The standard quantum limits on several macroscopic quantities and the conditions for attaining these limits are evaluated. Possibilities for exceeding them by means of quantum nondemolition measurements are examined. The best frequency stability in self-excited oscillators, the smallest mechanical displacements, and the highest Q values of mechanical and electromagnetic resonators which have been achieved are reviewed. The outlook for improving the sensitivity in several gravitational experiments is evaluated.
The standard quantum limits on several macroscopic quantities and the conditions for attaining these limits are evaluated. Possibilities for exceeding them by means of quantum nondemolition measurements are examined. The best frequency stability in self-excited oscillators, the smallest mechanical displacements, and the highest Q values of mechanical and electromagnetic resonators which have been achieved are reviewed. The outlook for improving the sensitivity in several gravitational experiments is evaluated.
Perfection of the technique of macroscopic physical experiments has recently been proceeding so intensively that we can now inquire naturally under what conditions in macroscopic experiments will an increase in sensitivity be limited by the quantum-mechanical properties of the test objects. In this article we determine the limiting values of the detectable accelerations (or forces) when free particles or oscillators are used as the test objects. The conditions for attaining the limiting sensitivity are discussed. It is shown possible to increase the sensitivity of a converter of mechanical into electrical oscillations by increasing the relaxation time of the electric resonator. The possibility is discussed of nondestructive recording of the n -quantum state of an oscillator. It is shown with the example of a concrete experimental design that one can determine the value of n (including n = 0) in such a way that the probability of transition to the adjacent levels after the measurement will be small.
Recent achievements in the isolation of macroscopic mechanical objects from a heat bath make it possible to implement quantum measurements with such systems. In this case, either a free mass or an oscillator can be used as a test object. The advantage of the first variant is in significantly longer relaxation times achieved for free masses. The advantage of the second variant is in the absence of restrictions on the limiting measurement accuracy associated with internal losses in the meter. This restriction can be bypassed, retaining a long relaxation time typical of free masses, if a test oscillator with a ponderomotive electromagnetic rigidity is used. Estimates show that the potential sensitivity of this test body for the modern level of technology may be considerably higher than the standard quantum limit.
The so-called standard quantum limits (SQL) of measurement errors of coordinate, momentum, amplitude of oscillations, energy, force etc. are due to back action of the meter on the system under test, whenever the meter responds to the coordinate of the system. These SQL are not fundamental and can be surmounted by various methods. In particular, in a coordinate measurement the SQL can be overcome by means of an appropriate correlation of conjugate meter variables. Conditions of quantum nonperturbing (nondemolition) and quasi-nonperturbing measurements of the energy of electromagnetic waves are discussed. Possible methods of these measurements are reviewed. Conditions for overcoming the SQL of wave energy measurement by the optical Kerr effect are analysed. The quantum limit of error of this measurement is discussed. The effects of dissipation, dispersion and generation of combination waves are considered. Results of experiments reported in the literature are discussed. The dependence of the quantum limit of detection of an external action upon a system on the initial state of the system is considered. The relation between the measurement error of an observable A and a perturbation of an observable B, when [A,B] is an operator, is examined.
In recent years advances in technology, especially in the field of quantum optics, have made possible repetitive quantum measurements on a single quantum object, an issue that remained an academic curiosity until 25 years ago. This book, first published in 1992, provides a tutorial introduction to this field. The book is coauthored by an experimentalist and a theorist: the former - Braginsky - was the first experimentalist after Weber to develop techniques for gravitational-wave detection; the latter - Khalili - contributed with Braginsky to develop the formal apparatus to describe the experimental devices for measurement schemes. After the first part, intended as a pedagogical appendix of a standard textbook, and devoted to the modern approach to quantum measurement, the second part is a review of some new methods of quantum measurements for macroscopic objects. The central problem is the detection of a small time-dependent classical force that acts on a quantum probe. This is the typical situation that occurs in gravitational-wave detection, where the probe is a macroscopic moving mass weakly coupled to a classical wave. The problem of gravitational-wave detection and the limitation to accuracy of measurement of position of a moving mass - the so-called standard quantum limit (SQL), which is a consequence of the random back-action of the measuring device on the mass - triggered the development of new quantum nondemolition (QND) measurements, i.e. measurements where the measured quantity is left unperturbed after the measurement. SQL and QND measurements (both Braginsky inventions) permeate the whole book as a transversal chapter. The aim is to give simple criteria and recipes to design a measuring device in order to optimize the accuracy of the measurement, and, at the same time, to minimize the perturbation that the device exerts on the measured object, so that it will not interfere with successive measurements on the same object. The continuous measurements are regarded as the limiting case of a sequence of repeated discrete measurements, when the interval between the measurements is much smaller than the characteristic time-scale on which the measured quantity changes. The analysis of continuous measurements give to the authors the opportunity to illustrate the watchdog effect and the quantum Zeno paradox (real effect), while deriving the master equation for the evolution of the object state. Then, an entire chapter is devoted to the analysis of devices for continuous measurement of small mechanical displacements. The book is easy to understand, and can serve as a complementary reading for graduate level courses in quantum mechanics. The material of the book can be useful for all scientists and engineers involved in researches related to high-sensitive quantum measurements, quantum information theory and quantum computation. The reader, however, should be aware that this book presents a very particular point of view, with no room left to very relevant concepts in quantum measurement theory, as, for example, squeezing, quantum amplification, joint-measurements of non-commuting observables and phase-measurements. More regrettably, the list of references is unsatisfactorily incomplete, with no mention of alternative developments, for example, regarding the SQL for measuring the position of a free mass. Here, schemes to breach the SQL have been proposed in the literature (Yuen H P 1983 Phys. Rev. Lett. 51 719, Ozawa M 1988 Phys. Rev. Lett. 60 385), whereas from the book one could conclude that such SQL would be unsurpassable. Also, a criticism is in order of the way of deriving some SQL's, based solely on the Heisenberg relation, even in consideration that the aim of such derivations is mostly pedagogical.
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. [S0034-6861(96)00103-1]
The quantum measurement process connects the quantum world and the classical world. The phrase ‘quantum measurement’ can have two meanings: measurement of a weak classical force, with the impact of quatum fluctuations on the measurement sensitivity, and the quantum mechanics of macroscopic objects: to try to prepare, manipulate and characterize the quantum state of a macroscopic quantum object through quantum measurement. Quantum noise leads to the Standard Quantum Limit (SQL), which provides the magnitude in which we must consider both measurement precision and measurement-induced back-action. The beginning of the chapter will be devoted to this thread of thought. The free-mass SQL actually provides a benchmark for the ‘quantum-ness’ of the system. We will show that a sub-SQL device can be used to prepare nearly pure quantum states and mechanical entanglement, as well as non-Gaussian quantum states that have no classical counterparts.