devices all fabricated on the same wafer.

Figure 4

Plot of Ramsey decay time $T_2^{*}$ vs nonlinearity $\Delta$ for each type of device. Each point comes from a fit to Eq. (3). For each bias flux, $T_1$ and $\Delta$ are measured in separate experiments. Dashed fit lines are drawn with the predicted slope of $-3/4$ in order to compare magnitudes. The fit lines for the standard and wide trace designs fall on top of one another. The high inductance devices show an increase in $T_2^{*}$ by a factor of 1.3. Confidence bounds, typically 2% of data values, cannot be seen on this scale.