Quantum teaching - superposition of experiment and theory

In this post, Kafir Soleimani details how, within the framework of the laboratory, the students smash the foundations of classical theory one by one, by recreating a series of ground-breaking quantum experiments published in the last four decades

By Kafir Soleimani, quantums in Hebrew

Physics is an experimental science, but I acquired my quantum education mostly in front of a blackboard in class or a book. I am not unusual in this, this situation continues even in the ten years that have passed since I started my studies. This year, I was privileged to establish a quantum physics teaching laboratory, intended for third-year undergraduate students. In this post I will detail how, within the framework of the laboratory, the students smash the foundations of the classical theory one by one, by recreating a series of groundbreaking quantum experiments published in the last four decades.

The first experiment we reproduce is the Bell experiment. This experiment decided a long-standing dispute among the pioneers of quantum theory, regarding the determinism of nature. The idea was presented in the paper of Einstein, Podolsky and Rosen (EPR) from 1935 [1]. In their founding article, the authors specified a necessary criterion for their method, which the theory must meet in order to be considered complete: the theory must provide a way to calculate all the physical quantities in the system without disturbing it. This criterion is intended to be a counterweight to the probabilistic nature of quantum mechanics, according to which a physical quantity does not exist in reality until the system is "disturbed" by performing a measurement. Under this assumption, the quantum entanglement phenomenon leads to a paradox. In case two systems are intertwined, it is possible to predict a size in the system without it being disturbed. However, quantum mechanics does not provide a way to calculate the same magnitude. Hence, quantum theory does not meet the EPR criterion.

A more accurate formulation of this paradox is the question of whether it is possible to break a basic idea called "local realism". This principle holds that an experiment conducted in one place cannot immediately affect the results of an experiment conducted in another place, since bodies are only affected by events that are below them in the light cone of space-time (an expansion on this topic will be published, perhaps, in a future post). However, quantum entanglement does not fulfill the principle of locality. EPR's conclusion from this was that the quantum theory is incomplete, and there are "hidden variables" that exist and are defined before the measurement - but are unknown to us.

In an article published by John Stewart Bell in 1964, he suggests a simple way to resolve the issue through an experiment based on quantum entanglement. The experiment that Bell describes offers two results - one will rule out the existence of the "hidden variables", while the other will confirm it [2]. The experiment was carried out in the early 80s by Alan Aspa [3], and as a result Aspa concluded that the theory of hidden variables does not resolve the contradiction between quantum theory and local realism, and therefore acceptance of quantum theory requires abandoning this principle. The accepted view today is that the world only upholds a weaker version of the principle of local realism, according to which there can be a simultaneous influence from some distance as long as it does not transfer information from one place to another.

Now, in 2022, as part of a quantum physics lesson, we are reproducing Aspa's experiment. With the help of crystal illumination at high intensity (a process called "pumping") we produce pairs of photons which are entwined in polarization. When the photons are intertwined in polarization if we measure the polarization of one we will know the polarization of the photon that is intertwined with it. This feature is not surprising in itself, since they could have been created with the same specific polarization. The polarization measurement of each photon is done using a polarizer after which a single photon detector is placed. The polarizer transmits only the AM field charge in its polarization axis, and blocks the perpendicular charge. When a photon meets a polarizer in the direction of 45 degrees to its polarization, it cannot split and therefore either it passes or it is blocked in a random process with equal probability in both cases. If the photon has passed, its direction is as the direction of the polarizer. The amazing thing about the Bell experiment is that the relationship between the polarizations of the photons is maintained even when they are passed through polarizers at different angles.

