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Applied Optics

Methods used to observe a dynamical quantum nonlocality effect in a twin Mach–Zehnder interferometer

Scott E. Spence, Allen Parks, David A. Niemi

Published Nov 7, 2012• 7 citations
Publisher

Abstract

Straightforward novel methods for stabilizing, tuning, and controlling a twin Mach-Zehnder interferometer for the purpose of observing a subtle dynamical quantum nonlocality effect in a recent optical experiment are presented and discussed. Weak measurements were required for observing a subtle quantum dynamical nonlocality effect that reveals itself in a change of a weak value. Consequently, emphasis is placed upon describing the approaches to apparatus stabilization and interaction strength control between photons and the apparatus. The details discussed in this paper should be of general interest to experimentalists engaging in weak measurement and weak value research.

DOI
10.1364/ao.51.007853

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Straightforward novel methods for stabilizing, tuning, and controlling a twin Mach-Zehnder interferometer for the purpose of observing a subtle dynamical quantum nonlocality effect in a recent optical experiment are presented and discussed. Weak measurements were required for observing a subtle quantum dynamical nonlocality effect that reveals itself in a change of a weak value. Consequently, emphasis is placed upon describing the approaches to apparatus stabilization and interaction strength control between photons and the apparatus. The details discussed in this paper should be of general interest to experimentalists engaging in weak measurement and weak value research.
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.
Although regarded today as an important resource in quantum information, nonlocality has yielded over the years many conceptual conundrums. Among the latter are nonlocal aspects of single particles which have been of major interest. In this paper, the nonlocality of single quanta is proved using a delayed choice modification of the complex-valued weak values in a square nested Mach--Zehnder interferometer with spatially separated measuring devices. We show that local hidden variables models may use hidden signaling and a list of contextual instructions to replicate quantum probabilities and the mean pointer shifts corresponding to the measured real part of weak values, but in doing so necessarily fail to reproduce the quantum variance of pointer shifts. Our analysis also demonstrates that the recently proposed weak values of quantum histories are inherently nonlocal physical quantities due to their dependence on the total Feynman sum that yields the complex-valued quantum probability amplitude for the studied quantum transition.
Abstract A Mach–Zehnder interferometer with an optical phase control by a twisted nematic (TN) liquid crystal (LC) device was studied. In a typical TN LC device, a change in the optical rotation state of π/2 can be obtained by applying a voltage of about 5 V with a cell thickness of several-micron. The TN cell is inserted into one optical path in the Mach–Zehnder interferometer. We obtained a pattern change when voltage was applied to the LC cell due to the change of the optical interference state. As a result, a change in the number of photons under weak light conditions is observed.
Recently, A. Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] performed a much-discussed experiment in which which-way information was obtained from the light in a nested Mach-Zehnder interferometer by weak measurement. The presented analysis using the two-state vector formalism drew the conclusions that the photons followed disconnected paths. We analyze this experiment using standard quantum optical methods and arrive at analytical expressions that match the experimental results without the need for such disconnected photon paths. We also propose a simple amendment to the experiment capable of displaying new phenomena, highlighting the advantages of our description.
Quantum theory allows direct measurement of the average of a non-Hermitian operator using the weak value of the positive semidefinite part of the non-Hermitian operator. Here, we experimentally demonstrate the measurement of the weak value and the average value of non-Hermitian operator by an interferometric technique. Our scheme is unique as we can directly obtain the weak value from the interference visibility and the phase shift in a Mach-Zehnder interferometer without using any weak measurement or postselection. Both the experiments discussed here were performed with laser sources, but the results would be the same with average statistics of single-photon experiments. Thus, the present experiment opens up the possibility of measuring the weak value and the average value of a non-Hermitian operator without weak interaction and postselection, which can have several technological applications.