Macroscopic quantum systems as measuring devices: dc SQUIDs and superselection rules

Using a Hilbert space formalism we present axiomatic models of both a current-fed thick superconducting ring and a de SQUID (superconducting quantum interference device) as quantum systems possessing superselection rules. A method of quantization by parts is introduced to establish a quantum theory of a system having a circuit configuration. This involves separate quantization of parts of a circuit: the whole system is then recovered by adding these separately quantized parts together. Our models make clear the difference between standard quantum interference and the interference effects exhibited by SQUIDs. They lead us to question a commonly accepted definition of a classical system, and also clarify the properties required of measuring apparatus in the quantum and classical realms.