Photon
General
Photons are elementary particles that serve as the quantum of electromagnetic radiation. They are the fundamental carriers of electromagnetic force and exhibit both wave-like and particle-like properties. Photons have zero rest mass, no electric charge, and travel at the speed of light in a vacuum (approximately 299.792.458 meters per second).
Basic Properties
A photon can be described as a quantum of electromagnetic radiation, representing the smallest discrete amount of electromagnetic energy. In quantum mechanics, electromagnetic radiation, such as light, is quantized into particles called photons.
Here are some key aspects of the photon as a quantum of electromagnetic radiation:
Energy Quantization
Photons carry energy that is quantized, meaning it can only exist in discrete amounts determined by the frequency (or wavelength) of the electromagnetic radiation. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength, as described by Planck's equation: ℎE=hf, where E is the energy of the photon, h is Planck's constant, and f is the frequency of the radiation.
Figure 305 - Relationship between the Temperature of an object and the spectrum ofbBlackbody Radiation it emits [1]
Wave-Particle Duality and uncertainty principle
Particles known as photons adhere to the principles of quantum mechanics, displaying properties akin to both waves and particles. Upon detection, a photon registers as a discrete entity, yet its likelihood of detection is computed using wave equations, a phenomenon termed wave-particle duality. This duality is evident in the probability distribution of photon detection, exhibiting wave-like behaviors such as diffraction and interference. Despite this, experimental evidence suggests that photons behave more akin to point-like particles when interacting with matter.
Figure 306 - Wave-particle Duality. Young’s interference fringes [2]
While introductory materials often simplify photon behavior using non-relativistic quantum mechanics, this approach overlooks their inherently relativistic nature due to their lack of rest mass. To address this, physicists resort to a theory known as quantum electrodynamics, wherein photons are considered quantized excitations of electromagnetic modes.
Another challenge lies in defining the uncertainty principle for photons. Although commonly associated with Heisenberg, its precise mathematical formulation was developed later by Kennard, Pauli, and Weyl. This principle asserts that when measuring certain paired quantities like position and momentum, there's an intrinsic limit to their precision. Coherent states, minimizing uncertainty within the confines of quantum mechanics, play a crucial role in quantum optics. However, unlike the position-momentum relation, there's a tradeoff between measurements of electromagnetic wave amplitude and phase, expressed informally in terms of photon number and phase uncertainty. Yet, unlike position and momentum, phase cannot be represented by a Hermitian operator, distinguishing this uncertainty concept.
Quantum Electrodynamics (QED)
In the realm of particle physics, quantum electrodynamics (QED) stands as the relativistic quantum field theory governing the dynamics of electromagnetism. It serves as a comprehensive framework for elucidating the intricate interplay between light and matter, marking the pioneering theory to seamlessly reconcile quantum mechanics with special relativity. At its core, QED intricately details the interaction of electrically charged particles through the exchange of photons, effectively encapsulating the quantum essence of classical electromagnetism and offering a holistic understanding of the interplay between matter and light.
Figure 307 - Photon-electron interactions with (a) transparency (no interaction),(b) excitation, (c) ionization – photoelectric effect, (d) scattering – Compton effect, (e) pair production.
From a technical standpoint, QED emerges as an exceedingly precise tool for calculating the probabilities associated with the positions and motions of particles, including massless entities such as photons, while also accounting for the spatial distribution (field) of these particles. Notably, it transcends the confines of the wave-particle duality posited by Einstein in 1905. Revered physicist Richard Feynman aptly dubbed it "the jewel of physics" owing to its remarkable predictive accuracy, particularly evident in its calculations of phenomena like the anomalous magnetic moment of the electron and the Lamb shift of hydrogen's energy levels. QED stands as the pinnacle of precision in physics, boasting unparalleled accuracy and undergoing rigorous testing to solidify its status as the most rigorously validated theory in the field.
