Echoes of the past: Jung's experience at the heart of the new method of X-ray spectroscopy

In 1803, a certain gentleman published a work in which he described an experiment that proved the wave theory of light. This gentleman was Thomas Jung, and his experience was called the "experiment with two slits." More than two centuries have passed, but Jung's experience was not forgotten and even became the foundation of the new X-ray spectroscopy method, which allows for a more detailed study of the physical properties of a solid. So, why Jung's experience is considered one of the fundamental ones in physics, how modern scientists applied it and what we got from this we learn from the report of the research group. Go.

A little background

As it was already said, back in 1803, Thomas Jung published a description of his unusual experiment. And since “who does not know the past, has no future,” we will briefly consider this experience with you.


Thomas Jung

So, for the experiment there were only three things needed: a light, a plate with two vertical cuts and a projection screen. In this case, the light radiation was monochromatic, that is, had a minimum frequency spread. Light is directed to a plate with slots, the width of which should be as close as possible to the radiation wavelength. A projection screen is needed to monitor the result.

And here there is a collision of two theories of light - the corpuscular and the wave.

The first assumes that light consists of particles. And the second is that it is a wave. Based on each of these theories, we must get a different result in Jung's experience.

And now let's connect a little fantasy. Imagine that you are playing an airsoft with our experienced slotted screen (yes, the enemy is not very good, but this is not the point). You shoot a gun with balls, some of which bounce off the screen, and some pass through the slits and fall into the projection screen. Gun - a source of light radiation. Balls - particles of light. Thus, on the screen we see two strips, that is, two areas of falling from a gun.


A schematic representation of Jung's experience.

With the wave theory is still more interesting, therefore more imagination is required. Now you play intergalactic airsoft, and your gun, excuse me, your blaster shoots waves. When you shoot a wave at a screen, the two slits become the beginning (source) of two new secondary waves that will intersect behind the screen. And here we will see on the screen several different results at once (areas of “hit”). This result is the interference of light, but it requires certain conditions.

First, the light sources (there are two of them in the experiment) must be coherent, that is, consistent. Creating two consistent light emissions is problematic, to say the least. Therefore, one beam of light is used, which is divided into two due to the same screen with slots. So we imitate coherence due to secondary waves of primary light radiation.

Secondly, the width of the slits plays an important role, since as it increases, the illumination of the screen will increase, that is, it will be more difficult to distinguish the maxima and minima of the interference pattern. Therefore, the width should be as close as possible to the radiation wavelength.

And thirdly, the distance between the slits affects the repetition frequency of the interference fringes.

As a result, Thomas Jung not only provided evidence of the interference of light, but also gave rise to even more disputes between the proponents of the two theories, the particle and wave.

In fact, Jung's experience did not particularly quarrel anyone (I hope, because scientists can also be fighters), but rather pushed him to an even deeper study of the light, its features and ways of explaining it.

With the growing interest in quantum physics, Jung's experience received another theory in his piggy bank - the quantum one. And here fantasy will not help us much, as it is extremely difficult to imagine a ball for airsoft, able to be both a particle and a wave, and be separated, and connected, and the devil knows what else to do. The bottom line is that scientists decided to conduct Jung's experiment with an electron, using it instead of light.

Scientists "shot" one electron at a time so that they would not have the opportunity to interact with each other. On the way, they had the same screen with two slits, as in Jung's classic experience, and then a screen for visualizing the results.

Logically, single electrons trapped in the slots should form two areas of impact on the screen, that is, as in the corpuscular theory. However, we know that quantum theory and classical logic often diverge. The result of the experiment with electrons was a lot of areas of impact, that is, as in the wave theory. In other words, the electron is both a particle and a wave (de Broglie wave, more precisely) at the same time. Thus, the electron is in a state of quantum superposition, that is, it possesses several states at once that cannot be realized simultaneously from the point of view of classical physics. Yes, sometimes it seems that classical and quantum physics is Ludwig van Beethoven and Ozzy Osbourne - both are cool, but in many ways very different.


Thomas Jung apparently could not imagine how far his experience would go, and how much new he can tell. And now we will consider the actions of our contemporaries, who have decided to apply the experience of Thomas Jung to implement a new type of X-ray spectroscopy.

