Just as with the two-slit experiments, the Mach–Zehnder interferometer builds up an interference pattern even when shooting photons one at a time. Remember that we also learned that Tonomura was able to do the same thing using single electrons, and more recently the team at the University of Vienna demonstrated two-slit interference using a collimated beam of fluorinated carbon-60 “buckyball” molecules.67 We have repeatedly asked: “Which slit did each of the particles go through?” Invariably, we have reached the conclusion that somehow each particle must behave as if it went through both slits at the same time in order to yield an interference pattern!
Just as in Schrödinger’s cat experiment, the particle is forced to be in two mutually exclusive states at the same time. According to the Copenhagen Interpretation, the particle in a two-slit experiment is in a superposition of quantum states until its position is finally measured when it hits the detector. The particle is neither in slit 1 nor in slit 2, but has an equal probability of being found in either one until a measurement is made.
What would happen, then, if we nevertheless try to determine which slit the particle goes through on its way to the screen? An easy way of doing this without affecting the path of the particles would be to tag the particles differently if they go through one or the other slit such that the path of the particle can be identified when it finally reaches the detector.
For example, we could place a vertical polarizer on one slit, and a horizontal polarizer on the other. The surprising result, as shown in Figure 133b, is that if you try to find out through which slit the particle goes, the superposition collapses to a single definite state, and the interference effects vanish.
Figure 133 The two-slit experiment can be modified in order to attempt to identify the path taken by photons. (a) The unmodified two-slit experiment produces the familiar interference pattern. (b) Labeling the paths by tagging the photons with different polarizations depending on which slit they pass through destroys the interference pattern. Note that the width of the slits and interference patterns are largely exaggerated to illustrate the concept.
Placing polarizers on a double-slit slide is not very easy, so let’s instead perform this experiment using our Mach–Zehnder interferometer.* Set up your interferometer to produce a clear interference pattern. Then, insert two pieces of linear-polarizing film, as shown in Figure 134a. One of the polarizers should be oriented vertically, while the other should be oriented horizontally. This will tag all photons going through one of the paths by forcing them to have vertical polarization, while the photons flying through the other leg of the interferometer are tagged with horizontal polarization. At least in principle, this would allow us to identify the path a photon took through the Mach–Zehnder interferometer before being detected at the screen.
Figure 134 We added polarizers to each of the legs of our Mach–Zehnder interferometer to conduct a which-way experiment. (a) Labeling the paths by tagging the photons with different polarization depending on which leg of the interferometer they take destroys the interference pattern. (b) Insertion of a 45° polarizer in front of the screen erases the which-way information, thus restoring the interference pattern. Note that the width of the interference pattern is largely exaggerated to illustrate the concept.
By setting the system in such a way that we may (at least in principle) identify which way the photon traveled, we are essentially performing an experiment in which we observe the particle nature of light. The photons gladly obey, and the interference pattern disappears. We can’t simultaneously observe the wave and particle nature of light. The explanation is that the quantum superposition collapses as soon as we measure a property of a photon that is in a superposition of states.
The same exact thing happens when experiments are performed with any other type of particle (electrons, neutrons, atoms, or buckyballs). Measuring the position, velocity, or another property of a particle in a superposition state always gives a definite value. However, at the instant of measurement, the superposition ceases to exist and the particle’s wavefunction collapses into a specific state.
For example, Stephan Dürr and his colleagues at the Max Planck Institute for Quantum Optics in Germany conducted a single-atom interferometry experiment in which individual rubidium atoms could be tagged through very subtle, different microwave transitions applied to the two paths.39 As expected, an interference pattern appeared when no tagging was applied. However, when the tagging equipment was turned on, the interference fringes were lost due to the storage of which-way information in the atoms.
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