Recently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system’s response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/$e^2$. .AE

• Received 1 March 1985

DOI:https://doi.org/10.1103/PhysRevB.32.76