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Medida fraca utilizando efeito miragem no interferômetro de Mach-Zehnder

Jabes Dias de Almeida Melo

Published Jul 27, 2020• 0 citations
OpenAlex

Abstract

Throughout the "creation" of Quantum Mechanics, a theory has been built that is based on a single way of measuring quantum systems. These measurements have always taken place so that the act of measuring disturbs the system to the point of collapsing it, and then it acquires all the properties of a single state. However, in the late 1980s, a new way of measuring a quantum system emerged, called the Weak Measurement. With it, we were able to deal with experiments with a new approach, where the configuration of the measurement is changed by a factor that disturbs the system very little. With the way of measuring before this new concept, it would be impossible to detect small changes in a quantum system, but now, the weak measurement reaches new horizons. We developed a form of weak measurement using a general coupling in terms of the superposition of an initial state and a final state, in the case of a qubit. With that, it was possible to see in more detail how the process of this way of measuring occurs, where we will see how the coupling between the two states must be done to carry out such an experiment. We have also developed a weak measurement in a quantum system using a Mach-Zehnder interferometer for such a study. In it, with the help of a value that will determine how weak the weak measure is, we can carry out a measure in which we do not need to disturb a system to obtain information.

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Throughout the "creation" of Quantum Mechanics, a theory has been built that is based on a single way of measuring quantum systems. These measurements have always taken place so that the act of measuring disturbs the system to the point of collapsing it, and then it acquires all the properties of a single state. However, in the late 1980s, a new way of measuring a quantum system emerged, called the Weak Measurement. With it, we were able to deal with experiments with a new approach, where the configuration of the measurement is changed by a factor that disturbs the system very little. With the way of measuring before this new concept, it would be impossible to detect small changes in a quantum system, but now, the weak measurement reaches new horizons. We developed a form of weak measurement using a general coupling in terms of the superposition of an initial state and a final state, in the case of a qubit. With that, it was possible to see in more detail how the process of this way of measuring occurs, where we will see how the coupling between the two states must be done to carry out such an experiment. We have also developed a weak measurement in a quantum system using a Mach-Zehnder interferometer for such a study. In it, with the help of a value that will determine how weak the weak measure is, we can carry out a measure in which we do not need to disturb a system to obtain information.
Summary form only given. Measurements are the very basis of Physics, especially in Quantum Mechanics, where they assume even a more fundamental role because of wave function collapse after a “strong” (projective) measurement. Furthermore, measuring a quantum-mechanical observable completely erases the information on its conjugate one (e.g. measurement of position erases information on momentum, and vice-versa). Nevertheless, in Quantum Mechanics other kinds of measurement are possible. For example, wave function collapse can be overcome through Weak Measurements, i.e. measurements performed with an interaction sufficiently weak not to collapse the original state, featuring several interesting properties. An example of these are weak values [1-3], realised for the first time in [4-6], that have been used for addressing fundamental questions [7-12] as Contextuality and are also a tool for Quantum Metrology [13-19]. One of the most intriguing properties of Weak Measurements is that, since they are not affected by wave function collapse, they can allow gathering simultaneous information on non-commuting observables [20], impossible with the standard (projective) measurement protocols. A second example is offered by Protective Measurements [21], a new technique able to extract information on the expectation value of an observable even measuring a single particle. In this talk, after a general introduction to WMs, we present the first realisation of sequential weak value measurements [22], i.e. a joint measurement of the weak value of (incompatible) polarizations on a single photon. Then, we present an experiment addressed to explore the connection between anomalous weak values and Contextuality [23], showing a clear violation of the inequality proposed in [12] while satisfying all the additional theoretical requests, unequivocally demonstrating the contextual nature of weak values. Finally, we present and discuss the first implementation of Protective Measurements, showing unprecedented measurement capability and demonstrating how the expectation value of an observable can be obtained with a single measurement on a single particle.
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.
The statistical properties of the detection events constituting the interference fringes at the output of an interferometer are well-known. Nevertheless, there is still no unified view of what is happening to a quantum system inside an interferometer. Strong measurements of path operators destroy the interference effect. In weak measurements, an observable is weakly coupled to a pointer system and the resulting weak values quantify the observable by minimally disturbing the system. Previous which-way experiments with weak measurements could extract either the real or imaginary part of a single weak value with each ensemble. Here, we present the simultaneous full complex quantification of two path weak values with a single ensemble in a Mach-Zehnder neutron interferometer. Magnetic fields, oscillating with different frequencies, change the energy state in each interferometer path. The time-dependent phase between the energy states distinctly marks each path. The resulting beating intensity modulation at the interferometer output gives both path weak values. For the present experiment, the weak values' absolute value and phase directly describe the observed amplitude and phase of the intensity modulation.
A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond to any physical attribute of the system being "weakly" measured, contrary to impressions given by most of the literature on weak measurements. A possible mathematical error in the seminal paper introducing "weak values" is explicitly identified. A mathematically rigorous argument obtains results similar to, and more general than, the main result of that paper and concludes that even in the infinite-dimensional context of that paper, weak values are not unique. This implies that the "usual" formula for weak values is not universal, but can apply only to specific physical situations. The paper is written in a more pedagogical and informal style than is usual in the research literature in the hope that it might serve as an introduction to weak values.
The real part of the weak value is identified as the conditional Bayes probability through the quantum analog of the Bayes relation. We present an explicit protocol to get the the weak values in a simple Mach-Zehnder interferometer model and derive the formulae for the weak values in terms of the experimental data consisting of the positions and momenta of detected photons on the basis of the quantum Bayes relation. The formula gives a way of tomography of the initial state almost without disturbing it in the weak coupling limit.