The Purcell effect is the enhancement of a quantum system's spontaneous emission rate by its environment. In the 1940s Edward Mills Purcell discovered the enhancement of spontaneous emission rates of atoms when they are incorporated into a resonant cavity. [1] [2] In terms of quantum electrodynamics the Purcell effect is a consequence of enhancement (or decreasing) of local density of photonic states at the emitter position. It can also be considered as an interference effect. The oscillator radiates the wave which is reflected from the environment. In turn the reflection excites the oscillator either out of phase resulting in higher damping rate accompanied with the radiation enhancement or in phase with the oscillator mode leading to the radiation suppression. [3]
For an emitter tuned to the fundamental mode of a cavity and placed at its center the magnitude of the enhancement is given by the Purcell factor [4]
where is the vacuum wavelength, is the refractive index of the cavity material (so is the wavelength inside the cavity), and and are the cavity quality factor and mode volume, respectively.
One way of seeing why the Purcell effect arises is by using cavity quantum electrodynamics. [5] Fermi's golden rule dictates that the transition rate for the atom–vacuum (or atom–cavity) system is proportional to the density of final states. In a cavity at resonance, the density of final states is enhanced (though the number of final states may not be). The Purcell factor is then just the ratio of the cavity density of states
to that of the free space density of states [6]
Here, and are the resonance frequency and bandwidth, respectively. Using
one gets
which is correct up to a numerical constant for high- cavity (Hermitian) modes. For low- modes (encountered, for instance, with plasmonic nanoresonators), the Purcell factor takes a slightly different form [7] that accounts for the non-Hermitian character of such modes.
It has been predicted theoretically [8] [9] that a 'photonic' material environment can control the rate of radiative recombination of an embedded light source. A main research goal is the achievement of a material with a complete photonic bandgap: a range of frequencies in which no electromagnetic modes exist and all propagation directions are forbidden. At the frequencies of the photonic bandgap, spontaneous emission of light is completely inhibited. Fabrication of a material with a complete photonic bandgap is a huge scientific challenge. For this reason photonic materials are being extensively studied. Many different kinds of systems in which the rate of spontaneous emission is modified by the environment are reported, including cavities, two, [10] [11] and three-dimensional [12] photonic bandgap materials.
Researchers at University of Rochester reported in 2023 that significant improvements in perovskite solar cell efficiency can be achieved by utilizing Purcell effect to extend the duration of photon induced electron-hole pairs spontaneous recombination time thus enabling them to reach the cell electrodes. [13]
The Purcell effect can also be useful for modeling single-photon sources for quantum cryptography. [14] Controlling the rate of spontaneous emission and thus raising the photon generation efficiency is a key requirement for quantum dot based single-photon sources. [15]
Finally, it is important to mention that the Purcell effect can enhance not only radiative processes but also non-radiative transitions such as dipole-dipole interactions and scattering, which has been already observed experimentally, for the first time, for atoms [16] and molecules. [17]
In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV, they would merge into a single force. Thus, if the temperature is high enough – approximately 1015 K – then the electromagnetic force and weak force merge into a combined electroweak force.
A photon is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can move no faster than the speed of light measured in vacuum. The photon belongs to the class of boson particles.
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.
Spontaneous emission is the process in which a quantum mechanical system transits from an excited energy state to a lower energy state and emits a quantized amount of energy in the form of a photon. Spontaneous emission is ultimately responsible for most of the light we see all around us; it is so ubiquitous that there are many names given to what is essentially the same process. If atoms are excited by some means other than heating, the spontaneous emission is called luminescence. For example, fireflies are luminescent. And there are different forms of luminescence depending on how excited atoms are produced. If the excitation is effected by the absorption of radiation the spontaneous emission is called fluorescence. Sometimes molecules have a metastable level and continue to fluoresce long after the exciting radiation is turned off; this is called phosphorescence. Figurines that glow in the dark are phosphorescent. Lasers start via spontaneous emission, then during continuous operation work by stimulated emission.
Mode volume may refer to figures of merit used either to characterise optical and microwave cavities or optical fibers.
The quantum Hall effect is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values
In particle physics, bremsstrahlung is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation, thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.
In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces. Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning "measuring gauge" or "standard".
