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Scientific discovery: researchers have seen phenomena from quantum mechanics in the movement of pendulums

The new system makes it possible to observe phenomena that occur within special "topological" materials by photographing the movement of pendulums using a normal camera

It is very difficult and sometimes even impossible to look into quantum systems, which consist of microscopic particles such as atoms or electrons. New research at Tel Aviv University has succeeded in building a large mechanical system that obeys the same dynamic laws as those found in quantum systems. The new system makes it possible to observe phenomena that occur within special "topological" materials by photographing the movement of pendulums using a normal camera. The research is the result of the collaboration of Dr. Yizhar Nedar from the Shurk Nuclear Research Center, Habiva Sirota-Katz from the Department of Biomedical Engineering, Dr. Mittal Geva and Prof. Yair Shukif from the School of Mechanical Engineering and Prof. Yoav Lahini and Prof. Roni Ilan from the School of Physics and Astronomy at Tel Aviv University, recently published in the scientific journal PNAS.

The researchers explain that concepts such as "wave function", "superposition" and "topological aggregation states" are usually attributed to quantum mechanics, which governs the microscopic world of electrons, atoms and molecules. According to the accepted description in these systems, the electron, which is a moving particle in an atom or a solid, can have properties that manifest wave phenomena, such as the probability of spreading through space like waves in a pond into which a stone has been thrown, the ability of the electron to be in several places at the same time, to mess with itself, and more.

Also, the wavy properties lead to a unique phenomenon that exists in certain insulating solids, where although the electrons in the insulating material do not move under the influence of an external field, the internal arrangement of the material is expressed in a so-called "topological" state. This means that the wave of the electrons has a size added that can "close on itself" in a number of different ways, similar to a cylinder compared to a Möbius ring. This state of the electrons, for which the Nobel Prize in Physics was awarded in 2016, is considered a new aggregation state of matter, and has been a very active research topic in recent decades.

Despite the great interest, in quantum systems and atomic crystals there is a limitation in the measurement of these phenomena. This is because in these systems, due to the nature of quantum mechanics, there is no way to measure the electronic wave function and its dynamics directly. Instead, researchers indirectly measure the wave and topological properties of electrons in a material, for example, by measuring the electrical conductivity of solids. 

Fifty pendulums in one row

As part of the research, the researchers thought what if we could build a large mechanical system, which would obey the laws of dynamics similar to those appearing in these quantum systems, and in which we could measure everything? Indeed, they built a system of fifty pendulums in a row, with wire lengths that varied slightly from one pendulum to another. In addition, the wires of each pair of adjacent pendulums were connected to each other at a variable and controlled height, so that the movement of each of them affects the movement of its neighbors.

On the one hand, the system obeyed our everyday laws of physics - Newton's laws, but the exact values ​​of the lengths of the pendulums and the connections between them created magic: Newton's laws themselves resulted in the wave created by the movement of the pendulum obeying the Schrödinger equation - the fundamental equation of quantum theory, which controls motion The electrons in atoms and in solids. The result is that the dynamics of the pendulums, visible to the eye in the macroscopic world (and simply measured by the researchers' mobile phones), accurately mimic the behaviors of electrons in the crystal.  

When the researchers deflected several pendulums in the row, then left them and let the resulting wave move forward freely, they were able to directly measure the development of the wave within the system - an impossible task when it comes to the movement of electrons. This capability enabled the direct measurement of three phenomena. The first is known as Bloch oscillations. In an electronic system, this phenomenon is attributed to the electrons being pulled in a certain direction by an electric voltage, and despite this, they do not move in the direction of the voltage, as in normal metals, but perform back-and-forth oscillations due to the presence of the periodic environment of the crystal. This phenomenon is attributed only to very clean solids, which are very difficult to find in nature. On the other hand, in the pendulum system, a wave is observed moving back and forth in a cyclical manner, exactly in accordance with Bloch's prediction.

The second phenomenon observed directly in the pendulum array is known as Zener tunneling. Tunneling is a unique quantum phenomenon, which allows the passage of particles through a barrier, contrary to classical intuition. In the case of Zener tunneling, this is reflected in the splitting of the wave packet under a sufficiently large external force, after which the parts move in opposite directions. One part of the wave goes back as in a normal Bloch oscillation, and another part manages to "tunnel" through a forbidden state and continues to advance. The splitting of the wave into two, and especially the connection between the tunneling result and the movement of the wave to the right or left, is a hallmark of the Schrödinger equation. Indeed, this was the main reason it made Schrödinger himself uneasy, which led him to formulate his famous paradox, according to which the Schrödinger equation implies that quantum tunneling in a single atom can lead to the wave of a whole cat splitting into a live-cat and a dead-cat. The researchers analyzed the movement of the pendulum and extracted from it the parameters of the movement - such as the ratio between the intensities of the two parts of the split wave, which is equivalent to the probability of quantum Zener tunneling. The experimental results showed excellent agreement with the predictions of the Schrödinger equation.

Tel Aviv University's Pendulum Experiment. Photo: Tel Aviv University spokesperson
Tel Aviv University's Pendulum Experiment. Photo: Tel Aviv University spokesperson

It is important to remember that in the end, the pendulum system is a system governed by the laws of classical physics, and therefore cannot simulate all the richness of quantum systems. For example, in quantum systems the very measurement can affect the behavior of the system (and cause the cat to be, finally, either alive or dead, when you watch it). whereas here there is no parallel phenomenon. But even within these limits, the pendulum array allows the measurement of interesting and non-trivial properties that exist in quantum systems, but which cannot be measured in them directly.

The third phenomenon observed directly in the experiment is the development of a wave packet in a medium with non-trivial topological properties. Here the researchers found a way to directly measure the topological characteristic from the dynamics of a wave packet in the medium - an almost impossible task in quantum materials. For this purpose, the pendulum system was aimed twice, so that the pendulums simulated the Schrödinger equation of electrons, once in a topological state, and once in a trivial (ie normal) state. From a comparison of very small differences in the movement of the pendulums between the two experiments it was possible to distinguish between the two situations. The diagnosis required a rather delicate measurement and was reflected in the difference of exactly half a swing of the pendulum between the two experiments, each of which lasted about 12 minutes, and included about 400 complete swings of the pendulum. This small difference is measured with a distinct precision and in accordance with the theory.

The experiment opens the door to the realization of additional, interesting and even more complex problems, such as the effects of noise and contamination or of energy leakage on the dynamics of wave packets in the Schrödinger equation. These are effects that can be easily simulated in the system, with the help of an initiated and controlled disturbance to the movement of the pendulums.

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