Half-integer Shapiro-steps in superconducting qubit with a π-Josephson junction

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