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Journal of Physics A Mathematical and General

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

F. E. Harrison, K. Kong Wan

Published Jul 7, 1997• 6 citations
Publisher

Abstract

Using a Hilbert space formalism we present axiomatic models of both a current-fed thick superconducting ring and a dc 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.

DOI
10.1088/0305-4470/30/13/023

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Using a Hilbert space formalism we present axiomatic models of both a current-fed thick superconducting ring and a dc 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.
The recovery of classical nonlinear and chaotic dynamics from quantum systems has long been a subject of interest.Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing.In this paper, we discuss the quantum to classical crossover of a superconducting quantum interference device (SQUID) ring.Such devices comprise a thick superconducting loop enclosing a Josephson weak link and are currently strong candidates for many applications in quantum technologies.The weak link brings with it a nonlinearity such that semiclassical models of this system can exhibit nonlinear and chaotic dynamics.For many similar systems an application of the correspondence principle together with the inclusion of environmental degrees of freedom through a quantum trajectories approach can be used to effectively recover classical dynamics.Here we show (i) that the standard expression of the correspondence principle is incompatible with the ring Hamiltonian and we present a more pragmatic and general expression which finds application here and (ii) that practical limitations to circuit parameters of the SQUID ring prevent arbitrarily accurate recovery of classical nonlinear dynamics.
In Chapter 2 we made use of a hypothetical arrangement of a strongly coupled superconducting ring, interrupted by a region of weak superconductivity, to derive the essential features of the Josephson effects. In practice this same arrangement is actually employed as the basis of one of the most useful superconducting devices developed so far, the single-junction, or rf, squid . (As mentioned in the Introduction, squid is an acronym for Superconducting QUantum Interference Device.) Here the essential physics behind the operation of these important devices will be described, and in the following section the practical realisation of an rf squid with its associated readout electronics will be explained. Chapter 4 will treat in a similar way dc squid s, which are related devices possessing two weak links in a single ring, whose mode of operation is rather different.
Abstract Superconductivity manifests macroscopic quantum phenomena. A superconducting circuit composed of Josephson junctions, Cooper pair boxes, and rf-/dc-SQUID, properly miniaturized, becomes quantized and demonstrates Rabi oscillations and entanglement. In this paper, we offer an overview of this approach. We begin with an introduction of the history and elementary theory of superconductivity. Then we describe the building blocks of superconducting classical circuits and derive their canonical quantizations. The set-up of qubits and superconducting quantum logic gates are then examined. Finally, ways to make measurements are discussed.
The recovery of classical chaotic dynamics from quantum systems has long been a subject of interest. Furthermore, recent work indicates that quantum chaos may well be significant in quantum information processing. In this paper we discuss the quantum to classical crossover of a superconducting quantum inference device (SQUID) ring. Such devices comprise of thick superconducting loop enclosing a Josephson weak link. These devices are currently strong candidates for many applications in quantum technologies. The weak link brings with it a non-linearity such that semi-classical models of this system can exhibit chaotic dynamics. For many similar systems an application of the correspondence principle together with the inclusion of environmental degrees of freedom through a quantum trajectories approach can be used to effectively recover classical dynamics. Here we show (i) that the standard expression of the correspondence principle is incompatible with the ring Hamiltonian and we present a more pragmatic and general expression which finds application here and (ii) that practical limitations to circuit parameters of the SQUID ring prevent arbitrarily accurate recovery of classical chaotic dynamics.
A dc superconducting quantum interference device (SQUID) consisting of a symmetric ring circuit with four Josephson junctions and two independent external currents I1{I}_{1}I1​ and I2{I}_{2}I2​, which enter the circuit at different points, has a phase boundary between the fully superconducting and the normal states that is different from that of a conventional SQUID. The control current I2{I}_{2}I2​ modifies the magnetic flux (\ensuremath{\varphi}) periodicity and the value of the maximum measuring current I1m{I}_{1m}I1m​(\ensuremath{\varphi}). For values of I2{I}_{2}I2​>Ic{I}_{c}Ic​ (critical current of Josephson junction) the fully resistive state exists over flux intervals centered around (n+(1/2)${\ensuremath{\varphi}}_{0}$, where n is an integer and ${\ensuremath{\varphi}}_{0}$ is the fluxoid quantum. A superconducting circuit without Josephson junctions is suggested which should have a phase boundary similar to that found here. Minimization procedures which are usually employed in analyzing SQUID's are discussed.