Time and the Quantum
Posted: Fri Apr 27, 2012 11:28 am
Hi all.
I have found a very interesting article[1] and would like to share it with you. It's about time and the quantum eraser. Let's do the experiment as depicted on the Figure 1 at the end of this post.
Figure 1A:
Light impinges from the left on the two-level atom located at sites 1 and 2. An atom excited to level a emits a photon gamma. We look at the interference of these photons at the screen. Because both atoms are finally in the state b after the emission of photons, it is not possible to determine which atom contributed the the photon gamma. A large number of such experiments are carried out; i.e., any one photon will yield one count on the screen, and it takes many such photon events to build up an interference pattern. This is an anlogue og the usual Young's double-slit experiment. Instead of the usual light beams through two pin holes, we have considered scattered light from two atoms. The key to the appearance of the interference is the lack of which-path information for the photons.
Figure 1B:
In the case where the atoms have three levels, the drive field excites the atoms from the ground state c to the excited state a. The atom in a state a can then emit photon gamma and end up in state b. Here, the photon detected on the screen leaves behind which-path information;that is, the atom responsible for contributing the photon gamma is in level b, whereas the other atom remains in level c. The precise mathematical description of photons gamma1 and gamma2 is the same in cases a and b. It is only the presence of the passive observer state that kills the interference. (NOT the presence of conscious mind!)
Figure 1C:
Here we introduce another field that takes the atom from level b to bprime and, after the emission of a photon phi at the bprime-c transition, ends up in level c. Now the final state of both the atoms is c, and a measurement of internal states cannot provide us the which-path information. It would therefore seem that the interference fringes will be restored, but a careful analysis indicates that the which path information is still available through the photon phi. A measurement on the photon phi can tell us which atom contributed to the photon gamma. The big question is whether we can erase the which-path information contained in the photon phi and recover the interference fringes?
Let us now turn to the Figure 2 at the end of this post.
We again consider two atoms of the type shown in Figure C located at sites 1 and 2. A pair of photons gamma and phi are emitted either by the atom 1 or by the atom 2. The gamma photon as before proceeds to the screen on the right and is detected by a detector on screen D at location x0. A repeat of this experiment yields essentially random distribution of photons on the screen.
What about the appearance and disapearence of interference fringes discussed above? For this purpose, we look at the photon phi. We consider only those instances where the phi photon scattered from atom 1 proceeds to the beam splitter B1 and the phi photon scatterd from the atom 2 proceeds to B2. At either of these 50/50 beam splitters, the photon phi has a 50% probability of proceeding to detectors D3 (from photon scattered from 1) and to D4 (for photon scattered from 2). On the other hand, there is also a 50% probability that the photon will be reflected and proceed to another 50/50 beam splitter B. For these photons there is an equal probability of being detected at detectors D1 and D2.
If the photon phi is detected at the detector D3, it has necessarily come from the atom 1 and could not have come from the atom 2. Similarly, detection at D4 means that the photon phi came from the atom 2. For such events, we can also conclude the the corresponding photon gamma was also scattered from the same atom.
That is, we have which-way information if detectors D3 and D4 register a count.
If the photon phi is detected at D1, there is an equal probability that it may have come from the atom 1 or it may have come from the atom 2. Thus we have erased the information about which atom scattered the photon phi, and there is no which-path information available for the corresponding photon gamma. The same can be said about the photon phi detected at D2.
After this experiment is done a large number of times, we shall have roughly 25% of phi photons detected each at D1, D2, D3 and D4. The corresponding spatial distribution of gamma photons will be as mentioned above completely random. Next we do a sorting process. We separate out all the events where the phi photons are detected at D1, D2, D3 and D4. For these four groups of events we locate the position of the detected gamma photons on the screen D.
The key result is that, for the events corresponding to the detection of phi photons at detectors D3 and D4 there are no interference fringes but we obtain conjugate (pi phase shifted) interference fringes for those events where the phi photons are detected at D1 and D2. For this set of data, there is no which-path information available for the corresponding gamma photons.
Suppose we place the phi photon detectors far away. Then the future measurements on these photons influence the way we think about the gamma photons today (or yesterday!). For example, we can conclude that gamma photons whose phi partners were succesfully used to ascertain which-path information can be described as having (in the past) originated from site 1 or site 2. We can also conclude that the gamma photons whose phi partners had their which-path informations erased cannot be described as having (in the past) originated from site 1 or site 2 but must be described, in the same sense, as having come from both sites. The future helps shape the story we tell of the past.
Imagine that the beam splitters and the four photon phi detectors are on the other site of the universe!
And imagine that you choose to place the beamsplitter B after the photon gamma reached the detector D.
(I can next time share with you the delayed choice quantm eraser experiment if there is an interest among people.)
