Interpretation of superposed left- and right-moving currents in a SQUID

Determine how a coherent superposition of left- and right-moving superconducting currents in a superconducting quantum interference device (SQUID) should be interpreted, specifying the physical meaning of such a superposition and its status as a macroscopic or microscopic quantum effect within the different theoretical formalisms used to model SQUID dynamics.

Background

The paper discusses how macroscopicity can depend on the chosen degrees of freedom and measurement perspective, using superconductivity and SQUIDs as a key example. Leggett highlighted superconductivity as a microscopic quantum effect while posing the question about interpreting superpositions of left- and right-moving currents in SQUIDs.

The authors note that this question remains unresolved due to multiple equivalent theoretical descriptions (e.g., mapping to a particle in a tilted double-well potential and considering collective variables like total flux or total current). Depending on whether one measures the total current or focuses on individual Cooper pairs and local processes (like Andreev reflection), conclusions about macroscopicity can differ. This underscores that a definitive interpretational framework is lacking.

References

In a seminal paper, Leggett argued that superconductivity itself is a paradigmatic example for a microscopic quantum effect , however, he also raised the question of how a superposition of left- and right moving currents in a SQUID should be interpreted. As reviewed in , this question is still under debate, even 40 years after it was raised.

— How many lives does Schrödinger's cat have?  (2412.05104 - López-Incera et al., 2024) in Section 5.1 (Transition from Cat B to Cat A), Applications