The Mach-Zehnder interferometer is a particularly simple device for demonstrating interference by division of amplitude. A light beam is first split into two parts by a beamsplitter and then recombined by a second beamsplitter. Depending on the relative phase acquired by the beam along the two paths the second beamsplitter will reflect the beam with efficiency between 0 and 100%. The operation of a Mach-Zehnder interferometer is often used as an example in quantum mechanics because it shows a clear path-choice problem. However, it is not at all obvious at first glance that it works as claimed, until reflection phase shifts are considered in detail.
The Mach-Zehnder interferometer is a particularly simple device for demonstrating interference by division of amplitude. A light beam is first split into two parts by a beamsplitter and then recombined by a second beamsplitter. Depending on the relative phase acquired by the beam along the two paths the second beamsplitter will reflect the beam with efficiency between 0 and 100%. The operation of a Mach-Zehnder interferometer is often used as an example in quantum mechanics because it shows a clear path-choice problem. However, it is not at all obvious at first glance that it works as claimed, until reflection phase shifts are considered in detail.
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.
The quantum beamsplitter—a two-level system (TLS) coupled to a one-dimensional continuum of electromagnetic modes—is the most elementary version of a beamsplitter that may not only refract and reflect, but also absorb and then reemit a photon. This raises the question of whether a single-photon pulse, once split by a first quantum beamsplitter, could be made to interfere with a second one. Here, we propose and theoretically analyze a quantum Mach–Zehnder interferometer (QMZ) as formed by two concatenated quantum beamsplitters. The distinctive feature of our QMZ is its considerable saturability for a single photon, arising from the broadband nature of the pulse. We show that (i) off-resonant monochromatic photons produce classical interference patterns, whereas (ii) resonant broadband pulses erase these patterns, and that (iii) off-resonant broadband pulses always preserve some degree of interference if the two TLSs are oppositely detuned.
The photon in the interferometer This chapter introduces many of the ideas of quantum theory by exploring three specific “case studies” of quantum systems. Each is an example of a qubit , a generic name for the simplest type of quantum system. The concepts we develop will be incorporated into a rigorous mathematical framework in the next chapter. Our business here is to provide some intuition about why that mathematical framework is reasonable and appropriate for dealing with the quantum facts of life. Interferometers In Section 1.2 we discussed the two-slit interference experiment with a single photon. In that experiment, the partial waves of probability amplitude were spread throughout the entire region of space beyond the two slits. It is much easier to analyze the situation in an interferometer , an optical apparatus in which the light is restricted to a finite number of discrete beams . The beams may be guided from one point to another, split apart or recombined as needed, and when two beams are recombined into one, the result may show interference effects. At the end of the interferometer, one or more sensors can measure the intensity of various beams. (A beam is just a possible path for the light, so there is nothing paradoxical in talking about a beam of zero intensity.) Figure 2.1 shows the layout of a Mach–Zehnder interferometer , which is an example of this kind of apparatus.
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.
The Mach-Zehnder interferometer (MZI) is a two-path phase-to-intensity transducer that becomes "mysterious" mainly when one conflates operational facts, minimal predictive calculus, and ontological storytelling.Controlled phase shifts are the central "knob" of the MZI: a tunable relative phase Φ converts directly into complementary output intensities at the two ports.In this model, photons enter the MZI with classical instructions: the "white" photons with E 2 = 1 (where E is the electric field of the sinusoidal electromagnetic wave at the given moment) are reflected on the beamsplitters, the "grey" photons with E 2 = 0.5 can be both reflected and transmitted through the beamsplitters (with 50:50 ratio), and the "black" photons with E 2 = 0 transmit through the beamsplitters.The movable mirrors and the second beamsplitter modify the "color" of photons.The 50:50 mixture of "white" and "black" photons at the input is separated by the first beamsplitter.The phase shifts are modified by movable mirrors so that the second beamsplitter organizes the resulting structure of photons at the two detectors.The interference patterns have been formed from two sub-ensembles of photons with their relative phase shift ΔΦ = π at the given port.We assume that this classical behavior of photons in the MZI can clarify the "riddle-like" discussions (e.g., delayed choice switching, the meaning of a dark port, and the role of which-way information).
The Mach-Zehnder Interferometer (MZI) is used to illustrate the long-standing wave-particle duality problem. How can the photon divide at the first beam splitter and yet terminate on either arm with its undiminished energy? Why is which-way (welcher weg) information incompatible with wave interference? How do we explain Wheeler’s delayed choice experiment? The position adopted is that the photon has two identities, one supporting particle features and the other wave features. There is photon kinetic energy that never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there is photon probability waves that do diffract and can reinforce or cancel. Interpretations of these two identities are suggested.