Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ “quantum tricks” such as squeezing and entanglement.

Quantum-enhanced measurements: beating the standard quantum limit.

Recent initial experiments in magnetic resonance force microscopy (MRFM) have detected the magnetic force exerted by electrons and nuclei in microscopic samples. The experiments generate a force signal by modulating the sample magnetization with standard magnetic resonance techniques. Sample sizes of a few nanograms generate readily detected force signals of order ${10}^{\ensuremath{-}14}$ to ${10}^{\ensuremath{-}16}$ Newtons. This article describes the present status of MRFM technology, with particular attention to the feasibility of detecting single-electron magnetic moments, and the possible applications of MRFM in biological imaging.

Magnetic resonance force microscopy

Significant progress has been made in recent years on the development of gravitational wave detectors. Sources such as coalescing compact binary systems, low-mass X-ray binaries, stellar collapses and pulsars are all possible candidates for detection. The most promising design of gravitational wave detector uses test masses a long distance apart and freely suspended as pendulums on Earth or in drag-free craft in space. The main theme of this review is a discussion of the mechanical and optical principles used in the various long baseline systems being built around the world — LIGO (USA), VIRGO (Italy/France), TAMA 300 (Japan) and GEO 600 (Germany/UK) — and in LISA, a proposed space-borne interferometer.

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Gravitational Wave Detection by Interferometry (Ground and Space)

We present a novel formulation for SQUID operation, which enables us to evaluate and compare the sensitivity and applicability of different devices. SQUID magnetometers for low-frequency applications are analyzed, taking into account the coupling circuits and electronics. We discuss nonhysteretic and hysteretic single-junction rf SQUIDs, but the main emphasis is on the dynamics, sensitivity, and coupling considerations of dc-SQUID magnetometers. A short review of current ideas on thin-film, dc-SQUID design presents the problems in coupling and the basic limits of sensitivity. The fabrication technology of tunnel-junction devices is discussed with emphasis on how it limits critical current densities, specific capacitances of junctions, minimum linewidths, conductor separations, etc. Properties of high-temperature superconductors are evaluated on the basis of recently published results on increased flux creep, low density of current carriers, and problems in fabricating reliable junctions. The optimization of electronics for different types of SQUIDs is presented. Finally, the most important low-frequency applications of SQUIDs in biomagnetism, metrology, geomagnetism, and some physics experiments demonstrate the various possibilities that state-of-the-art SQUIDs can provide.

SQUID magnetometers for low-frequency applications

We have constructed and tested a laser interferometer transducer for a long, wideband, laser-linked gravitational radiation antenna. Photon-noise-limited performance was achieved using 80 microW from a single mode Spectra-Physics 119 laser in a modified Michelson interferometer on a vibration isolation table in a quiet room. A piezoelectric driver on one of the interferometer mirrors was used to generate subangstrom (3 x 10(-14)-m) vibrations of known amplitude. The measured displacement sensitivity of the system in the kilohertz region was 1.3 x 10(-14)m/Hz(1/2), which compares well with the calculated photon noise limit of 1.06 x 10(-14) m/Hz(1/2). This is the smallest vibrational displacement measured directly with a laser to date.

Photon-noise-limited laser transducer for gravitational antenna

Detection of gravitational radiation by some form of Michelson interferometer illuminated by a laser depends on observing the small relative displacements or forces which would be induced in test masses by a gravitational wave. The uncertainty principle would appear to set one limit to the sensitivity for detection of such displacements by a linear position-sensing system such as an optical interferometer. The authors discuss this limit, and also show how one method of treating photon statistics and photon recoil effects yields a similar limit. This is done in the spirit of the 'Heisenberg microscope'.

https://iopscience.iop.org/article/10.1088/0022-3735/11/7/030/pdf

Limits to the measurement of displacement in an interferometric gravitational radiation detector

The noise theory of an RF SQUID is extended to include those components of flux noise which appear physically linking the SQUID loop. This noise is a consequence of phase fluctuations of the quantum transitions in the SQUID and can react on the system whose parameters are being measured by the SQUID sensor. In particular, gravitational wave detector is considered whose motion is sensed by an RF SQUID system; and it is shown that the back-reaction, combined with other noise, imposes a limit to the detector sensitivity.

http://iopscience.iop.org/article/10.1088/0022-3735/10/10/014/pdf

W A Edelstein

Papers

Limits to the measurement of displacement in an interferometric gravitational radiation detector

An extension to the noise theory of RF SQUIDs with implications for gravitational radiation detectors