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Single Photon


Single Photon

Contents

History
Control
Applications
Classical Theory
Standard Model

History

Photo-Electric Effect
  • It started in 1900 when Max Planck postulated that the energy in a black body is quantized (as discrete particles now called photons) depending on the frequency , and is given by the formula E = h, where h = 6.625x10-27 erg-sec is known as the Planck's constant. This idea was verified by Einstein in 1905 with the Photo-Electric Effect (see Figute 01). Planck then went on to derive a correct formal for "Black Body Radiation" based on the quantized photons.
  • Figure 01 Photo-Electric Effect [view large image]


  • Detection of photons is facilitated by the development of "quantum optics" which deals with the interaction between photons, and atoms / molecules. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing.
  • Nanowires
  • The development of sensitive "single photon detectors" capable of measuring single photons was essential. Early devices, such as photomultiplier tubes, allowed for the detection of individual photons and paved the way for more sophisticated experiments.

  • Single photon source is unavailable before 1974. The latest advance is the nanowires (see "On-chip indistinguishable photons using III-V nanowire/SiN hybrid integration" and Figure 02). III-V materials = (old)group III (new 13) and V (new 15) elements of the periodic table) are essential in modern electronics and photonics due to their superior electronic and optical properties. SiN is a waveguide.

  • The invention of the laser and developments in non-linear optics enabled the generation of single photons and entangled photon pairs with high precision and control. Techniques like spontaneous parametric down-conversion (SPDC) became standard for producing entangled photons.

  • Advances in materials science and nanotechnology have led to the development of reliable single photon sources, such as quantum dots and defect centers in diamonds, which can emit single photons on demand. Single photon physics is integral to quantum computing and quantum information science. Photons are used as qubits in optical quantum computers and for transmitting information in quantum networks.
  • Figure 02 Nanowires News
    [view large image]


  • Latest news on nanowires technology in 2024 (from "On-chip ...") illustrated pictorially below :

    within a waveguide
  • We demonstrate on-chip generation of indistinguishable photons based on a nanowire Quantum Dot (QD). From a growth substrate containing arrays of positioned-controlled single-dot nanowires, we select a single nanowire which is placed on a SiN waveguide fabricated on a Si-based chip. Coupling of the quantum dot emission to the SiN waveguide is via the evanescent mode in the tapered nanowire. Post- selected 2-photon interference visibilities using continuous-wave excitation above band and into a p shell of the dot were 100% consistent with a single-photon source having negligible multiphoton emission probability. Visibilities over the entire photon wave packet, measured using pulsed excitation, were reduced by a factor of 5 when exciting quasiresonantly and by a factor of 10 for above-band excitation.
    Nanowires The role of excitation timing jitter, spectral diffusion, and pure dephasing in limiting visibilities over the temporal extent of the photon is investigated using additional measurements of the coherence and line-width of the emitted photons (see Figure 03).

    Figure 03 Single Photon Generation [view large image]

    Within a year or so acquainting, it is found that the vanilla version of "ChatGPT" and the microsoft versiion of "Copilot" are incomparable advisers in science. It can be accessed anytime, have lot of information on all subjects in science and free. In very simple term, it consists of a database containing lot of information + a language model for input / output operation. The input has to be sensible (garbage-in, garboge-out) and the user should acknowledge the source of information (no cheating).
    BTW, it makes mistake sometimes like associating wave function to photon, better double check.

  • Courtesy of Copilot (in Italic) :
    Superconducting Nanowire Single-Photon Detectors (SNSPDs) offer several advantages, making them highly effective for various applications in quantum technology and photonics. Here are some of the key benefits:

    " High Detection Efficiency: SNSPDs can achieve near-unity detection efficiency, meaning they are capable of detecting almost every photon that reaches them.

    Nanowires " Low Dark Count Rate: They have a low rate of false signals (dark counts), which is crucial for applications requiring high signal-to-noise ratios.
    " Fast Timing Resolution: With the ability to resolve the timing of photon detection down to picoseconds, SNSPDs are suitable for high-speed applications.
    " Short Recovery Times: They can quickly recover between detection events, allowing for high counting rates, which is beneficial for communication and computing applications.
    " Broad Spectral Range: SNSPDs can detect photons across a wide range of wavelengths, from infrared to visible light.