Absorption and Emission
Photons can be absorbed or emitted by matter through interactions with charged particles, such as electrons in atoms. When an electron absorbs a photon, it gains energy and may transition to a higher energy level. Conversely, when an electron transitions to a lower energy level, it emits a photon corresponding to the energy difference between the initial and final states.
Absorption:
Absorption occurs when a photon, carrying energy due to its electromagnetic nature, interacts with an atom, molecule, or solid material. When the energy of the photon matches the energy difference between the ground state and an excited state of the atom, molecule, or solid, the photon can be absorbed, and its energy is transferred to the system.
Electron Transition
In an atom or molecule, electrons occupy specific energy levels or orbitals. When a photon with energy matching the energy difference between two energy levels interacts with the system, it can elevate an electron from a lower energy level (ground state) to a higher energy level (excited state).
Conservation of Energy and Momentum
The energy and momentum of the incoming photon must be conserved during the absorption process. If the photon has insufficient energy to promote an electron to the higher energy level, absorption won't occur.
Excited State
Once the electron is in the excited state, it can remain there temporarily before returning to a lower energy state. The excited state may last for a very short time, ranging from nanoseconds to even fractions of a second, depending on the specific system.
Figure 308 - Photon Absorption
Emission
Emission is the process by which a system in an excited state releases energy in the form of a photon and transitions back to a lower energy state.
Spontaneous Emission
In spontaneous emission, the system transitions from an excited state to a lower energy state without external influence. This process occurs randomly and is governed by quantum mechanics.
Stimulated Emission
In stimulated emission, an external photon interacts with the system, causing it to transition to a lower energy state and emitting a photon with the same energy, phase, and direction as the stimulating photon. This process is the basis of laser operation.
Conservation Laws
Similar to absorption, the emission process must also conserve energy and momentum.
Photon Characteristics
The emitted photon typically carries the energy difference between the higher and lower energy states of the system.
Figure 309 - Photon Emission
Both absorption and emission processes play crucial roles in various phenomena, including the behavior of light in materials, the operation of lasers, and the interactions of matter with electromagnetic radiation in fields such as spectroscopy and quantum mechanics.
Quantum Field Theory
In quantum field theory (QFT), photons are described as excitations of the electromagnetic field. QFT is a framework that combines elements of quantum mechanics and special relativity to describe the behavior of fundamental particles and their interactions in terms of fields.
Quantum Fields
In QFT, fields are fundamental entities that permeate all of spacetime. Each type of particle is associated with its own field, and particles themselves are seen as excitations or quanta of these fields. The electromagnetic field, for example, corresponds to photons.
Figure 310 - Electromagnetic Field
Particle and Wave Duality
Photons, like other particles in QFT, exhibit both particle-like and wave-like behavior. They can be thought of as localized packets of energy (particles) or as waves propagating through space. This duality is inherent in the nature of quantum mechanics and is captured by the mathematical formalism of QFT. (See figure 306)
Quantization
In QFT, the fields are quantized, meaning that they can only take on discrete values of energy and momentum. Photons are quantized excitations of the electromagnetic field, meaning that the energy and momentum of a photon are quantized in discrete units determined by the frequency (or wavelength) of the associated electromagnetic wave.
Interactions
Photons interact with charged particles through the electromagnetic force. These interactions are mediated by the exchange of virtual photons between charged particles. For example, when two charged particles repel each other, they exchange virtual photons, which transfer momentum between them.
Quantum Electrodynamics (QED)
Quantum electrodynamics is the specific QFT that describes the behavior of photons and charged particles interacting via the electromagnetic force. In QED, interactions between photons and charged particles are described using Feynman diagrams, which depict the various possible ways in which particles can interact.
Field Equations
The behavior of photons in QFT is governed by the field equations, such as Maxwell's equations in the case of electromagnetism. These equations describe how the electromagnetic field evolves over spacetime and how photons propagate through space.
