Publisher Summary This chapter discusses the behavior of macroscopic quantum circuits. Quantum circuits are electromagnetic circuits whose behavior is governed by the laws of quantum, rather than classical, mechanics. Macroscopic refers to the typical magnitudes of the expectation values of the currents and voltages, which these circuits display. Currents and voltages, rather than magnetic and electric fields, are the quantities that are measured in order to classify the behavior of low-frequency circuits. The chapter shows how the methods to probe macroscopic quantum circuits divide into two categories. The circuit can either be probed directly with classical measurement apparatus, or probed indirectly by coupling this apparatus to the local environment of the circuit. In fact, this classification is not unique to quantum circuits. Success has been found in probing quantum circuits indirectly, by examining their local environment. By this method, evidence for the macroscopic superposition of currents has been obtained.

Chapter 4: Quantum Phenomena in Circuits at Low Temperatures

A brief review of the history of ten workshops/conferences on “Squeezed States and Uncertainty Relations” and main achievements in the related fields of quantum physics for the period from 1991 to 2007 are presented.

Squeezed states and uncertainty relations since 1991

We discuss the response of a superconducting weak-link ring to externally applied adiabatic noise and show that this can be used as a probe of the low-lying energy eigenstates of the ring. We compare the observable consequences of this with new experimental results.

The response of a superconducting weak-link ring to external adiabatic noise

Superconducting rings, superselection rules and quantum measurement problems

We discuss the dynamical behaviour of coupled quantum objects. This leads to a novel method of observing macroscopic quantum behaviour.

Coupled quantum object dynamics

We calculate the dynamical behaviour of a classical circuit weakly coupled to a macroscopic quantum circuit, in the adiabatic limit. The quantum circuit generates characteristic signatures in these dynamics. The relevance of these results to SQUID magnetometer experiments is discussed.

The Dynamics of a Quantum Circuit Connected to a Classical Lossy Oscillator

The coherent behavior of a weak link in the limit where the stored electric energy dominates the charge tunneling energy is discussed. Particular attention is paid to the realization of the source term in the Hamiltonian.

Weak-link behavior in the small-charge tunneling limit

To illustrate the duality between electric and magnetic views of quantum circuits, we compare and contrast the origins of the Josephson frequency and the current bias frequency in each case.

Electromagnetic duality in quantum circuits

We discuss the quantum mechanical superposition of macroscopically different states in the light of experiments performed on superconducting circuits, and conclude that compelling evidence for this effect exists.

D. A. Poulton

Papers

The Dynamics of a Quantum Circuit Connected to a Classical Lossy Oscillator

Coupled quantum object dynamics

Weak-link behavior in the small-charge tunneling limit

Electromagnetic duality in quantum circuits

Macroscopic superposition in superconducting circuits