THE DELAYED CHOICE QUANTUM EXPERIMENT

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1 Project optic physics 2008 Professor: Andres La Rosa THE DELAYED CHOICE QUANTUM EXPERIMENT by THOMAS BENJAMIN 1 st of June,

2 Introduction The delayed choice quantum experiment, and electron coupling. It is an experience of quantum physics linked to the double-slit experiment which creates interference from a photon going through two small slits. The delayed choice quantum experiment basically uses the same process and creates an interesting time paradox, one can see the consequence of something that has not happened yet, it gives the feeling of getting some information from the future. We first need to understand properly the double-slit experience before can explain this phenomenon. 1. The double-slit experiment... p3 2. The delayed choice quantum experiment... p6 3. Interpretation... p9 2

$The light diffracts at the opening and creates a spherical wavefront.$

3 The double-slit experiment: The aim of this experience is to set up interference patterns between two beams of light coming from the same source. The two beams are projected through two different slits. The pattern shown here is the pattern created by a single source through a single slit. The light diffracts at the opening and creates a spherical wavefront. figure 1a With two slits you get two waves that are propagating spherically as shown: This gives us the energy for the top wave: figure 1b 3

4 E 1 = E 0 * sin(w * t) It also provides the energy for the bottom wave: E 2 = E 0 * sin(w * t Δp) In these equations, E 0 is the amplitude, w the pulsation (equal to 2 π f), Δp is the difference of phase. Since the beam r1 and r2 don't have the same path, when r1 and r2 hit the screen, the distance from the source to the point on the screen is not the same: figure 2 Notice the approximation of the optical path difference. The two beams don t hit the screen in phase, creating a destructive-constructive interference pattern as is shown in the figure below: 4

5 figure 3 The two beams add their intensity, and create constructive or destructive interference. The red wave shown on figure 3 shows the intensity of light seen through a single slit, the center will be the brightest as expected. The pattern changes as a function of a, b, and λ, respectively the size of the slit, the gap between the two slits and the wave length. Paradox : If we do the same experience with only on photon, the first expectation would be that there would be no interference pattern since we need two beams to get an optical path difference. This has been shown experimentally to be false, we do have interference with only one photon. The photon goes through both slit at the same time and creates interference with itself. This is a famous paradox in quantum physics. We can also observe that as soon as we want detect which slit that the photon travels through, we don't have interference anymore. As long as you don't detect the photon, the one photon will travel through both slits simultaneously. If you try to experimentally 5

6 find which slit the photon has been through, you destroy this double state, or superposition state, and you end up with only one photon and no interference. The delayed choice quantum experiment (1) First, we need to understand how the delayed choice quantum experience works. As we can see in figure 4, if instead of B and C, we put 2 mirrors, in order to reconstruct the classic double-sit experience. From the same source, we have two beams and the length of the path will depend upon the distance AB and AC (that one that is changed experimentally). By moving the mirrors, you can create an optical path difference between the waves, and create an interference pattern. figure 4 6

7 B and C are actually two engines make for parametric down conversions; these engines enable us to catch photons and then create two entangled photons which keep the same properties as the initial photon. It is important to clearly know what the term entangled photons mean to understand the rest of this experiment. Entanglement (2) : The quantum entanglement is a quantum mechanical phenomenon. Two entangled photons are link to each other, in order that you need one to describe properly of the other one, no matter how far they are from each other. For example, the spin of the photon, up or down, is actually the superposition of both states as long as you don't measure the photon. In the case of two entangled photons, one has to be down and one has to be up. When you measure the spin of the first photon, let's say spin-up, the second one has to be spin-down, even when they are far apart. There is no transmission of information faster than the speed of light as quantum physics shows, so even though they are simultaneously linked, there is no useful information transmitted during this process. See the Interpretation section for greater detail Back to figure 4, one of the entangled photon goes to I and is supposed to interfere with a photon coming from C. The other entangled photon keeps going down until it reaches the mirror D. There, the photon has a 50% chance to go through, and a 50% chance to be reflected. Here things start to be interesting. If the photon is reflected, it keeps going until it reaches F, we will talk about this later, but if the photon goes through the mirror, it will be captured at J. The object J is just a simple photon detector. If the entangled photon is detected, another words captured by the photon detector, we will observe the same phenomena as when the photon is looked at in the double slit experience, the superposition state of the photon will be destroyed. Since the two photons are entangled, when you destroy the superposition state for one, you also destroy it for the other. In other words, if the photon strikes the detector, we don't have anymore interference at the interference detector, I. Let's assume we know that the photon has been reflected and keep going on its way to F. F is a half reflective mirror, with a 50% chance it goes through and a 50% chance the photon is reflected. 7

