Polarization Correlation of Photons Emitted in an Atomic Cascade - by Carl Alvin Kocher 1967 - Article review

This document contains article review "Polarization Correlation of Photons Emitted in an Atomic Cascade" by Carl Alvin Kocher written 1967
To order to read the article select: https://escholarship.org/uc/item/1kb7660q

• The text in italics is copied from the article.
  
• Immediate followed by some comments
  

Contents

• 1. Introduction: An Outline of the Experiment
• 2. Theory
• 3. The Problem of Multiple Scattering of Resonance Radiation
• 4. Experimental Procedures; Observed Counting Rates
• 7. Results and Discussion
• 8. Appendices

Reflection

• Reflection 1 - Physical theory, Quantum theory, Correlation experiments, Thought experiments, Laws and Observations.
• Reflection 2 - Fig 1

This thesis describes observations of the correlation in linear polarization of two photons emitted successively in an atomic cascade. Calcium atoms in an atomic beam are excited optically (41S0 --> 61p1) by ultraviolet continuum radiation from a high-intensity low-voltage H2 arc lamp. Photon pairs emitted in the cascade 61S0 --> 41p1 --> 41S0 (5513A and 4227A) are detected by conventional photomultipliers fitted with rotatable linear polarizers of the Polaroid type. The coincidence counting rate, recorded by a time-to-height converter and multichannel pulse-height analyzer, is found to be consistent with the theoretical correlation (El·E2)^2, where El and E2 denote the observed linear polarizations

What that means is theoretical correlation and observations are in line with the physical model of a calcium atom.

1. One of the most remarkable features of the quantum theory is its prediction of correlations in systems of several particles.

That is correct. One of the most remarkable features of this document is a demonstration of 2 correlated photons.

2. A measurement made on one particle can affect the result of a subsequent measurement on another particle of the same system, even though the particles may be non-interacting and separated in space.

That is the question i.e. if the measurement of one particle actual has a physical effect on the state of the other particle i.e on the result of the subsequent measurement of the other particle. That is extremely difficult to demonstrate.
The problem is that before the measurements are made, both particles can already be correlated and polarised. That implies that the actual measurement of either photon has no physical influence on its surroundings including any form of communication with the outside world.

3. The experiment described in this thesis is an attempt to observe a photon polarization correlation in a two-stage atomic cascade.

The experiment discussed is extremely clever.

4. An isolated atom, optically excited, returns to the ground state by way of an intermediate state, with the spontaneous emission of two successive photons.

This is important.
You can add the text: which are both polarised and correlated.

5. Quantum theory predicts that a measurement of the linear polarization of one photon can determine precisely the linear polarization of the other photon.

How can any theory predict such a correlation without any experimental evidence? i.e. without knowing that such a correlation actual exists. See also :

The plan of the experiment is simple: photon pairs from excited atoms are counted in coincidence, the coincidence rate being recorded as a function of the observed polarizations.

If the cascade is chosen so that the photons have wavelengths in the visible region, then the linear polarizers can be of the Polaroid type, and photomultipliers serve as single-photon detectors.

After an extensive search through tables of atomic energy levels, the cascade 61S0 --> 41P1 -->41S0 in calcium Fig. 1 was selected as the best candidate for the experiment.

That means in priciple many candidates are avaible which emit particles which are correlated and others which emit photons which are not polarized

The wavelengths of the cascade photons lamda1 and lambda2 are suitably short: y1 = 5513A and y2 = 4227A, respectively.

The theory of polarization correlations is well known. This paper .. will discuss two approaches to the 'problem. The first consists of an explicit demonstration that the conservation laws of angular momentum and parity imply a definite correlation in the photon polarizations [F-l,W-2, Y-1]. The second exploits the rotational symmetries of the states which take part in a cascade. Because of its generality, the latter approach is usually taken in the development of the theory of angular correlations of radiations emitted by nuclei [B-6, F-3]

This text gives an indication what the current state of the art is; the theory behind the experiments. It is advised to read the actual document.
It should be mentioned the reasoning can also be done in a different direction. That means that the result of the experiment, namely the correlation in the photon polarization is a confirmation of the conservation laws of angular momentum and parity.

After this test had proved that correlated Yl, Y2 photon pairs could be detected, the linear polarizers were installed, in preparation for attempts to observe the polarization correlation.

The present investigation is probably the first observation of photon polarization correlation in atomic spectrscopy. Similar problems have been pursued which involve correlations of radiations emitted by nuclei, most notably of gamma-rays in the MeV region. All of these experiments, directly or indirectly, are studies of the properties of many-particle quantum states.

One of the best known correlation experiments is the observation of the linear polarization correlation of the 0.5 MeV photon pairs emitted simultaneously in the annihilation of singlet positronium (Section II).

For several reasons, cascade experiments involving more than one polarization measurement are not ordinarily performed. One reason, discussed by Wightman, is that it is difficult to measure the polarization of MeV gamma-rays. Another is that although the determination of the relative parities of the nuclear states requires measurement of photon polarization, a single polarization measurement is sufficient if the angular correlation is also observed.

In the domain of atomic physics, the polarization of resonance fluorescence has been studied since the 1920's. Most of the relevant theory is described in the text by Heitler. Quantum interference effects, observable in level crossings, are an interesting manifestation of photon correlations. The technique of single photon counting has not been fully exploited in the visible region. A number of experiments have been proposed, but, comparatively few have been performed.