The basis of the study

A striking example of the belonging of something to both particles and waves in quantum mechanics is the inelastic X-ray scattering (RIXS). From the point of view of particles in RIXS, an x-ray photon pushes an electron from the nucleus of an atom into the valence shell. At this moment, a highly excited atomic state is formed, in which there is a very localized “void” with a size of several picometers. Such an intermediate state decays very quickly, which corresponds to the fact that the void is filled with a valence electron when re-emitting a photon. The final excited state can correspond to orbital, magnetic, or interband excitation.

Researchers focus on the study of X-ray waves propagating through the above localized intermediate state, and after forming the interference.

Scientists take us a little bit into the past, more precisely in the 90s. According to them, even then it became obvious that even if the scattering in RIXS is inelastic, and the hole in the atomic nucleus (better to call it the term “vacancy”) is very local, all the same the amplitudes of its formation and annihilation must be coherently summed up when using the identical ions involved in the delocalization of the final state of arousal. Because of all this, interference is possible.


Image number 1

And now, in 1994, interference was expected for RIXS in diatomic molecules, which corresponds to Jung's experience. This is possible due to the fact that the intermediate state of RIXS contains a single vacancy of a nucleus, which can be on any of two atoms in a molecule (image No. 1). In the final state, the electron is in an excited molecular orbital, which is delocalized by two atoms. X-ray radiation creates interference in the form of sinusoidal interference oscillations on the graph.

Ba ₃ CeIr ₂ O ₉ (BCIO), an insulator that is a crystalline solid with a quasi-molecular electronic structure ( 2A). Such characteristics allow a much clearer consideration of the interference, which is a clear sign of the symmetry of low-energy electronic excitations.

Research results

So, to begin with, scientists have grown individual BCIO crystals. Each of the Ir ⁴⁺ ions inside the structural dimers showed a 5d ⁵ configuration with one vacancy in the t _2g shell.


Image No. 2

Scientists note that the minimum distance between neighboring ions (Ir-Ir) was 2.5 Å. Accordingly, intradimeric ion interaction is rather strong and contributes to the formation of quasi-molecular orbitals with strong binding-anti-binding cleavage. This situation is very different from when there is one Ir.⁴⁺ , when a strong spin-orbital coupling (λ ≈ 0.4-0.5 eV) separates the local t _2g -manifold and leads to spin-orbit-entangled j = 1/2 moments ( 2B ).

In the case of a strong spin-orbit interaction, binding / anti-binding states can be formed from the spin-orbit-entangled j = 1/2 state ( 2D ). However, a strong Ir – Ir interaction can extinguish j = 1/2 moments. In this case, the t _2g orbitals become a much more suitable basis for the formation of binding / anti-binding states ( 2C ).


Image No. 3

In the image of 3A, we can see the results of the RIXS sample of Ba ₃ CeIr₂ O ₉ with a fixed radiation tuned to L3, the edge of Ir (2p → 5d), which resonantly enhances inelastic scattering from excitations inside t _2g . 5d t _2g - e ^δ _g splitting is higher than 3 eV, while the observed functions ( a , B and ℽ on the graph) are in the range of 0.5 ... 1.5 eV. Thus, they can be attributed to intra-t _2g excitations. It is also worth noting that there are no features typical for individual j = 1/2 moments of the graph, and the peak of spin-orbit excitation reaches a maximum of 1.5 λ.

The researchers note another important observation: the integral intensity of the functions demonstrates the pronounced features of the interference of two rays, in other words, a clear sinusoidal oscillation as a function of q _c ( 3B ). Thus, we obtained the experience of Young, only in this case, instead of the distance between the slits, we have the distance between the ions (Ir-Ir).

This study is one of the most difficult of those that I have met, therefore I strongly recommend that you read the report of scientists and additional materials to it, if you are interested in details, nuances and details of this work.

Epilogue

Scientists believe that the most important feature of RIXS interferometry is the ability to determine the symmetry of low-energy excitations, which helps to distinguish between two different orbitals described on images 2C and 2D.

Of course, the study of the new method of X-ray spectroscopy will not end there, because scientists have only slightly described the tip of the iceberg. Further experiments with other types of materials can open up new ways of implementing this technique. In any case, the improvement of the latest methods of studying the physical properties of even the already studied (supposedly) objects is a good thing.

In addition, this study was a good example of the fact that discoveries and observations made several centuries ago are still capable of not only surprising, but also being incredibly useful for creating new technologies, methods, etc.

Thank you for your attention, remain curious, despite the complexity of the material that interests you :), and the great work week, guys.

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