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Physical Review Letters

Can a noninvasive measurement of magnetic flux be performed with superconducting circuits?

Claudia D. Tesche

Published May 14, 1990• 121 citations
Publisher

Abstract

A gedanken experiment is described in which the noninvasive determination of joint probability densities for the magnetic flux linking a superconducting quantum-interference device is determined using variable threshold superconducting switches followed by superconducting magnetometers. As a result, it is demonstrated that an important prediction of quantum mechanics can be tested in principle against those of macrorealistic theories using superconducting circuits.

DOI
10.1103/physrevlett.64.2358

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A gedanken experiment is described in which the noninvasive determination of joint probability densities for the magnetic flux linking a superconducting quantum-interference device is determined using variable threshold superconducting switches followed by superconducting magnetometers. As a result, it is demonstrated that an important prediction of quantum mechanics can be tested in principle against those of macrorealistic theories using superconducting circuits.
Abstract Superconducting quantum interference devices (SQUIDs) are made by a superconducting loop interrupted by one or more Josephson junctions. They are described in terms of a macroscopic variable, the magnetic flux, which shows quantum effects such as tunnelling through a potential barrier. Besides making up the source of a quantum state, SQUIDs also provide the instruments necessary for its probing: as a fact, SQUID based magnetometers have a sensitivity approaching the quantum limit. In this paper I will review the working principle of these devices and illustrate the system of SQUIDs realized in my group to test the quantum behavior at a macroscopic level.
We propose a novel device, based on a series of dc SQUIDs (direct current Superconducting QUantum Interference Devices), each one with different sensitive area, that can be used to perform absolute measurements of magnetic field. With this array, we overcome the limit of a single dc SQUID of being sensitive only to variations of the linked magnetic flux. The overall voltage-flux characteristic of our device, in fact, has a non-periodic shape that allows a clear identification of the point with zero magnetic field. We present a discussion of the working principle and of the main characteristics, which have been partially tested on a prototype.
Superconducting quantum interference devices (SQUIDs) are among the most sensitive detectors for out-of-plane magnetic field components. However, due to their periodic response with short modulation period M=1Φ0M = 1 Φ_0M=1Φ0​, determined by the magnetic flux quantum Φ0≈2.068×10−15 WbΦ_0 \approx 2.068\times 10^{-15}\,\mathrm{Wb}Φ0​≈2.068×10−15Wb, it is difficult to infer the value of the magnetic flux unambiguously, especially in case the magnetic flux enclosed in the SQUID loop changes by many flux quanta. Here, we demonstrate that by introducing a second degree of freedom in the form of a second SQUID, we substantially enhance the modulation period MMM of our device without sacrificing sensitivity. As a proof of concept, we implement our idea by embedding two asymmetric direct current SQUIDs into a common tank circuit. By measuring the reflection coefficient of the device, we extract the two lowest energy eigenfrequencies as a function of the external magnetic flux created by a superconducting field coil, from which we experimentally deduce a modulation period M≥15Φ0M \geq 15 Φ_0M≥15Φ0​, as well as the magnetic offset-field B0=22 nTB_0 = 22\,\mathrm{nT}B0​=22nT present in our experiment.
Time-dependent external flux is ubiquitous across circuit quantum electrodynamics and calls for accurate modeling. Contrary to long-held belief, it is recently predicted---but not yet verified---that the allocation of time-dependent flux cannot be arbitrary in the Hamiltonian. This study provides an experimental verification of this prediction by applying fast flux pulses to a fluxonium qubit and taking measurements of the quantum state following the pulses. Given the widespread use of time-dependent flux in experiments with superconducting qubits, verification of this theory is critical to our understanding of circuit quantum electrodynamics.
We have realized and tested a fast stroboscopic detector for magnetic flux measurements. The key element of our detector is a hysteretic dc superconducting quantum interference device (SQUID). Stroboscopic read-out of the magnetic flux coupled with the SQUID is accomplished by biasing the SQUID with fast current pulses. The shorter these pulses, the more stroboscopic and less invasive the measurement we are performing. In order to reduce the duration of the current pulses, we take advantage of the superconducting-normal transition induced by laser light in thin superconducting films. The interaction of laser light with superconducting thin films has been investigated thoroughly in the past and many applications have been proposed which rely on the fast typical times with which superconductivity is broken and a resistive behavior arises. We have measured a threshold resolution of 6.9mΦ0 at 4.2 K, and this value corresponds to the thermodynamic limit of the SQUID. The detector has been accurately characterized: An improved and more sensitive version might prove useful for quantum mechanics and quantum computation experiments, for example, in detecting the state of flux qubits.
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.