For more information read actual paragraph.
What the text indicates that many more experiments are performed in the past, which more or less try to do the same.

The polarization correlation of cascade photons serves as a beautiful illustration of a well-known problem in the quantum theory of measurement, first described in 1935 by Einstein, Podalsky, and Rosen and elucidated by Bohr.

In the calcium experiment each of the detected photon beams is unpolarized, since the orientations of the 41P1 states are random.
Consequently, the transmission probability is one-half for either of the linear polarizers, irrespective 'of its orientation.
Einstein, Podolsky, and Rosen would attempt to describe the photon pair as "two systems".
They reason as follows: "since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of, anything that may be done to the first system".

That is only partly correct. It is correct to describe the photon pair as "two systems" but that does not mean, that certain measurements can not be performed, which show correlation. Specific if the orientation of the polarizers is identical. This correlation can be the result of the internal structure or physical model of the calcium atom. Fig 1 shows enough information.

This assertion implies that the polarization measurements on the two photons are independent, and that the coincidence probability should be independent of the orientation of the polarizers.

The first part is true, but the second part can not be guaranteed.

The conflict between this apparently reasonable conclusion and the correlation predicted by quantum theory has been discussed in various contexts.
Although it is generally agreed that the usual interpretation of quantum theory is sufficient to explain correlation experiments,

This raises the question what is the physical explanation of correlations in this experiment.

some authors have attempted to restore the classical notion of causality through the introduction of "hidden variables."

There is no reason to introduce "hidden variables" or external physical influences. The explanation lies in the detailed description of the physical experiment, the position and moment when the two photon's are created as explained in Fig 1. At that moment all the physical parameters of all the particles created (including the correlated photons), are established

This idea is still the subject of some speculation.

The solution is: to try to perform more different, but almost identical, experiments

However, it may well be argued that a hidden variable model contributes little to our understanding of nature if the new theory cannot be distinguished experimentally from standard quantum theory.

If the standard quantum theory is in agreement which Fig 1 IMO, there is no reason to search for any other explanation.

Furry has explored the consequences of the assumption that a particle belonging to a composite system has independent reality.

This requires the definition of 'independent reality' as if there are different realities.

Taking the present experiment as an example, Furry would suppose that the polarization states of Y1 and Y2 are definite.
A correlation in linear polarization would be observed if the photons from each atom were linearly polarized in the same direction.
All polarization directions would be equally probable, perhaps determined by some sort of hidden variable.

There are three options:

1. The polarization of both photons are completely random, and all equally probable. There is no correlation i.e. = 0.
2. The polarization of one photon is completely random. The polarization direction of the second is the same. There is correlation i.e. = 1
3. The polarization of one photon is completely random. The polarization direction of the second is perpendicular. There is correlation i.e. = -1

The cause of each is different, but depends about the immediate details of the reaction that created both photons. This correlation can only be established when the experiment is repeated. When there is correlation the act of measuring the correlation has nothing to do with this.

Unfortunately, this linear polarization would preclude a correlation in circular polarization.

Why?

Bohm and Aharonov, considering the case of positronium annihilation, point out that Furry's assumption is inconsistent with the experimental result of Wu and Shaknov.
The calcium cascade experiment may be examined from the point of view of such an assumption.
This treatment is included here, not because it has any relevance to physics, but because it answers a question which has been raised on several occasions.
As usual, let "phi" be the angle between the polarizer axes, and let "psi" be the angle between the axis of polarizer #1 and the polarization direction for the photon pair.
The transmission probabilities are P1 = cos^2(psi) for YI and 2 P2 = cos^2(psi + phi) for Y2.
The coincidence probability is P = P1.P2 for a given value of "psi".
The angles "ps" must be distributed uniformly between o and pi.
Thus, on average, etc
This "correlation function" resembles the result from Quantum theory, 1/2 cos^2(phi)
However, its maximum and minimum values are 3/8 and 1/8 instead of 1/2 and 0.

If Furry's model were meaningful, P+/P1 = 1/3 (perfect polarizers); whereas the experimental ratio is close to zero, in agreement with quantum theory.

This sentence, consisting of three parts, requires more detail.

The paradox of Einstein, Podolsky, and Rosen arises from a disparity between a formal theory and the authors' intuitive sense.
Einstein said of Bohr's interpretation, "To believe this is logically possible without contradiction, but it is so very contrary to my scientific instinct that I cannot forego the search for a more complete conception".
The search must continue, but it should be recognized that the common-sense intuition cannot always be trusted to furnish a useful mental picture of phenomena which lie outside the domain of experience.

The only way to understand the physical reality is by means of experiments. When the result create a paradox, more experiments have to be performed

A very important concept, in order to understand, is to start with clear definitions.
A law is a detailed description of a certain phenomena that has been observed, mainly in a mathematical notation.
A theory is a detailed description of a certain phenomena that has not been observed. When it is observed the theory becomes a law.
Quantum theory is a description of the phenomena related to elementary particles and it constituents.
common-sense intuition is outside realm of science. It is a process inside the mind of humans. If you can concretize it, then it can be included as part of a theory.
Human experience can not directly be used in science. If it can be described accurately then it can be included as part of a theory.

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