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The Double-Slit & the Mach-Zehnder Interferometer: Re-visiting through Asymmetry

Chandrasekhar Roychoudhuri

Published Apr 20, 2023• 3 citations
Publisher

Abstract

It is generally believed that the “mystery” behind understanding Quantum Mechanics (QM) and the global drives to construct quantum computers using “Entanglement”, can be understood from how the two-beam superposition effect (SE) emerges out of a 2-slit, and a Mach-Zehnder Interferometer (MZI). This chapter rehabilitates the classical analyses of these two superposition effects, while exploiting functional asymmetries, either deliberately introduced or intrinsic in the two-beam apparatuses. We are using mathematical formalism already well-established in classical optics since 1800’s, but with the extra emphasis that any final data generation requires some real physical interaction between the detector and the two light signals simultaneously stimulating the detecting molecules. This critical step of physical interaction process is not explicitly underscored by either the classical or the quantum physics. However, the asymmetry, either in the propagation or in the interaction process, is utilized to bring out the contradictions with the QM interpretations. For the 2-slit system, we deliberately introduce asymmetry on one of the slits. For MZI, the asymmetry is already built into the classical reflection property of a typical beams splitter.

DOI
10.9734/bpi/fraps/v3/6355a

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It is generally believed that the “mystery” behind understanding Quantum Mechanics (QM) and the global drives to construct quantum computers using “Entanglement”, can be understood from how the two-beam superposition effect (SE) emerges out of a 2-slit, and a Mach-Zehnder Interferometer (MZI). This chapter rehabilitates the classical analyses of these two superposition effects, while exploiting functional asymmetries, either deliberately introduced or intrinsic in the two-beam apparatuses. We are using mathematical formalism already well-established in classical optics since 1800’s, but with the extra emphasis that any final data generation requires some real physical interaction between the detector and the two light signals simultaneously stimulating the detecting molecules. This critical step of physical interaction process is not explicitly underscored by either the classical or the quantum physics. However, the asymmetry, either in the propagation or in the interaction process, is utilized to bring out the contradictions with the QM interpretations. For the 2-slit system, we deliberately introduce asymmetry on one of the slits. For MZI, the asymmetry is already built into the classical reflection property of a typical beams splitter.
The chapter discusses the Mach–Zehnder interferometer (MZI), which uses beam splitters in combination with mirrors to place a photon into a superposition of paths. In a final beam splitter, the two paths may be recombined to interfere, showing wave behavior. If the final beam splitter is removed, the photon is definitely in one path or the other, showing particle behavior. The polarization of light allows additional applications—one can use a polarizing beam splitter to separate and reconstitute the wave functions of a photon polarized at an angle. In a delayed-choice experiment, one decides which kind of experiment one is to do, particle or wave, after the photon has already entered the arms of the MZI. The chapter discusses a version of this that puts the MZI and a second-detector photon in an entangled state of particle and wave results.
Interferometers IntroductionThe discussion of modules and computerization in previous chapters gives us the means to consider empirically useful quantized detector networks (QDN).In this chapter we shall focus on a particular class of network known as interferometers.Interferometers play a crucial role in quantum mechanics (QM) because they demonstrate the "paradox" of wave-particle duality in a direct way.On the one hand, discrete signals are detected by the observer and those signals are usually interpreted as particles or quanta.On the other hand, the observed frequencies built up over many runs show effects interpreted as due to the interference of waves.In the previous chapter, we used computer algebra (CA) to discuss the Wollaston interferometer (WI), a relatively simple interferometer.We shall use the same approach in the following discussion of the Mach-Zehnder interferometer (MZI), apparatus that allows the observer to investigate optical transmission through various materials. The Mach-Zehnder InterferometerThe basic structure of an MZI is given in Figure 13.1.A source S of light sends a monochromatic, unpolarized beam 1 0 into one input channel of beam splitter B 1 .Output channel 1 1 is deflected by mirror M 1 onto a module labeled φ that contains some medium under investigation, such as a crystal or liquid.The net effect is to create a phase change in that deflected beam by an amount φ, and then that modified beam, 1 2 , is passed into beam splitter B 2 .The second output channel, 2 1 , from B 1 , meanwhile, is deflected by mirror M 2 into beam splitter B 2 .The two deflected beams, 1 2 and 2 2 , that pass into B 2 interfere and are finally monitored by detectors 1 3 and 2 3 .Our analysis of the MZI follows the CA approach used for the WI in the previous chapter.
Abstract The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.
\n\nThe Mach-Zehnder interferometer (MZI) is a regular yet simple instrument to test wave-particle duality. One key device in a standard MZI is the beam splitter 2 (BS2). Here we make a simple quantum mechanics analysis about the wave function evolution and find that the strong and exclusive interaction of BS2 with the incident microscopic particle beam (photons, electrons, etc.) is the fundamental reason why standard MZIs could not allow for the simultaneous observation of wave and particle properties of these particles. A weak-measurement (WM) MZI setup is then proposed, where BS2 is replaced with a deliberately designed highly transparent interference screen operating via either weak absorption or weak-scattering effect. Quantum-mechanical analysis on this WM-MZI shows that the overall power to make simultaneous observation of interference fringe (wave nature) and which-path information (particle nature) of microscopic particles can be significantly enhanced compared with the standard MZIs.\n
Abstract Now that we have explored qubits and the phenomenon of superposition, we can ask the question: how do we know that superposition actually happens? is the evidence that shows that a quantum particle really does exist in two different locations at this same time while in a quantum superposition? The nature of science means that experiments are constantly updating previous results, so are there other interpretations of the experimental results that can explain the data without the need for superposition? In this chapter we’ll explore the experimental evidence interpretations other than quantum superposition. Further, while a flipping coin is a simple model of a qubit, it is not very useful for building a quantum computer because it does not exhibit all of the properties of a true quantum superposition. For example, we cannot manipulate the superposition amplitudes. In this chapter, we will study some real physical examples of quantum particles in a superposition containing two states. These examples include a photon in a beam splitter and the Mach–Zehnder interferometer.
In this paper we describe within the formalism of Quantum Optics (QO) a double Mach-Zehnder interferometer (MZI). For single photon Fock states this experimental setup is shown to exhibit a counter-intuitive behavior: for certain values of the path length difference of the first MZI, the singles photon-count statistics at the output detectors does not change, whatever the difference in path length for the second MZI. For simultaneously impinging light quanta, we show that this setup is able to show the same HOM antibunching effect previously obtained with a beam splitter. However, by adding substantial delays in each MZI, we can obtain the same effect even if the "photon wave packets" do not overlap at the second beam splitter.