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=, 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.

中文翻译：

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具有 π-约瑟夫森结的超导量子比特中的半整数夏皮罗步

通过电阻分流结模型研究了一种由0-和π-约瑟夫森结(JJs)组成的超导量子干涉器件(SQUID) ，称为π -SQUID。π -SQUID在电压V =的微波辐照下显示半整数夏皮罗阶 (SS) ，除了整数n外，角频率为 Ω 和半整数n /2 。我们证明了π -SQUID 可以是一个具有自发回路电流的π -qubit，通过该回路电流可以感应出半整数 SS。使 0- 和π -JJs 等价是半整数 SS 和实现π -qubit 的关键。