8 F is called a quantum eraser. As you can see, the two photon detectors H and G will catch the photon, but you have absolutely no possibilities to know if the photon comes from the mirror E or D. It has come from either of the two mirrors E or D, you end up with a 50% chance the photon hits H and a 50% chance it hits G. Since the photon captors H and G do not give you any information about which way the photon took, they do not destroy the superposition state, and the interference detector, I, shows that the photon had interfered with itself. Now that we understand how the experiment works, let's place some boundary conditions on the problem: let's assume that the distance BD and the distance CE are greater than the distance BI (respectively CI). It means that the photon on its way to I (photon 1) will reach I, the interference detector before the other entangled photon (photon 2) reaches D, the semitransparent mirror. But the photon that reaches the interference detector will create interference only if the photon 2 is reflected by D or E. This is where the delayed choice occurs! The photon that reaches the interference detector will interfere with itself or not BEFORE the second entangled photon is reflected or not. When the photon traveling to the photon detector hits the screen, the path of the other photon is still unknown, so it should create interference. The experiment shows that we have interference only half of the time, as you might expect if BD was smaller than BI (respectively CE smaller than CI). In other words, the first photon behaves like it already know which path the second photon is going to take, as if the random and future choice of the second photon was known by the first photon in the present. This is what is called the delayed choice quantum experience. 8

9 Interpretation : Let's imagine we put a perfectly reflective mirror M on a planet 100 light years away, set in order to send you back what you send to it. The time travel for information is roughly the same than for light. So the time to send a message and get it back will be 200 years. Now, imagine that during the parametric down conversion, one photon is sent in direction of the interference detector, I as usual, and the other photon to this mirror M out of space. The photon will go there, come back on Earth and hit the mirror D or E. The experience is the still the same, the distance between the mirrors is just longer. Let's say one scientist has in his lab the source of light, the two photons are created by the parametric down conversion. This occurs during the year 2008 (basically the top part of figure 5) The scientist send on the mirror M the following message: Is the string theory is true? and turns his photon generator on in order to get some interference or not. 200 years later, some scientists will receive the message Better or worst? and answer by putting a perfectly reflective mirror for YES and no mirror at all for NO (Basically the bottom part of figure 5, mirror D and E are mirrors used to answer). The scientist in 2008 will, just after he sends the question, get interference if two hundreds years later they answered YES, or no interference if they answered NO by using the photon detector. 9

This is unfortunately not that easy, when you check the interference pattern to see your answer, if there is no interference, you will observe figure 6a.

When you do have interference, you will observe the superposition of figure 6b and figure 6c, which are respectively the interference from photons caught by G and the interference from photons catch

give exactly the same interference pattern as 6a. To be able to see the interference, you need to know which photon belongs to which interference pattern (6b or 6c).

10 This is unfortunately not that easy, when you check the interference pattern to see your answer, if there is no interference, you will observe figure 6a. All the photon just hit randomly the screen, this means the photon has been detected. When you do have interference, you will observe the superposition of figure 6b and figure 6c, which are respectively the interference from photons caught by G and the interference from photons catch in H. figure 6a figure 6b figure 6c We actually receive these two different interferences at the same time; their respective maximum in intensity is shifted in order that the addition of 6b and 6c give exactly the same interference pattern as 6a. To be able to see the interference, you need to know which photon belongs to which interference pattern (6b or 6c). The only way, to read and understand it, is to check the correlation between the captor G and H and the interferences. These information is only available only when the light arrives, meaning that you lose all the benefit of the interference before the reflection or absorption of the second photon. You basically receive the key to decode the answer when the second photon reacts, 200 years later. This is the same result as in the EPR experience (3), when one photon collapses, his entangled photon also collapses, but the only way to be aware of it, is to receive classic information on whether the second photon has collapsed or not. As expected by the theory of the general relativity, the causality can not travel faster than the speed of light. The actual quantum physics seems to explain properly this phenomena. 10

11 References: (1) : Other experience describe on wikipedia : (2) Bengtsson and K. Zyczkowski, "Geometry of Quantum States. An Introduction to Quantum Entanglement", Cambridge University Press, Cambridge, (3) On the Einstein-Poldolsky-Rosen paradox (1964), 11

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