    Figure 04 Nanowires Detector [view large image]

    " Low Timing Jitter: The precision in timing measurements is high, which is important for accurate time-correlated photon counting.

    These characteristics make SNSPDs ideal for use in quantum computing, secure communication, and precise timing applications, among others. See Figure 04.
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    Control

    Controlling a single photon, despite it having no charge and always moving at the speed of light, is a sophisticated process that involves quantum mechanics and photonics technology. Figure 05 shows an example of the steps to route single photons through a circuit (see "On-Chip Quantum Nanophotonic Circuits") :

  • Pulsed Laser to trigger the photon emission,
  • Enhancing the single photon emission rate.
  • Enhancing single photon emission directionality to a specific direction.
  • Single Photon Circuit
  • On-chip propagation of the emitted photons.
  • On-chip splitting of a photon into different branches.
  • On-chip recombining of two photons from different SPSs- resulting in photon interference.
  • Figure 05 Single Photon Circuit [view large image]

    Here are the general methods used to control single photons by courtesy of Copilot (in Italic) :

    1. Photon Sources: Single-photon sources emit light as individual particles or photons. These sources can be engineered to control when and how photons are emitted.
    2. Optical Cavities: By placing an atom in a specially designed optical cavity, the emission of photons can be controlled, directing them into a single optical mode with high efficiency.
    3. Quantum Dots: These semiconductor particles can confine electrons and holes, allowing for the emission of single photons when energy levels change.
    4. Photon Routing: Single-photon routers can control the path of a photon through quantum networks. This is achieved by manipulating the quantum state of the photon or the medium through which it travels.
    5. Waveguides: Photons can be directed along specific paths using waveguides, which are structures that guide waves, such as light, to travel in a particular direction.
    6. Electro-Optic Modulators: These devices can alter the speed of photons passing through them by changing the refractive index of the material with an electric field, effectively controlling the timing of photon arrival.

    These methods allow for precise control over single photons, which is essential for applications in quantum computing, quantum communication, and other advanced technologies.

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    Applications

      Application of single photon can be categorized into 2 eras :
    1. In the 20 century to theoretical physics
    2. In the 21 century to quantum technology
    1. Theoretical physics :


    2. Quantum technology :

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    Classical Theory

    Electromagnetic wave is a classical entity derived from the Maxwell equations. Photons are better described within the framework of Standard Model where they are understood as excitations of the electromagnetic field.

    Maxwell Equations Electromagnetic Wave (Classical Concept) :

    An electromagnetic wave is described classically by Maxwell's equations. These equations govern the behavior of electric and magnetic fields in space and time. When solving Maxwell's equations for free space (no charges or currents), you obtain wave-like solutions that represent the propagation of electric and magnetic field disturbances - these are the classical electromagnetic waves.

    Figure 08 Maxwell Equations [view large image]

    EM Wave The EM wave and formulas are shown in Figure 09 (u = E or B), where T = period, and = wave-length.
    Polarization refers to the orientation of the oscillations of the electric or magnetic field vector.
    Phase refers to the relative position (usually the origin) of the wave at a given point in time and space.

    Figure 09 EM Wave
    [view large image]

    Even though polarization is a classical concepts, it plays a crucial roles in the context of single photons and quantum information.

    By courtesy of ChatGPT (in Italic) :

    Polarization :
    In quantum mechanics, polarization describes the quantum state of a photon regarding its spin angular momentum. A single photon can be in a superposition of polarization states, and its polarization state can be manipulated and measured to perform quantum operations. The key quantum features of polarization include:
    " Quantum Superposition: A photon can exist in a superposition of multiple polarization states, such as being both horizontally and vertically polarized simultaneously.
    " Entanglement: Polarization states of different photons can become entangled, meaning the polarization state of one photon is directly related to the polarization state of another, regardless of the distance between them.