Electromagnetic Spectrum
The electromagnetic (EM) spectrum encompasses a broad range of electromagnetic waves, each associated with photons—fundamental particles that carry energy and exhibit both wave-like and particle-like properties. Understanding photons is key to comprehending the diverse behaviors and applications of electromagnetic radiation across the spectrum. At the core of the EM spectrum are photons, which vary in energy depending on their frequency. Higher frequency photons have more energy, while lower frequency photons have less. This relationship is described by Planck's equation, E = hf, where E is energy, h is Planck's constant, and f is frequency.
Different regions of the electromagnetic spectrum correspond to photons with specific energy ranges, each with its own unique characteristics and applications:
Radio Waves
Radio waves have the lowest frequencies and longest wavelengths in the EM spectrum.
Associated with photons of relatively low energy.
Applications include communication (radio broadcasting, Wi-Fi, and cell phones), radar, and radio astronomy.
Microwaves
Microwaves have slightly higher frequencies and shorter wavelengths compared to radio waves.
Used in cooking (microwave ovens), communication (satellite communication), and radar technology.
Infrared Radiation
Lies beyond microwaves and is associated with heat.
Used in night vision technology, remote temperature sensing, and infrared photography.
Visible Light
The portion of the spectrum visible to the human eye, ranging from longer-wavelength red light to shorter-wavelength violet light.
Different colors correspond to specific ranges of frequencies and energies.
Applications include illumination, photography, and colorimetry.
Ultraviolet (UV) Radiation
Beyond visible light, with higher frequencies and shorter wavelengths.
Used in sterilization, fluorescence analysis, and tanning beds.
Can cause sunburn and skin damage.
X-Rays
Have higher frequencies and shorter wavelengths than UV radiation.
Used in medical imaging (X-ray radiography, CT scans) for diagnosing fractures, tumors, and other conditions.
Also utilized in airport security scanning and materials analysis.
Gamma Rays
Have the highest frequencies and shortest wavelengths in the EM spectrum, corresponding to the most energetic photons.
Used in cancer treatment (gamma knife surgery), sterilization, and probing the structure of atomic nuclei.
Can cause ionization and damage to biological tissues.
Figure 311 - Electromagnetic Spectrum
Astrophysical and Cosmological Significance
Photons play a crucial role in cosmology, the study of the origin, evolution, and eventual fate of the universe. Here are two key aspects of cosmology where photons are central:
Cosmic Microwave Background Radiation (CMBR)
The cosmic microwave background radiation is a relic of the early universe, often described as the afterglow of the Big Bang. Approximately 380,000 years after the Big Bang, the universe cooled enough for neutral atoms to form, allowing photons to travel freely through space. These photons, which were once in the form of intense radiation, have since cooled due to the expansion of the universe, stretching into the microwave region of the electromagnetic spectrum.
The CMBR provides a snapshot of the universe when it was only about 380,000 years old, offering invaluable information about its early conditions, such as temperature fluctuations and density variations. This radiation is nearly isotropic, meaning it appears almost the same in all directions.Observations of the CMBR have provided strong evidence supporting the Big Bang theory and have helped to refine our understanding of cosmological parameters, such as the universe's age, composition, and geometry.
Observational Astronomy Techniques
Observational astronomers use various techniques to detect photons from celestial objects, enabling the study of distant galaxies, stars, and other cosmic phenomena. Some key techniques include:
Optical Astronomy
Observing celestial objects in the visible light spectrum using telescopes equipped with optical instruments such as lenses and mirrors. This technique allows astronomers to study the colors, spectra, and positions of stars, galaxies, and other objects.
Radio Astronomy
Detecting radio waves emitted by celestial sources using radio telescopes. Radio astronomy enables astronomers to study phenomena such as pulsars, quasars, and the cosmic microwave background radiation.
Infrared Astronomy
Observing objects in the infrared portion of the electromagnetic spectrum, which is sensitive to heat emitted by celestial bodies. Infrared telescopes can penetrate dust clouds that may obscure visible light observations, allowing astronomers to study star formation regions, protoplanetary disks, and distant galaxies.
