Tuning the Gap of a Superconducting Flux Qubit

We experimentally demonstrate the in situ tunability of the minimum energy splitting (gap) of a superconducting flux qubit by means of an additional flux loop. Pulses applied via a local control line allow us to tune the gap over a range of several GHz on a nanosecond time scale. The strong flux sensitivity of the gap (up to $\sim 0.7\mathrm{GHz}/\mathrm{m}{\Phi }_0$) opens up the possibility to create different types of tunable couplings that are effective at the degeneracy point of the qubit. We investigate the dependence of the relaxation time and the Rabi frequency on the qubit gap.

Figure 1

(a) The flux qubit with $\alpha$-junction. (b) The ground state $|0⟩$ (black) and excited state $|1⟩$ (red) energy levels of the flux qubit vs magnetic energy of the qubit $ϵ$. As the $\alpha$-junction becomes smaller (dashed line) the gap $\Delta$ increases and the persistent-current $I_p$ (slope) decreases. (c) The qubit double-well potential. (d) Simplest implementation of a tunable-$\alpha$ qubit. The SQUID loop on the left serves as a tunable junction. (e) Tunable-$\alpha$ circuit used in this experiment. The eight-shaped gradiometric topology of the $ϵ$-loop allows for independent control of $\alpha$. The gradiometer loop is used to trap $N$ fluxoids to prebias the qubit at its degeneracy point ($\epsilon =0$).

Figure 2

(a) Atomic force micrograph (AFM) of the sample. The eight-shaped $(12\mu \mathrm{m}{)}^2$ gradiometer qubit is shown in blue with centered on the left the $\alpha$-loop (white box). The readout and control circuitry in the top layer are shown in red. Both layers are fabricated of aluminum using electron beam lithography and two-angle shadow evaporation. The inset (b) shows the $\alpha$-loop in a separate AFM graph and without the SQUID layer. Its area has been minimized to reduce crosstalk to the control circuitry. The two $\alpha$-junctions are designed to be half the size of the larger junctions. The inset (b) covers a second tunable-$\alpha$ qubit that is turned off ($N=0$) in this experiment. (c) Schematic representation of control and measurement pulses.

Figure 3

Microwave frequency $F$ vs magnetic frustration $f_{\epsilon }$ at $\alpha$ values 0.67 (a), 0.64 (b), and 0.61 (c). This change in $\alpha$ is obtained by applying a negative, zero or positive current pulse $I_{\alpha }$ at fixed magnetic field $B$. The color indicates the switching probability of the SQUID. The energy gaps and persistent currents obtain from a fit to Eq. (1) are $(\Delta ,I_p)=(1\mathrm{GHz},525\mathrm{nA})$, (4.6 GHz, 441 nA), and (8 GHz, 345 nA) for (a),(b), and (c), respectively. In the experiment $f_{\epsilon }$ is varied by changing the current $I_{\epsilon ,\mathrm{dc}}$ (top axes).

Figure 4

Qubit properties $\alpha$ (a), qubit gap $\Delta$ (b), persistent-current $I_p$ (c) and relaxation time $T_1$ at resonance frequency 6.8 GHz (d), 8.0 GHz (e) and 14 GHz (f) as a function of frustration $f_{\alpha }$. The solid lines trough the data points (circles) are obtained using the calculated parameters $C=3\mathrm{fF}$ and $\beta =0.063$ and by fitting $I_c=964\mathrm{nA}$, $I_{c\alpha }=0.53I_c$; here $N=1$. For further details see text.

Figure 5

(a) Rabi oscillations at $F=6.8\mathrm{GHz}$ and fixed power for different values of the gap ($\Delta$ is 0.45 GHz (bottom trace) to 0.95 GHz (top trace)). For clarity individual traces are shifted vertically. (b) The Rabi frequency of each trace in (a) is plotted as a function of the gap $\Delta$. The dashed line is a linear fit through the origin.