Now I will briefly detail the course of the experiment. We count how many times per second the two photons managed to cross the polarizers and call this value "combination rate". Each of the polarizers is placed in a different angular orientation at one of 4 different angles, and the "combination rate" measurement is repeated for the 16 combinations of the two angles. While classical calculation predicts that the sum of the "combination rates" in the various combinations cannot be greater than a certain value, the quantum Torah predicts a very large sum of "combination rates" (which cannot be explained with the help of classical Torah). In preparation for the experiment, the students demonstrate a barrier arising from classical principles on the "rates of combinations", and are present to see that this does not agree with the measurements. After that, they write down the quantum state explicitly, calculate the "combination rates" quantumly and see that it correctly describes the system.

The second experiment we reproduce shows the wave-particle duality of light. The particle description of light was abandoned in the 19th century, when Thomas Young showed that two light sources collided with each other on a screen, creating bright and dark areas (a clear wavy feature). However, an experiment that negates the wave description was performed only in the late 70s by Jeff Kimball [4]. The reason for referring to Kimball's experiment as a pioneering experiment in denying the wave description of light is that the experiment shows a particle property of light (antibunching), this is in contrast to the demonstration of the photoelectric effect (1905) which does not settle the question of whether the electromagnetic field is quantized, or whether it is the atom, or both.

In reproducing this experiment, we introduce a beam of single photons into a beam splitter, which splits the incoming beam into two beams of identical luminance. A detector is placed in front of each beam that detects when a photon reaches it and emits a "reading". From the particle theory, it is not possible for both detectors to announce a reading at a given moment. Thus, we conclude that the light in the beam consists of discrete portions (quanta) that cannot be split. In order to complete the duality experiment, the two beams exit the beam splitter and enter another beam splitter. After the second splitter, we see an entanglement between the rays which cannot be described by the particle model. The meaning of this result is that the photon was in both exit beams of the first beam splitter at the same time and entangled with itself (!) in the second beam splitter.

During the six weeks that the laboratory lasts, we also reproduce additional experiments for these two, such as "Quantum Erasure" [5], and the HOM experiment (named after the physicists Hong, Ou and Mandel) which forms the basis for quantum computers [6]. Before each experiment, the students formulate two quantitative hypotheses - one based on the classical theory and the other on the quantum theory. At the end of the experiment we compare the measurements to the hypotheses, and see that the classical description fails.

In conclusion, in my personal opinion, the experiments that the students perform as part of this laboratory contribute to the formation of a complete and reliable picture regarding quantum theory, which is lacking in theoretical learning based on lectures and reference books only. In addition, the students acquire experimental skills in quantum technologies, and develop the ability to raise hypotheses and confirm or refute them through the planning and execution of an appropriate experiment.

Kafir Soleimani is the director of the Facebook and LinkedIn community "Quantim in Hebrew" and a doctoral student in the research group of Prof. Yaron Bromberg, Rakah Institute of Physics, The Hebrew University of Jerusalem

Sources

• [1] Einstein, Albert, Boris Podolsky, and Nathan Rosen. "Can quantum-mechanical description of physical reality be considered complete?" Physical review 47.10 (1935): 777.
• [2] Bell, John S. "On the einstein podolsky rosen paradox." Physics Physique Fizika 1.3 (1964): 195.
• [3] Aspect, Alain, Philippe Grangier, and Gérard Roger. "Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell's inequalities." Physical review letters 49.2 (1982): 91.
• [4] Kimble, H. Jeff, Mario Dagenais, and Leonard Mandel. "Photon antibunching in resonance fluorescence." Physical Review Letters 39.11 (1977): 691.
• [5] Kim, Yoon-Ho, et al. "Delayed "choice" quantum eraser." Physical Review Letters 84.1 (2000): 1.
• [6] Hong, Chong-Ki, Zhe-Yu Ou, and Leonard Mandel. "Measurement of subpicosecond time intervals between two photons by interference." Physical review letters 59.18 (1987): 2044.
• [7] The experimental system: https://qutools.com/qued

More of the topic in Hayadan:

• The next generation of magnetic computer memories
• "Quantum computing brings us to worlds that were impossible in classical computing"
• Basic concepts in quantum physics: what is spin?