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Two-Stage Cascaded Beam Splitting Method A Verdict Experiment on Photon Indivisibility Eliminating Detector Threshold Effect

Jingyuan Guo

Published Jun 18, 2026• 0 citations
Publisher

Abstract

The indivisibility of photons is the cornerstone of quantum optics, whose classic experimental evidence comes from the single-photon beam splitting coincidence experiment proposed by Grangier, Roger and Aspect in 1986. This paper points out that there is a systematic loophole in this experiment that has not been strictly excluded: all photodetectors have an energy response threshold. If a single photon is split into sub-pulses with energy below the threshold by the beam splitter, the experiment will be unable to distinguish between the two physical pictures of "the photon is truly indivisible" and "the photon is divisible but its split energy is below the detection threshold", and its conclusion relies on untested implicit assumptions. To address this loophole, this paper proposes an improved experimental scheme of two-stage cascaded beam splitting + four-channel coincidence measurement: the incident light is evenly distributed to four detectors through two stages of 50/50 beam splitters, and a step-by-step photon accumulation injection process is adopted, with the core verdict criterion that "the number of newly triggered detectors after a single photon injection is greater than 1". This criterion is a pure logical constraint, which does not require pre-calibration of the detector threshold and is not affected by non-ideal errors of the splitting ratio. It can serve as a strict verdict experiment on whether photons are divisible. (本文采用中英交替双语排版:每段英文后紧跟对应中文翻译,确保双语言内容完全一致。)