[1]: Y. Aharonov, M. S. Zubairy: Time and the Quantum, Science, Vol.307, 2005
http://www.columbia.edu/cu/physics/pdf-files/Scully.pdf
I have found a very interesting article[1] and would like to share it with you. It's about time and the quantum eraser. Let's do the experiment as depicted on the Figure 1 at the end of this post.
Figure 1A:
Light impinges from the left on the two-level atom located at sites 1 and 2. An atom excited to level a emits a photon gamma. We look at the interference of these photons at the screen. Because both atoms are finally in the state b after the emission of photons, it is not possible to determine which atom contributed the the photon gamma. A large number of such experiments are carried out; i.e., any one photon will yield one count on the screen, and it takes many such photon events to build up an interference pattern. This is an anlogue og the usual Young's double-slit experiment. Instead of the usual light beams through two pin holes, we have considered scattered light from two atoms. The key to the appearance of the interference is the lack of which-path information for the photons.
Figure 1B:
In the case where the atoms have three levels, the drive field excites the atoms from the ground state c to the excited state a. The atom in a state a can then emit photon gamma and end up in state b. Here, the photon detected on the screen leaves behind which-path information;that is, the atom responsible for contributing the photon gamma is in level b, whereas the other atom remains in level c. The precise mathematical description of photons gamma1 and gamma2 is the same in cases a and b. It is only the presence of the passive observer state that kills the interference. (NOT the presence of conscious mind!)
Figure 1C:
Here we introduce another field that takes the atom from level b to bprime and, after the emission of a photon phi at the bprime-c transition, ends up in level c. Now the final state of both the atoms is c, and a measurement of internal states cannot provide us the which-path information. It would therefore seem that the interference fringes will be restored, but a careful analysis indicates that the which path information is still available through the photon phi. A measurement on the photon phi can tell us which atom contributed to the photon gamma. The big question is whether we can erase the which-path information contained in the photon phi and recover the interference fringes?
Let us now turn to the Figure 2 at the end of this post.
We again consider two atoms of the type shown in Figure C located at sites 1 and 2. A pair of photons gamma and phi are emitted either by the atom 1 or by the atom 2. The gamma photon as before proceeds to the screen on the right and is detected by a detector on screen D at location x0. A repeat of this experiment yields essentially random distribution of photons on the screen.
What about the appearance and disapearence of interference fringes discussed above? For this purpose, we look at the photon phi. We consider only those instances where the phi photon scattered from atom 1 proceeds to the beam splitter B1 and the phi photon scatterd from the atom 2 proceeds to B2. At either of these 50/50 beam splitters, the photon phi has a 50% probability of proceeding to detectors D3 (from photon scattered from 1) and to D4 (for photon scattered from 2). On the other hand, there is also a 50% probability that the photon will be reflected and proceed to another 50/50 beam splitter B. For these photons there is an equal probability of being detected at detectors D1 and D2.
If the photon phi is detected at the detector D3, it has necessarily come from the atom 1 and could not have come from the atom 2. Similarly, detection at D4 means that the photon phi came from the atom 2. For such events, we can also conclude the the corresponding photon gamma was also scattered from the same atom.
That is, we have which-way information if detectors D3 and D4 register a count.
If the photon phi is detected at D1, there is an equal probability that it may have come from the atom 1 or it may have come from the atom 2. Thus we have erased the information about which atom scattered the photon phi, and there is no which-path information available for the corresponding photon gamma. The same can be said about the photon phi detected at D2.
After this experiment is done a large number of times, we shall have roughly 25% of phi photons detected each at D1, D2, D3 and D4. The corresponding spatial distribution of gamma photons will be as mentioned above completely random. Next we do a sorting process. We separate out all the events where the phi photons are detected at D1, D2, D3 and D4. For these four groups of events we locate the position of the detected gamma photons on the screen D.
The key result is that, for the events corresponding to the detection of phi photons at detectors D3 and D4 there are no interference fringes but we obtain conjugate (pi phase shifted) interference fringes for those events where the phi photons are detected at D1 and D2. For this set of data, there is no which-path information available for the corresponding gamma photons.
Suppose we place the phi photon detectors far away. Then the future measurements on these photons influence the way we think about the gamma photons today (or yesterday!). For example, we can conclude that gamma photons whose phi partners were succesfully used to ascertain which-path information can be described as having (in the past) originated from site 1 or site 2. We can also conclude that the gamma photons whose phi partners had their which-path informations erased cannot be described as having (in the past) originated from site 1 or site 2 but must be described, in the same sense, as having come from both sites. The future helps shape the story we tell of the past.
Imagine that the beam splitters and the four photon phi detectors are on the other site of the universe!
And imagine that you choose to place the beamsplitter B after the photon gamma reached the detector D.
(I can next time share with you the delayed choice quantm eraser experiment if there is an interest among people.)
[1]: Y. Aharonov, M. S. Zubairy: Time and the Quantum, Science, Vol.307, 2005
http://www.columbia.edu/cu/physics/pdf-files/Scully.pdf