Quantum erasing against the time stream: The unfathomable paths of photons
Page 3: Quantum etching for amateurs and professionals
A quantum particle such as a photon therefore behaves like a wave when passing through a sufficiently narrow double slit and passes through both slits simultaneously.
What if you don't want to admit this and simply look it up? In the case of light, this can be done relatively easily by sending the light paths behind the slits through two differently oriented polarization filters. For example, the light from one slit passes through a filter with horizontal polarization and the light from the other slit passes through a filter with vertical polarization. As is well known, the electromagnetic waves behind the filters only oscillate in one plane, which is now tilted by 90° relative to each other for both slits. The direction of polarization of the light therefore reveals which slit it has passed through. If you let the light fall onto a projection screen, you will, oh wonder, no longer see interference fringes, but what you would expect if the photons had only passed through one slit at a time as particles and their scattered fields were superimposed on the screen.
It becomes interesting when this information about the photons on the way to the screen is deleted again. This can be achieved with another linear polarization filter, which is tilted by 45° against the other two. The filter allows photons from both light paths to pass through with the same probability and the polarization of both light paths is identical again behind the filter. In this way, the interference pattern can be restored. The information about the light path has been erased, so to speak.
The experiment can even be reproduced at home using simple means:
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A smart aleck might throw in, well, how are photons that have passed through different slits and are forced by the polarizing filters to oscillate in mutually perpendicular planes supposed to interfere with each other at all? The wave crests and troughs cannot cancel each other out at right angles! The laws governing the ability of polarized light to interfere are also known as Fresnel-Arago laws.
Depending on the phase difference, the field strength vector of the superimposed light waves would actually describe Lissajous figures with a frequency ratio of 1:1, i.e. small lines, ellipses or circles, which, however, cannot be seen, as we are only concerned here with the amplitudes of the electric and magnetic fields. You get linear (line), circular (circle) or partly circular (ellipse) polarized light, which replaces the light and dark interference fringes, and the naked eye cannot distinguish between them.
Unless a linear polarizing filter with a 45° inclination to the other two filters is inserted into the beam path behind them. The 45° inclined filter bends the oscillations of the light waves back into one and the same plane and restores their ability to interfere. In other words, the filter shows you the places where the superimposed light is linearly polarized in the direction of the polarizing filter, and then the interference works again. But where else is something being erased? The clever guy actually has a point. The polarizing filter quantum eraser experiment can also be explained using classical wave mechanics alone.
However, there are also variants of the quantum eraser experiment that work without a polarization filter. In the following setup, which is also known as a Mach-Zehnder interferometer, a "beam splitter" is used instead of a double slit to generate two light paths and cause them to overlap.
A beam splitter is a partially mirrored glass plate that reflects one half of the light like a mirror and transmits the other half like a window. In the photon model, a photon has a 50 percent chance of being reflected or transmitted. In the wave model, half of the light intensity passes straight through the glass plate and the other half is reflected by the partially mirrored surface.
(Image: Alderamin)
(Image: Alderamin)
To explain the phase difference: A reflection on the outer surface of a beam splitter or full mirror shifts the phase of the light waves by half a wavelength (λ/2). Reflection within the beam splitter glass, on the other hand, does not cause a shift. When passing through the glass, the wavelength is extended by an unspecified amount k, which depends on the properties of the glass and the length of the light path through the glass – assuming that the beam splitters have identical properties. If the reflection of the red light path takes place at the top of the beam splitter BS1 and that of the blue light path at the bottom of BS2, the phase shifts of the blue path to D1 add up to λ+2k, and this is also the shift on the red path to D1. This means that the waves are in phase and are amplified.
On the path to D2, the blue light path experiences k twice when passing through the glass and λ/2 at the full mirror VS2, which results in a total of λ/2 + 2k. The red light path is reflected twice on an outer side, that is +λ, once inside the beam splitter glass (+0) and passes diagonally through the thickness of the glass twice, that is +2k. In total, therefore, λ+2k.
This means that the red and blue light paths are shifted against each other by λ/2, i.e. they are in antiphase and cancel each other out.In the diagrams above, the portion of the light reflected at the beam splitter BS1 is shown in red and the portion passing through is shown in blue. Light wave crests are symbolized as wavy lines to illustrate the phase shift. The light paths separate at the reflective upper side of beam splitter BS1. Both light paths are brought together again at the top right via full mirrors VS1 and VS2. In image A, the light paths merely intersect. Based on the direction from which the beams come, detectors D1 and D2 at the end of the paths always measure photons that have traveled a certain path. If you only send individual photons through the beam splitter, only one of the detectors will register a photon at a time – The same photon never triggers both detectors.
However, if a second beam splitter BS2 is added, as shown in the lower section, the light paths from the perspective of both detectors can be merged again: The blue light path can pass upwards through BS2 or be reflected to the right on its underside. The red light path can pass through it to the right or be reflected upwards on the underside after passing through the glass.
At this point, please note for later that the reflection on the outside of the glass shifts the phase of the light waves by half a light wave (i.e. the wave is turned upside down, so to speak, and the crests and troughs are swapped), whereas a reflection in the glass on its outside does not change the phase. In addition, the refractive properties of the glass itself, which are related to the lower speed of light within the glass body, ensure that the light waves are shifted against their original phase after passing through the glass.
Due to the laws of optics, there is no difference in transit time for the light paths to detector D1, so that the light waves overlap in phase in the right-hand detector and the light signal is maximized. In the image above, both light paths to D1 have been reflected once at the surface of a beam splitter (and both again at a solid mirror) and once diagonally through it, which compensates for the differences in transit time; of course, the setup must be adjusted precisely to match the path lengths exactly.
On the way to D2, both light paths pass diagonally through glass twice (the red beam when reflected in BS2, the blue beam once each when passing through both beam splitters), and both are reflected at a solid mirror VS1 and VS2 respectively. The light paths differ in that the red light path is reflected twice with a phase jump (and once without), which leads to the original phase position again: The waves are turned upside down twice. In contrast, the blue light path is only reflected once with a phase difference of half a wavelength, which leads to a path difference of half a wavelength compared to the red light path and thus to destructive interference.
Therefore, no light arrives at D2. If you remember the double slit experiment, the constructive interference of light waves with the same phase leads to the bright stripes and the destructive interference of light waves shifted by half a wavelength leads to dark stripes. In a sense, D1 sees a bright interference fringe and D2 a dark one. The added beam splitter BS2 erases the previously existing "which path" information and restores the interference capability of both light paths. This time completely without polarization.
In the wave model, it is perfectly clear why D1 measures a maximum signal and D2 none. However, if you send individual photons through the Mach-Zehnder interferometer, then a photon should actually take the red path with 50% probability at the beam splitter at the bottom left or the blue path with 50% probability. At the beam splitter at the top right, it should take the blue light path with 50% to the right and 50% upwards; in other words, a total of 25% of all photons should arrive at D1 via the blue path and 25% at D2. The same applies to the red path, so that a total of 50% of all photons should end up at each detector via one of the two paths. However, according to the wave model, this is not the case: 100 % of the photons end up at D1 and 0 % at D2.
As soon as there are several equal paths to the detectors, the photons on them behave like waves, even if only a single photon is sent through the Mach-Zehnder interferometer at a time. In the double-slit experiment, a photon passes through both slits, in the Mach-Zehnder interferometer it passes through both paths. Simultaneously. In terms of quantum physics, each photon is in a superposition of both possible paths and the light waves become a quantum-physical probability wave function that interferes with itself in front of the detectors and makes the path to the upper detector impossible, while only allowing the path to the right detector. Wave beats particle.