    It is also used to encode and manipulate quantum information in single photons, leveraging their quantum properties:
    1. Quantum Bits (Qubits): In quantum computing, a photon's polarization state can represent a qubit. For instance, horizontal polarization might represent a logical "0" and vertical polarization a logical "1". Superpositions of these states form the basis of quantum computation.
    2. Quantum Key Distribution (QKD): In protocols like BB84, the polarization states of single photons are used to encode and transmit cryptographic keys securely. The phase can also be used in protocols like differential phase shift QKD.
    3. Quantum Gates: Operations on qubits can be implemented by manipulating the polarization and phase of photons. Quantum gates like the Hadamard gate, which creates superposition states, and the controlled-NOT (CNOT) gate, which entangles qubits, can be realized using linear optical elements and phase shifters.
    4. Quantum Entanglement: Polarization and phase are integral to creating and measuring entangled photon states. Entanglement is a resource for quantum teleportation, superdense coding, and many quantum computing algorithms.

    Summary
    Polarization is a classical concepts with deep implications in quantum mechanics. In quantum physics, it describes the quantum states of photons, facilitate quantum information processing, and enable technologies like quantum computing, quantum cryptography, and quantum communication. These properties allow us to harness the peculiarities of quantum mechanics to perform tasks that are impossible with classical systems alone.

    Polarization is not the only classical concepts that play important roles in the physics of single photons. Here are some additional classical concepts and their implications in the quantum realm:
    1. Amplitude
    In classical wave theory, the amplitude of an electromagnetic wave is the magnitude of its electric field vector. It is related to the intensity or brightness of the light wave.
    In quantum mechanics,
    amplitude is meaningless for photon. Instead, it should be described using quantum field theory where fields and their quantization take the central role.
    2. Frequency and Wavelength
    Classical Concept - Frequency (or wavelength) is a fundamental property of waves, describing the number of oscillations per unit time (or the distance between successive peaks of the wave). In classical optics, it determines the color of light.
    Quantum Concept - For photons, frequency (or wavelength) is directly related to the photon's energy via Planck's relation E = h (where E is energy, h is Planck's constant, and is frequency). The energy levels of photons can be used in various quantum processes, such as in quantum dots, atomic transitions, and in distinguishing different quantum states.
    3. Wave Vector (Momentum)
    Classical Concept - The wave vector
    k (see Figure 09) describes the direction of propagation of a wave and its spatial frequency.
    Quantum Concept - In quantum mechanics, the wave vector of a photon is directly related to its momentum
    p = h/ according to the De Broglie relation. This relationship is used in various quantum phenomena, including diffraction, interference, and the momentum transfer in interactions with atoms and molecules.
    4. Coherence
    Classical Concept - Coherence refers to the fixed phase relationship between the electric field vectors at different points in space and time. It is a measure of the predictability of the phase of the wave over time and is crucial in phenomena such as interference and diffraction.
    Quantum Concept - In quantum optics, coherence relates to the quantum state of light. Single-photon sources often strive to produce photons that are coherent, which is essential for many quantum information processes. The coherence properties of single photons are critical in applications like quantum cryptography and quantum computing.
    5. Interference and Diffraction
    Classical Concept - Interference occurs when two or more waves superimpose, leading to a pattern of constructive and destructive interference. Diffraction involves the bending and spreading of waves around obstacles and through slits.
    Quantum Concept - For single photons, interference and diffraction are explained by the superposition principle in quantum mechanics. Experiments like the double-slit experiment demonstrate that even single photons exhibit interference patterns, highlighting the wave-particle duality of light. These principles are exploited in various quantum technologies, such as quantum interference devices and quantum lithography.
    6. Refraction and Dispersion Classical Concept - Refraction is the bending of light as it passes from one medium to another, and dispersion is the spreading of light into its component wavelengths due to different refractive indices for different wavelengths.
    Quantum Concept - In the quantum realm, refraction and dispersion still apply, but they are interpreted through the interaction of photons with the atomic structure of the medium. These effects are essential in designing optical components for quantum devices, such as waveguides and photonic crystals that manipulate single photons for quantum communication and computing.
    7. Energy Levels and Transitions
    Classical Concept - Classically, energy levels and transitions in atoms and molecules are described by electronic states and the absorption/emission of light at specific wavelengths.
    Quantum Concept - In quantum mechanics, photons are emitted or absorbed during transitions between discrete energy levels of atoms and molecules. This quantization is fundamental to processes like spontaneous emission, stimulated emission (which is the basis for lasers), and absorption spectroscopy. Quantum optics uses these principles to control and measure quantum states of light and matter.

