Introduction
In the basic double slit experiment, a very narrow beam of coherent light from a source that is far enough away to have almost perfectly parallel wave fronts is directed perpendicularly towards a wall pierced by two parallel slit apertures. The widths of the slits and their separation are approximately the same size as the wavelength of the incident light.
If a detection screen (anything from a sheet of white paper to a digital camera) is put on the other side of the double slit wall, a pattern of light and dark fringes, called an interference pattern, will be observed.
Early in the history of this experiment, scientists discovered that, by decreasing the brightness of the light source sufficiently, individual particles of light that form the interference pattern are detectable. They next tried to discover by which slit a given unit of light (photon) had traveled.
Unexpectedly, the results discovered were that if anything is done to permit determination of which path the photon takes, the interference pattern disappears: there is no interference pattern. Each photon simply hits the detector by going through one of the two slits. Each slit yields a simple single pile of hits; there is no interference pattern.
It is counterintuitive that a different outcome results based on whether or not the photon is constrained to follow one or another path well after it goes through the slit but before it hits the detector.
Two inconsistent accounts of the nature of light have long contended. The discovery of light's interfering with itself seemed to prove that light could not be a particle. It seemed that it had to be a wave to explain the interference seen in the double-slit experiment (first devised by Thomas Young in his classic interference experiment of the eighteenth century).
In the early twentieth century, experiments with the photoelectric effect (the phenomenon that makes the light meters in cameras possible) gave equally strong evidence to support the idea that light is a particle phenomenon. Nothing is observable regarding it between the time a photon is emitted (which experimenters can at least locate in time by determining the time at which energy was supplied to the electron emitter) and the time it appears as the delivery of energy to some detector screen (such as a CCD or the emulsion of a film camera).
Nevertheless experimenters have tried to gain indirect information about which path a photon "really" takes when passing through the double-slit apparatus.
In the process they learned that constraining the path taken by one of a pair of entangled photons inevitably controls the path taken by the partner photon. Further, if the partner photon is sent through a double-slit device and thus interferes with itself, then very surprisingly the first photon will also behave in a way consistent with its having interfered with itself, even though there is no double-slit device in its way.
In a quantum eraser experiment, one arranges to detect which one of the slits the photon passes through, but also to construct the experiment in such a way that this information can be "erased" after the fact.
In practice, this "erasure" of path information frequently means removing the constraints that kept photons following two different paths separated from each other.
In one experiment, rather than splitting one photon or its probability wave between two slits, the photon is subjected to a beam splitter. If one thinks in terms of a stream of photons being randomly directed by such a beam splitter to go down two paths that are kept from interaction, it is clear that no photon can then interfere with any other or with itself.
If the rate of photon production is reduced so that only one photon is entering the apparatus at any one time, however, it becomes impossible to understand the photon as only moving through one path because when their outputs are redirected so that they coincide on a common detector then interference phenomena appear.
In the two diagrams to the right, photons are emitted one at a time from the yellow star. They each pass through a 50% beam splitter (green block) that reflects 1/2 of the photons, which travel along two possible paths, depicted by the red or blue lines.
In the top diagram, one can see that the trajectories of photons are clearly known — in the sense that if a photon emerges at the top of the apparatus it appears that it had to have come by the path that leads to that point (blue line), and if it emerges at the side of the apparatus it appears that it had to have come by way of the other path (red line).
Next, as shown in the bottom diagram, a second beam splitter is introduced at the top right. It can direct either beam towards either path; thus note that whatever emerges from each exit port may have come by way of either path.
It is in this sense that the path information has been "erased".
Note that total phase differences are introduced along the two paths because of the different effects of passing through a glass plate, being reflected off its first surface, or passing through the back surface of a semi-silvered beam splitter and being reflected by the back (inner side) of the reflective surface.
The result is that waves pass out of both the top upwards exit, and also the top-right exit. Specifically, waves passing out the top exit interfere destructively, whereas waves passing out the upper right side exit interfere constructively.
A more detailed explanation of the phase changes involved here can be found in the Mach-Zehnder interferometer article. Also, the experiment depicted above is reported in full in a reference.
If the second beam splitter in the lower diagram could be inserted or removed one might assert that a photon must have traveled by way of one path or the other if a photon were detected at the end of one path or the other. The appearance would be that the photon "chose" one path or the other at the only (bottom left) beam splitter, and therefore could only arrive at the respective path end.
The subjective assurance that the photon followed a single path is brought into question, however, if (after the photon has presumably "decided" which path to take) a second beam splitter then makes it impossible to say by which path the photon has traveled.
What once appeared to be a "black and white" issue now appears to be a "gray" issue. It is the mixture of two originally separated paths that constitutes what is colloquially referred to as "erasure." It is actually more like "a return to indeterminability."
Read more about this topic: Delayed Choice Quantum Eraser
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