Quantum Measurements

A term that is nearly synonymous with complex numbers or functions is their phase. The rising preoccupation with the wave function phase in the last few decades is beyond doubt, to the extent that the importance of phases has of late become comparable to that of the moduli. (We use Dirac s terminology [7], which writes a wave function by a set of coefficients, the amplitudes, each expressible in terms of its absolute value, its modulus, and its phase. ) There is a related growth of literatm e on interference effects, associated with Aharonov-Bohm and Berry phases [8-14], In parallel, one has witnessed in recent years a trend to construct selectively and to manipulate wave functions. The necessary techifiques to achieve these are also anchored in the phases of the wave function components. This bend is manifest in such diverse areas as coherent or squeezed states [15,16], elecbon bansport in mesoscopic systems [17], sculpting of Rydberg-atom wavepackets [18,19], repeated and nondemolition quantum measurements [20], wavepacket collapse [21], and quantum computations [22,23], Experimentally, the determination of phases frequently utilizes measurement of Ramsey fringes [24] or similar" methods [25]. 

L, S. Schulman, Time Arrows and Quantum Measurement, University Press, Cambridge, 1997,... 

An even deeper dilemma confronts an honest physicist when trying to understand what really happens during a quantum measurement. Despite using (macroscopically) intuitive descriptions of the quantum-entangled objects, what really happens remains a deep mystery. Or, consider the following simple thought experiment using CA. 

Phase interference in optical or material systems can be utilized to achieve a type of quantum measurement, known as nondemolition measurements ([41], Chapter 19). The general objective is to make a measurement that does not change some property of the system at the expense of some other property(s) that is (are) changed. In optics, it is the phase that may act as a probe for determining the intensity (or photon number). The phase can change in the course of the measurement, while the photon number does not [126],... 

To illustrate an application of nonlinear quantum dynamics, we now consider real-time control of quantum dynamical systems. Feedback control is essential for the operation of complex engineered systems, such as aircraft and industrial plants. As active manipulation and engineering of quantum systems becomes routine, quantum feedback control is expected to play a key role in applications such as precision measurement and quantum information processing. The primary difference between the quantum and classical situations, aside from dynamical differences, is the active nature of quantum measurements. As an example, in classical theory the more information one extracts from a system, the better one is potentially able to control it, but, due to backaction, this no longer holds true quantum mechanically. 

The results presented above are rather satisfactory because in this new paradigm the quantum measurement process depends, in the last instance, on the standard used. We are, in principle, free to choose the size, or the scale, of the mother wavelet Axo more suitable for the measurement precision that we want to attain. 

What is true is that, in any case, whether with the common microscope, or with the superresolution microscope, in order to be observed, the object points must be submitted to some kind of interaction. Since we are dealing with optical microscopes, the interaction occurs with photons. In such circumstances the photon, on interacting with the microparticle, is diffused by it. As a result of this interaction, which is fundamental in all direct concrete quantum measurements, a certain amount of momentum is transferred from the photon to the microparticle, leading to an uncertainty in the momentum of the microparticle. 

An important experiment carried out as recently as summer 1982 by the French physicist, Aspect, has unequivocally demonstrated the fact that physicists cannot get round the Uncertainty Principle and simultaneously determine the quantum states of particles, and confirmed that physicists cannot divorce the consciousness of the observer from the events observed. This experiment (in disproving the separabilty of quantum measurements) has confirmed what Einstein, Bohr and Heisenberg were only able to philosophically debate over - that with quantum theory we have to leave behind our naive picture of reality as an intricate clockwork. We are challenged by quantum theory to build new ways in which to picture reality, a physics, moreover, in which consciousness plays a central role, in which the observer is inextricably interwoven in the fabric of reality. 

Gondolo, P. 1996. Phenomenological introduction to direct dark matter detection, in XXXI Rencontres de Moriond Dark Matter in Cosmology, Quantum Measurements, Experimental Gravitation, Les Arcs, France [hep-ph/96-05290],... 

It is interesting to note that the Gottingen school, who later developed matrix mechanics, followed the mathematical route, while Schrodinger linked his wave mechanics to a physical picture. Despite their mathematical equivalence as Sturm-Liouville problems, the two approaches have never been reconciled. It will be argued that Schrodinger s physical model had no room for classical particles, as later assumed in the Copenhagen interpretation of quantum mechanics. Rather than contemplate the wave alternative the Copenhagen orthodoxy preferred to disperse their point particles in a probability density and to dress up their interpretation with the uncertainty principle and a quantum measurement problem to avoid any wave structure. 

This chapter deals with a quantum state-based approach to quantum measurements differing from dominant views exposed in standard quantum mechanics textbooks [1-3]. 

This chapter is organized as follows In Section 2, quantum states are briefly described. Section 3 presents aspects of standard quantum measurement model. Section 4 includes double-slit, Einstein-Podolsky-Rosen, and Tonomura s experiments. Section 5 illustrates calculations of quantum states for quantum measurements. In Section 6, atom interferometer experiment of Scully et al. is analyzed. A detailed discussion is presented in Section 7, emphasizing a physical perception of quantum mechanics. 

This is a moment of maximal difficulty to grasp. The material system that sustains the quantum state must be the same as the one detected at the end if the experiment is so designed. In between, it is the quantum state that describes the whereabouts of the system not as a localized material one but as presence at Fence space. It is here where one has to calculate quantum states for quantum measurements. Being infinite in number, they cover all possible behaviors. What is decisive is the presence of a Hilbert space that forces first calculations based on quantum states and at last, the laboratory requirement would impose, at the recording apparatus, the presence of the material system. 

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