    Summary
    These classical concepts, when applied to single photons in the quantum domain, provide a framework for understanding and manipulating the fundamental properties of light at the quantum level. They enable the development of advanced quantum technologies and deepen our understanding of the wave-particle duality of light. The interplay between classical and quantum descriptions enriches both fields and drives innovation in photonics and quantum information science.


    Here's a comment about the Schrödinger Equation :

    Wave Function It is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. However, it is non-relativistic and primarily applies to particles with mass. The situation with photons, which are massless particles that always travel at the speed of light, is quite different.
    Hence, the wave function should not be associated to photons.
    Relativistic means the formulation is invariant under the Lorentz transformation of space-time.

    Figure 10 Wave Function
    [view large image]

    Figure 10 shows the Schrödinger Equation where , V the potential acting on the particle, and m is the mass. The wave function could be bound (Figure 10,a) or free (for V = 0).
    Photons are better described within the framework of quantum field theory, where they are understood as excitations of the electromagnetic field. Such approach aligns with the principles of relativity and accurately describes the behavior of light and other electromagnetic radiation. See Standard Model.

    SPDC There is more confusion with the entanglement of 2 photons in Spontaneous parametric down-conversion (SPDC, see Figure 11). After pondering the problem for a whole day, here's the discussion with ChatGPT (which did not offer a satisfactory explanation) :

    I think the confusion about the massless photon in entanglement is due to the different facets it manifests in different circumstances. For example, it is an electromagnetic wave in diffraction; it is a massless boson in the calculation of cross-section for many QED processes, and then in entanglement like SPDC it is the byproduct of a composite system like the pump photon. What do you think?

    Figure 11 SPDC
    [view large image]

    ChatGPT :

    You're touching on some interesting and nuanced aspects of how photons are understood in different contexts in physics. Indeed, the concept of the photon can appear different depending on the framework and the phenomenon being considered. Let's break down these facets:

    Electromagnetic Wave: In classical electromagnetism, light is described as an electromagnetic wave. This wave picture explains phenomena such as interference and diffraction. The wave properties of light are described by Maxwell's equations, which treat light as continuous waves of electric and magnetic fields oscillating in space and time.

    Massless Boson: In the realm of quantum field theory, specifically Quantum Electrodynamics (QED), the photon is treated as a massless gauge boson. It is the quantum of the electromagnetic field, mediating the electromagnetic force between charged particles. This picture is crucial for calculating cross-sections in particle interactions and understanding processes like electron-photon scattering (Compton scattering) or the creation of electron-positron pairs.

    Entanglement and SPDC (Spontaneous Parametric Down-Conversion): In quantum optics, especially in experiments involving entanglement, photons are often described in terms of their quantum states. SPDC is a process where a single photon (the pump photon) interacts with a nonlinear crystal to produce a pair of entangled photons (signal and idler photons). Here, the focus is on the quantum correlations between the produced photons, and the description relies heavily on quantum mechanics and the wavefunction
    (?) of the system.

    The confusion can arise because these descriptions, while fundamentally connected, emphasize different properties of the photon:

    Wave-particle duality: Photons exhibit both wave-like and particle-like properties. The wave description is often more intuitive for explaining diffraction and interference, while the particle description is essential for explaining phenomena like the photoelectric effect or photon-photon interactions.

    Context-dependent properties: In different experimental setups or theoretical frameworks, different properties of photons are more relevant. In diffraction, wave properties dominate; in particle physics, the role of photons as force carriers is central; and in quantum optics, the focus is on their quantum state and entanglement properties.

    Composite systems and entanglement: In entanglement scenarios, especially those involving SPDC, photons are part of a larger quantum system. The entangled state is a property of the composite system rather than the individual photons, emphasizing the non-local and holistic nature of quantum mechanics.

    In summary, the different manifestations of photons—electromagnetic waves, massless bosons, and entangled quantum states—are all correct but context-dependent descriptions. They reflect the multifaceted nature of photons as understood through classical, quantum mechanical, and quantum field theoretical lenses. This multi-perspective understanding is what makes photons such a rich and fascinating subject in physics.


    In addition, atoms and molecules emit or absorb photon as they move down or up the energy levels (see Figure 10,a for example)

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    Standard Model

    The Standard Model of particle physics is the theory describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying all known elementary particles.

