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arXiv:2605.28847

New class of quantum transitions exhibiting large-scale intercorrelations: Color of the sky

Kenzo Ishikawa, Masaki Takesada

Published May 16, 2026• 0 citations
arXivHTMLPDF

Abstract

The absolute value of the transition probability of the Rayleigh scattering is computed for the first time and applied to the scattering of solar light with molecules in the atmosphere and to the laser scattering with nanopartilces. The probability has a new contribution of unique properties from long-range correlations specific to the quantum mechanics. The magnitude is sufficient to resolve longstanding puzzle on diffusion lights in the sky and anomalous photon spectrum in laser experiments. The earth's albedo from the new calculations on Rayleigh scattering agrees with observations with satelites.

DOI
10.48550/arxiv.2605.28847

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The absolute value of the transition probability of the Rayleigh scattering is computed for the first time and applied to the scattering of solar light with molecules in the atmosphere and to the laser scattering with nanopartilces. The probability has a new contribution of unique properties from long-range correlations specific to the quantum mechanics. The magnitude is sufficient to resolve longstanding puzzle on diffusion lights in the sky and anomalous photon spectrum in laser experiments. The earth's albedo from the new calculations on Rayleigh scattering agrees with observations with satelites.
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A general expression is found for the Green's function of a two-level system interacting with a classical monochromatic field of arbitrary frequency and intensity. The Green's function is first used to calculate the transition probability from the lower to the upper state as a function of the frequency and intensity of the field and a comparison of the results is made with experiment. It is then used to study the problem of scattering. It is found that the spectrum of the scattered radiation consists of a line at the frequency of the field (Rayleigh line) and two satellites symmetrically displaced from the Rayleigh line by an amount depending both on the intensity and frequency of the field. In addition there are emissions at three, five, etc., times the frequency of the field, and accompanying satellites. The cross sections for the production of the Rayleigh line and its satellites, and for the third-harmonic line and its satellites have been calculated for a range of values of the frequency and intensity of the incident field.
“Why is the sky blue?” or “why are clouds white?” are examples of basic questions that always intrigued the mind of young, and not-so-young, students before their exposure to the fundamentals of light–matter interaction, a phenomenon that occurs anytime and anywhere in our universe and constitutes the main thrust in this chapter. It starts by highlighting the basic aspects of absorption and spontaneous and stimulated emission, described (in terms of quantum mechanics) by using Einstein coefficients and transition moments ; further along, the (classical) macroscopic connection with the Beer–Lambert law is derived. The journey continues by visiting elastic scattering and its two modalities, Rayleigh and Mie scattering , depending on the scattering particle size. In the final step, inelastic Brillouin and Raman scattering are discussed, placing emphasis on the laser-spectroscopic techniques underlying these types of photon–matter interactions. The chapter ends with a brief description how prehistoric humans already knew how to prepare colors for paintings (as exemplified in the Altamira cave in Cantabria, Spain); and a short exposé into state-of-the-art single-molecule spectroscopy using a single photon. This thread of spanning an arc between (historical) breakthroughs and cutting-edge research will be common to all chapters of the book.
We study the angular correlation function of speckle patterns that result from multiple scattering of photons by cold atomic clouds. We show that this correlation function becomes larger than the value given by Rayleigh law for classical scatterers. These large intensity fluctuations constitute a new mesoscopic effect specific to atom-photon interactions, that could not be observed in other systems such as weakly disordered metals. We provide a complete description of this behavior and expressions that allow for a quantitative comparison with experiments.
The initial theoretical finding that eventually led to laser development was Einstein’s prediction, based upon statistical considerations, that the energy of quanta of light be given by Planck’s constant times the frequency of the light. A new theoretical development based upon Weyl’s gauge field theory predicts that photon energies are quantized with the energy given by N2hν. Such quantization of photon energy changes the character of the photon from the Einstein photon that does not have a quantum number. Photon energy that includes a quantum number means that for a given energy the frequency may have more than one value. Conversely, photons of a given frequency may be found that have more energy than the Einstein photon. Further, the phat photons, all at a given frequency will have energy proportional to the number of phat photons and N2. For these phat photons the electric field strength, which causes breakdown in optical fibers or air, depends linearly on N. Thus, more energy may be transmitted using phat photons of higher quantum numbers than increasing the number of photons of lesser quantum numbers while still keeping the electric field below the breakdown level. Further, while the stimulated and spontaneous emission probabilities are proportional to 1/N2 the Rayleigh scattering cross section diminishes by 1/N8. This reduction in the scattering cross section means that a laser emitting phat photons with N<1 will lose less energy traveling through the Earth’s atmosphere than lasers using N=1. This reduction in energy losses through the atmosphere means increased efficiency for Earth based beamed applications. This presentation discusses the fundamental theory, emission probabilities, and cross section calculations.
We suggest a quantum description of Rayleigh light scattering on atoms. We show that an entangled state of the excited atom and the incident photon is formed during the scattering. Due to entanglement, a photon is never completely absorbed by the atom. The formation of the scattering spectrum is considered as a relaxation of incident photons to the reservoir of free space modes that are in thermal equilibrium. Additional excitations of the reservoir modes occurring during scattering are treated as scattered light. We show that even if the frequency of incident photons is incommensurate with an atomic transition frequency, the scattered light spectrum has a maximum at the frequency of incident photons. In addition, the linewidth of the scattered light is much smaller than that of the spontaneous emission of a single atom. Therefore, the process can be considered as elastic.