Half-integer Shapiro-steps in superconducting qubit with a $\pi$-Josephson junction

TL;DR

This paper investigates a superconducting SQUID with 0- and π-Josephson junctions, revealing half-integer Shapiro-steps induced by spontaneous currents, which could enable π-qubits for quantum computing.

Contribution

It demonstrates the occurrence of half-integer Shapiro-steps in a π-SQUID and proposes its potential as a π-qubit with spontaneous currents.

Findings

Half-integer Shapiro-steps observed under microwave irradiation.

Spontaneous loop currents induce half-integer SS.

Equivalence of 0- and π-JJs is key for half-integer SS.

Abstract

A superconducting quantum interference device (SQUID) comprising 0- and $\pi$-Josephson junctions (JJs), called $\pi$-SQUID, is studied by the resistively shunted junction model. The $\pi$-SQUID shows half-integer Shapiro-steps (SS) under microwave irradiation at the voltage $V$ = $(\hbar/2e)\Omega (n/2)$, with angular frequency $\Omega$ and half-integer $n$/2 in addition to integer $n$. We show that the $\pi$-SQUID can be a $\pi$-qubit with spontaneous loop currents by which the half-integer SS are induced. Making the 0- and $\pi$-JJs equivalent is a key for the half-integer SS and realizing the $\pi$-qubit.