Suppression of tunneling in a superconducting persistent-current qubit

We consider a superconducting persistent-current qubit consisting of a three-junction superconducting loop in an applied magnetic field. We show that by choosing the field, Josephson couplings, and offset charges suitably, we can perfectly suppress the tunneling between the two oppositely directed states of circulating current, leading to a vanishing of the splitting between the two qubit states. This suppression arises from interference between tunneling along different paths and is analogous to that predicted previously for magnetic particles with half-integer spin.

Figure 1

Schematic of the circuit for the three-junction qubit, after Ref. 12. There are two superconducting islands, denoted 1 and 2, whose voltages are $V_1$ and $V_2$. The three junctions in the circuit are indicated by crosses; the $i\text{th}$ junction has capacitance $C_i$ and Josephson coupling energy $E_{Ji}$. An external flux $\Phi =f{\Phi }_0$ passes through the circuit. The superconducting islands 1 and 2 are also connected to applied voltages $V_A$ and $V_B$ through capacitors $C_{gA}$ and $C_{gB}$; the voltage across these capacitors is $V_{gA}=V_A-V_1$ and $V_{gB}=V_B-V_2$.

Figure 2

Contour plot of the potential $\mathcal{U}({\varphi }_1,{\varphi }_2)$ for the special case $\alpha =1.3$ (see text). The horizontal and vertical axes represent ${\varphi }_1$ and ${\varphi }_2$. Darker shading means larger values of $\mathcal{U}$. For this choice of $\alpha =1.3$, the state denoted by a box with vertical lines in the lower right of the white square can tunnel to another state only along the heavy line; for other directions, the tunneling barrier is much higher. The white square represents the unit cell used in the text.

Figure 3

Contour plot of the splitting $2\sqrt{F^2+{\mid t\mid }^2}$. The horizontal and vertical axes represent $(Q_A+Q_B)∕e$ and $f$. Darker shading means larger values of the splitting. Except for the value of $\alpha$, we have used the same parameters as in Ref. 12 (see text). The splitting vanishes when $(Q_A+Q_B)∕e$ is an odd integer and $f=1∕2$.