    By courtesy of ChatGPT (in Italic) :

    The physics of a single photon is a part of the Standard Model of elementary particles :
    " Photon: The photon is described as a gauge boson, specifically the force carrier of the electromagnetic interaction. It is massless and mediates the electromagnetic force between charged particles. This description comes from Quantum Electrodynamics (QED), which is the quantum field theory of the electromagnetic force.

    Gauge Theory and Quantum Electrodynamics (QED)
    " Gauge Theory: The electromagnetic force is described by a U(1) gauge theory. The photon is the gauge boson associated with this U(1) symmetry. This theoretical framework successfully explains the interactions of photons with charged particles through the exchange of virtual photons.
    " QED: Quantum Electrodynamics provides the detailed mathematical formulation of how photons interact with charged particles. It incorporates principles of quantum mechanics and special relativity to describe these interactions.

    Single Photon Physics :
    When we talk about the physics of a single photon in various contexts, we are often considering:
    " Quantum Optics: This field studies the quantum mechanical properties of light and its interaction with matter. It includes the behavior of single photons in experiments, such as interference, entanglement, and quantum state manipulation.
    " Quantum Information Science: Single photons are used as qubits or information carriers in quantum communication and quantum computing. Relationship Between Classical and Quantum Descriptions
    " Classical Electromagnetic Waves: Described by Maxwell's equations, which are derived from the classical theory of electromagnetism.
    " Single Photon Quantum States: Described by quantum mechanics and specifically by QED within the Standard Model. This includes phenomena like superposition and entanglement, which are purely quantum mechanical and have no classical counterpart.

    Summary
    " Standard Model: Single photon is a fundamental particle within the Standard Model, described as a massless gauge boson of the electromagnetic force.
    " Gauge Theory (QED): Provides the quantum field theoretical framework that explains how photons interact with charged particles.
    " Single Photon Physics: Studied within quantum optics and quantum information science, utilizing the principles of quantum mechanics to explore and exploit the unique properties of photons.
    So, the physics of a single photon is part of the Standard Model of elementary particles, which describes it as an entity within Gauge Theory, specifically through Quantum Electrodynamics (QED).

    In general :
    Quantum Electrodynamics (QED) is a part of the Standard Model of particle physics :
    It is the quantum field theory that describes how light (photons) and matter (specifically electrons and positrons) interact. It is one of the most precise and successful theories in physics, providing extremely accurate predictions for phenomena such as the electron's magnetic moment and the Lamb shift in hydrogen.
    Its role in the Standard Model -
    " Gauge Theory: QED is a gauge theory based on the U(1) symmetry group. This means it describes the interactions of charged particles through the exchange of photons, the gauge bosons of the electromagnetic force.
    " Interactions: In QED, interactions between charged particles are mediated by virtual photons, which can be represented in Feynman diagrams. These diagrams provide a visual and mathematical representation of the interactions.

    The Standard Model :
    It is the comprehensive theory that describes the fundamental particles and their interactions, except for gravity. It includes:
    " Electromagnetic Force: Described by QED, with photons as the gauge bosons.
    " Weak Force: Described by the Glashow-Weinberg-Salam theory, with W and Z bosons as the gauge bosons.
    " Strong Force: Described by Quantum Chromodynamics (QCD), with gluons as the gauge bosons.

    Components of the Standard Model :
    1. Electromagnetic Interaction (QED):
    " Gauge boson: Photon ()
    " Governs interactions between charged particles like electrons and positrons.

    Standard Model 2. Weak Interaction:
    " Gauge bosons: W and Z bosons
    " Responsible for processes like beta decay in nuclei.
    3. Strong Interaction (QCD):
    " Gauge bosons: Gluons
    " Governs interactions between quarks and gluons within protons, neutrons, and other hadrons.
    4. Matter Particles:
    " Fermions: Quarks and leptons, organized into three generations.

    Figure 12 Standard Model
    [view large image]

    The photon is in the U(1) Unitary Group (see Figure 12).


    Summary
    QED is a crucial component of the Standard Model, specifically dealing with the electromagnetic force. It is integrated within the Standard Model framework, which also includes the weak and strong nuclear forces. Thus, the detailed interactions and behaviors of single photons, as described by QED, are fundamental to the overall understanding of particle physics within the Standard Model.