X-ray and Gamma-ray Astronomy
Observing high-energy photons emitted by sources such as black holes, neutron stars, and supernova remnants. X-ray and gamma-ray telescopes detect these photons to study extreme environments and energetic processes in the universe, providing insights into phenomena such as accretion disks, gamma-ray bursts, and active galactic nuclei.
Multi-wavelength Astronomy
Combining observations from different parts of the electromagnetic spectrum to gain a comprehensive understanding of celestial objects and phenomena. By studying an object's emission across multiple wavelengths, astronomers can uncover its physical properties, composition, and evolutionary stage.
Actual Research Projects
Large Hadron Collider (LHC) - ATLAS and CMS Experiments
The LHC, located at CERN in Switzerland, is the world's largest and most powerful particle accelerator.
The ATLAS and CMS experiments at the LHC study the fundamental particles and forces of the universe, including the interactions involving photons.
These experiments have contributed significantly to our understanding of the properties of photons and their role in particle physics.
Quantum Communication and Quantum Key Distribution (QKD) Projects
Various research groups and companies worldwide are actively working on quantum communication technologies based on photons.
Projects include the development and deployment of quantum key distribution (QKD) systems for secure communication.
Examples include the Quantum Internet Alliance in Europe, the Quantum Communication Infrastructure (QCI) project in China, and research initiatives at institutions such as MIT and the University of Geneva.
Advanced LIGO, Virgo and Einstein Telescope Gravitational-Wave Detectors
The Laser Interferometer Gravitational-Wave Observatory (LIGO) in the United States and the Virgo interferometer in Italy are leading facilities for detecting gravitational waves. These detectors use laser light (photons) to measure tiny ripples in spacetime caused by distant cosmic events, such as the merger of black holes or neutron stars. Advanced LIGO and Virgo collaborations continue to improve sensitivity and expand the capabilities of gravitational-wave astronomy.
The latest project in the study domain of Gravitational Waves is the Einstein Telescope. It is a proposed third-generation gravitational wave detector. Unlike the current second-generation detectors like LIGO and Virgo, the Einstein Telescope will be an underground observatory, enabling it to achieve greater sensitivity and detect a broader range of gravitational wave frequencies.
The project involves building a triangular array of tunnels, each several kilometers long, with arms arranged in an equilateral triangle. Inside these tunnels, laser interferometers will measure tiny changes in distance caused by passing gravitational waves. The Einstein Telescope promises to provide unprecedented insights into cosmic phenomena, such as black hole mergers, neutron star collisions, and the early universe. It could revolutionize our understanding of gravity and the universe's evolution.
Photonic Integrated Circuits and Quantum Photonics Research
Numerous research groups focus on developing photonic integrated circuits (PICs) and quantum photonics platforms for quantum information processing and communication.
Projects aim to create scalable and efficient photonic devices for quantum computing, quantum cryptography, and quantum metrology.
Examples include research at the Centre for Quantum Photonics at the University of Bristol, the Quantum Photonics Laboratory at the University of Tokyo, and industrial efforts by companies like IBM and Google.
Large-Scale Astrophysical Surveys and Observatories
Several large-scale observational projects are dedicated to studying the universe across different wavelengths of the electromagnetic spectrum, including photon-based observations.
Projects such as the Hubble Space Telescope, the James Webb Space Telescope (JWST), the Chandra X-ray Observatory, and ground-based observatories like the Very Large Telescope (VLT) in Chile investigate a wide range of astrophysical phenomena involving photons.
Figure 312 - Artist's impression of the Einstein Telescope (c)NIKHEF [3]
Literature
References
[1] LibreText Chemistry. Quantization of Energy. Howard University
[2] Y. Tsuchiya, E. Inuzuka, T. Kurono, M. Hosoda, Photon-Counting Imaging and its Application, Advances in Electronics and Electron Physics, Vol. 64A, pp. 21-31, 1986
[3] Max Planck Institute for Gravitational Physics – Einstein Telescope. Marco Kraan