DOI
10.5281/zenodo.20742703

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The indivisibility of photons is the cornerstone of quantum optics, whose classic experimental evidence comes from the single-photon beam splitting coincidence experiment proposed by Grangier, Roger and Aspect in 1986. This paper points out that there is a systematic loophole in this experiment that has not been strictly excluded: all photodetectors have an energy response threshold. If a single photon is split into sub-pulses with energy below the threshold by the beam splitter, the experiment will be unable to distinguish between the two physical pictures of "the photon is truly indivisible" and "the photon is divisible but its split energy is below the detection threshold", and its conclusion relies on untested implicit assumptions. To address this loophole, this paper proposes an improved experimental scheme of two-stage cascaded beam splitting + four-channel coincidence measurement: the incident light is evenly distributed to four detectors through two stages of 50/50 beam splitters, and a step-by-step photon accumulation injection process is adopted, with the core verdict criterion that "the number of newly triggered detectors after a single photon injection is greater than 1". This criterion is a pure logical constraint, which does not require pre-calibration of the detector threshold and is not affected by non-ideal errors of the splitting ratio. It can serve as a strict verdict experiment on whether photons are divisible. (本文采用中英交替双语排版:每段英文后紧跟对应中文翻译,确保双语言内容完全一致。)
We report on two experiments using an atomic cascade as a light source, and a triggered detection scheme for the second photon of the cascade. The first experiment shows a strong anticorrelation between the triggered detections on both sides of a beam splitter. This result is in contradiction with any classical wave model of light, but in agreement with a quantum description involving single-photon states. The same source and detection scheme were used in a second experiment, where we have observed interferences with a visibility over 98%.
The 'graininess' in the energy content of light is reported in experiments ranging from the blackbody spectrum and photo-electric effect to revivals in the Jaynes-Cummings model. Laser shot noise and antibunching of correlations in resonance fluorescence signify a departure from continuous wave behavior for light. Such phenomena underlie the unique sense in which a photon is regarded as an indivisible particle, experimentally tied to the fact that a beam splitter does not split a single photon of a two-photon pair. We consider three arguments for indivisibility - quantization of energy, particle-like fluctuations, and which-way measurements. We argue that in each case, photon indivisibility is an inference based on energy conserving interactions where the detection mechanism involves countable electrons subject to space and bandwidth limitations. The indivisibility of the photon thus remains an open question, and one that we can use to probe the foundations of quantum electrodynamics.
In a thought experiment, Einstein proposed that a single light quantum (photon) would go one way or another at a beam-splitter. Here, newly described beam-split tests of the photon implement gamma-rays from spontaneous decay of 109Cd and 57Co, whereby a single primary gamma-ray splits and is detected in coincidence in two detectors. The experimental coincidence rates are found to substantially exceed the chance coincidence rate. These results directly violate the quantum mechanical probabilistic model of light, and indirectly violate the concept of quantized charge. These are full-height pulses, characteristic of the chosen gamma under study. To help understand how all this can possibly be true, I have identified conceptual and experimental flaws in previous works, and have developed the long abandoned loading theory. This developed loading theory avoids wave-particle duality by thresholds, a pre-loaded state, and by having electromagnetic energy emitted quantized but absorbed continuously. By forcing a choice between conservation of energy and photons, the experimental results spell the long overdue death of the photon. ______________________________
As low light detection technologies are advancing, novel experiments like single molecule spectroscopy, quantum computation, quantum encryption are proliferating. Quantum mechanical detectors can produce only discrete "clicks" at different rates based on the propagating field energy through them, irrespective of whether the photons are divisible or indivisible packets of energy. This is because electrons are quantized elementary particles and they are always bound in quantized energy levels in different quantum systems. Highly successful quantum formalism is not capable of providing the microscopic picture of the processes undergoing during QM interactions; that is left to human imaginations allowing for sustained controversies and mis-interpretations. This paper underscores the paradoxes that arise with the assumption that photons are indivisible elementary particles based on the obvious but generally ignored fact that EM fields do not operate on (interfere with) each other. Then we propose that atomic or molecular emissions emerge and propagate out as space and time finite classical wave packets. We also suggest experiments to validate that the amplitude of a photon wave packet can be split and combined by classical optical components using the specific example of an N-slit grating.
The production of maxima and minima by the superposition of two or more light signals provides fundamental support for the wave nature of light. This result is based on the study of wave interference phenomena which remains the only approach to explain the production of those maxima and minima. In a system that is prepared to work with only one photon at a time, any detector can signal only one or zero. In 1986, a rigorously controlled experiment was designed by Grangier, G. Roger, and A. Aspect, [Europhys Lett. 1(4), p. 173, 1986] that guaranteed a single-photon beam. The explanation of the experimental results implied the interference of the wave function of a single-photon with itself. Thus, the explanation of interference that is accepted for an ensemble of photons was assumed to be valid for a single photon. In this study, we prepare a Mach-Zehnder interferometer using the same type of beam splitters used by Grangier et al. to test the assumption mentioned above. Our results allow us to explain the results of Grangier et al. because of the interaction between light and the beam splitters. Our results also verify that their wave interpretation of the results is not valid. Here, we present the essential findings of the extensive experimental evidence that supports our ideas.
Beam splitter Compared with other fundamental experiments in physics, optical tests of quantum mechanics are often distinguished by their simplicity. Most quantum optical experiments do not require a whole industry - an optical table of equipment and a few people are often sufficient. Good ideas, good research problems are more important. “Research is to see what everybody has seen and to think what nobody has thought” (Jammer, 1989). A simple optical beam splitter, for instance, is already a nice device to demonstrate the quantum nature of light. Quite a number of puzzling quantum effects have been seen by splitting or recombining photons at a small cube of glass. Additionally, the beam splitter serves as a theoretical paradigm for other linear optical devices. Interferometers, semitransparent mirrors, dielectric interfaces, wave guide couplers, and polarizers are all described sufficiently well by a simple beam splitter model. The quantum effects of almost all passive optical devices can be understood assuming appropriate beam splitter models. (It's all done with mirrors.) Heisenberg picture An ideal beam splitter is a reversible, lossless device in which two incident beams may interfere to produce two outgoing beams. For instance, a dielectric interface inside a cube or plate of glass splits a light beam into two, see Fig. 5.1. We may reverse this situation by sending the two beams back to the cube, where they interfere constructively to restore the original beam.