In condensed matter physics, the density of states (DOS) of a system describes the number of allowed modes or states per unit energy range. The density of states is defined as , where is the number of states in the system of volume whose energies lie in the range from to . It is mathematically represented as a distribution by a probability density function, and it is generally an average over the space and time domains of the various states occupied by the system. The density of states is directly related to the dispersion relations of the properties of the system. High DOS at a specific energy level means that many states are available for occupation.
In chemistry and physics, Raman scattering or the Raman effect is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a molecule as incident photons from a visible laser are shifted to lower energy. This is called normal Stokes-Raman scattering.
Resolved sideband cooling is a laser cooling technique allowing cooling of tightly bound atoms and ions beyond the Doppler cooling limit, potentially to their motional ground state. Aside from the curiosity of having a particle at zero point energy, such preparation of a particle in a definite state with high probability (initialization) is an essential part of state manipulation experiments in quantum optics and quantum computing.
In physics, the radiative efficiency limit is the maximum theoretical efficiency of a solar cell using a single p–n junction to collect power from the cell where the only loss mechanism is radiative recombination in the solar cell. It was first calculated by William Shockley and Hans-Joachim Queisser at Shockley Semiconductor in 1961, giving a maximum efficiency of 30% at 1.1 eV. The limit is one of the most fundamental to solar energy production with photovoltaic cells, and is one of the field's most important contributions.
A composite fermion is the topological bound state of an electron and an even number of quantized vortices, sometimes visually pictured as the bound state of an electron and, attached, an even number of magnetic flux quanta. Composite fermions were originally envisioned in the context of the fractional quantum Hall effect, but subsequently took on a life of their own, exhibiting many other consequences and phenomena.
Bumblebee models are effective field theories describing a vector field with a vacuum expectation value that spontaneously breaks Lorentz symmetry. A bumblebee model is the simplest case of a theory with spontaneous Lorentz symmetry breaking.
Laser linewidth is the spectral linewidth of a laser beam.
The semiconductor luminescence equations (SLEs) describe luminescence of semiconductors resulting from spontaneous recombination of electronic excitations, producing a flux of spontaneously emitted light. This description established the first step toward semiconductor quantum optics because the SLEs simultaneously includes the quantized light–matter interaction and the Coulomb-interaction coupling among electronic excitations within a semiconductor. The SLEs are one of the most accurate methods to describe light emission in semiconductors and they are suited for a systematic modeling of semiconductor emission ranging from excitonic luminescence to lasers.
The Elliott formula describes analytically, or with few adjustable parameters such as the dephasing constant, the light absorption or emission spectra of solids. It was originally derived by Roger James Elliott to describe linear absorption based on properties of a single electron–hole pair. The analysis can be extended to a many-body investigation with full predictive powers when all parameters are computed microscopically using, e.g., the semiconductor Bloch equations or the semiconductor luminescence equations.
A nanophotonic resonator or nanocavity is an optical cavity which is on the order of tens to hundreds of nanometers in size. Optical cavities are a major component of all lasers, they are responsible for providing amplification of a light source via positive feedback, a process known as amplified spontaneous emission or ASE. Nanophotonic resonators offer inherently higher light energy confinement than ordinary cavities, which means stronger light-material interactions, and therefore lower lasing threshold provided the quality factor of the resonator is high. Nanophotonic resonators can be made with photonic crystals, silicon, diamond, or metals such as gold.
A quantum dot single-photon source is based on a single quantum dot placed in an optical cavity. It is an on-demand single-photon source. A laser pulse can excite a pair of carriers known as an exciton in the quantum dot. The decay of a single exciton due to spontaneous emission leads to the emission of a single photon. Due to interactions between excitons, the emission when the quantum dot contains a single exciton is energetically distinct from that when the quantum dot contains more than one exciton. Therefore, a single exciton can be deterministically created by a laser pulse and the quantum dot becomes a nonclassical light source that emits photons one by one and thus shows photon antibunching. The emission of single photons can be proven by measuring the second order intensity correlation function. The spontaneous emission rate of the emitted photons can be enhanced by integrating the quantum dot in an optical cavity. Additionally, the cavity leads to emission in a well-defined optical mode increasing the efficiency of the photon source.
In quantum optics, fhe Tavis–Cummings model is a theoretical model to describe an ensemble of identical two-level atoms coupled symmetrically to a single-mode quantized bosonic field. The model extends the Jaynes–Cummings model to larger spin numbers that represent collections of multiple atoms. It differs from the Dicke model in its use of the rotating-wave approximation to conserve the number of excitations of the system.