Superluminal communication

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https://en.wikipedia.org/wiki/Superluminal_communication

Superluminal communication is a hypothetical process in which information is conveyed at faster-than-light speeds. The current scientific consensus is that faster-than-light communication is not possible, and to date it has not been achieved in any experiment.

Superluminal communication other than possibly through wormholes is likely impossible because, in a Lorentz-invariant theory, it could be used to transmit information into the past. This would complicate causality, but no theoretical arguments conclusively preclude this possibility.

A number of theories and phenomena related to superluminal communication have been proposed or studied, including tachyons, neutrinos, quantum nonlocality, wormholes, and quantum tunneling.

Proposed mechanisms

Spacetime diagram showing that moving faster than light implies time travel in the context of special relativity. A spaceship departs from Earth from A to C slower than light. At B, Earth emits a tachyon, particle that travels faster than light but forward in time in Earth's reference frame. It reaches the spaceship at C. The spaceship then sends another tachyon back to Earth from C to D. This tachyon also travels forward in time in the spaceship's reference frame. This effectively allows Earth to send a signal from B to D, back in time.

Tachyons

Tachyonic particles are hypothetical particles that travel faster than light, which could conceivably allow for superluminal communication. Because such a particle would violate the known laws of physics, many scientists reject the idea that they exist. By contrast, tachyonic fields – quantum fields with imaginary mass – do exist and exhibit superluminal group velocity under some circumstances. However, such fields have luminal signal velocity and do not allow superluminal communication.

Quantum nonlocality

Quantum mechanics is non-local in the sense that distant systems can be entangled. Entangled states lead to correlations in the results of otherwise random measurements, even when the measurements are made nearly simultaneously and at far distant points. The impossibility of superluminal communication led Einstein, Podolsky, and Rosen to propose that quantum mechanics must be incomplete (see EPR paradox).

However, it is now well understood that quantum entanglement does not allow any influence or information to propagate superluminally.

Practically, any attempt to force one member of an entangled pair of particles into a particular quantum state, breaks the entanglement between the two particles. That is to say, the other member of the entangled pair is completely unaffected by this "forcing" action, and its quantum state remains random; a preferred outcome cannot be encoded into a quantum measurement.

Technically, the microscopic causality postulate of axiomatic quantum field theory implies the impossibility of superluminal communication using any phenomena whose behavior can be described by orthodox quantum field theory. A special case of this is the no-communication theorem, which prevents communication using the quantum entanglement of a composite system shared between two spacelike-separated observers.

Wormholes

If wormholes are possible, then ordinary subluminal methods of communication could be sent through them to achieve effectively superluminal transmission speeds across non-local regions of spacetime. Considering the immense energy or exotic matter with negative mass/negative energy that current theories suggest would be required to open a wormhole large enough to pass spacecraft through, it may be that only atomic-scale wormholes would be practical to build, limiting their use solely to information transmission. Some hypotheses of wormhole formation would prevent them from ever becoming "timeholes", allowing superluminal communication without the additional complication of allowing communication with the past.

Fictional devices

Tachyon-like

The Dirac communicator features in several of the works of James Blish, notably his 1954 short story "Beep" (later expanded into The Quincunx of Time). As alluded to in the title, any active device received the sum of all transmitted messages in universal space-time, in a single pulse, so that demultiplexing yielded information about the past, present, and future.

Superluminal transmitters and ansibles

The terms "ultrawave" and "hyperwave" have been used by several authors, often interchangeably, to denote faster-than-light communications. Examples include:

• E. E. Smith used the term "ultrawave" in his Lensman series, for waves which propagated through a sub-ether and could be used for weapons, communications, and other applications.
• In Isaac Asimov's Foundation series, "ultrawave" and "hyperwave" are used interchangeably to represent a superluminal communications medium. The hyperwave relay also features.
• In the Star Trek universe, subspace carries faster-than-light communication (subspace radio) and travel (warp drive).
• The Cities in Flight series by James Blish featured ultrawave communications which used the known phenomenon of phase velocity to carry information, a property which in fact is impossible. The limitations of phase velocity beyond the speed of light later led him to develop his Dirac communicator.
• Larry Niven used hyperwave in his Known Space series as the term for a faster-than-light method of communication. Unlike the hyperdrive that moved ships at a finite superluminal speed, hyperwave was essentially instantaneous.
• In Richard K. Morgan's Takeshi Kovacs novels human colonies on distant planets maintain contact with earth and each other via hyperspatial needlecast, a technology which moves information "...so close to instantaneously that scientists are still arguing about the terminology".

A later device was the ansible coined by Ursula K. Le Guin and used extensively in her Hainish Cycle. Like Blish's device it provided instantaneous communication, but without the inconvenient beep.

The ansible is also a major plot element, nearly a MacGuffin, in Elizabeth Moon's Vatta's War series. Much of the story line revolves around various parties attacking or repairing ansibles, and around the internal politics of ISC (InterStellar Communications), a corporation which holds a monopoly on the ansible technology.

The ansible is also used as the main form of communication in Orson Scott Card's Ender's Game series. It is inhabited by an energy based, non-artificial sentient creature called an Aiúa that was placed within the ansible network and goes by the name of Jane. It was made when the humans realized that the Buggers, an alien species that attacked Earth, could communicate instantaneously and so the humans tried to do the same.

Quantum entanglement

• In Ernest Cline's novel Armada, alien invaders possess technology for instant "quantum communication" with unlimited range. Humans reverse engineer the device from captured alien technology.
• In the Mass Effect series of video games, instantaneous communication is possible using quantum-entanglement communicators placed in the communications rooms of starships.
• In the Avatar continuity, faster-than-light communication via a subtle control over the state of entangled particles is possible, but for practical purposes extremely slow and expensive: at a transmission rate of three bits of information per hour and a cost of $7,500 per bit, it is used for only the highest priority messages.
• Charles Stross's books Singularity Sky and Iron Sunrise make use of "causal channels" which use entangled particles for instantaneous two-way communication. The technique has drawbacks in that the entangled particles are expendable and the use of faster-than-light travel destroys the entanglement, so that one end of the channel must be transported below light speed. This makes them expensive and limits their usefulness somewhat.
• In Liu Cixin's novel The Three-Body Problem, the alien Trisolarans, while preparing to invade the Solar System, use a device with Ansible characteristics to communicate with their collaborators on Earth in real time. Additionally, they use spying/sabotaging devices called 'Sophons' on Earth which by penetration can access any kind of electronically saved and visual information, interact with electronics, and communicate results back to Trisolaris in real-time via quantum entanglement. The technology used is "single protons that have been unfolded from eleven space dimensions to two dimensions, programmed, and then refolded" and thus Sophons remain undetectable for humans.

Psychic links

Psychic links, belonging to pseudoscience, have been described as explainable by physical principles or unexplained, but they are claimed to operate instantaneously over large distances.

In the Stargate television series, characters are able to communicate instantaneously over long distances by transferring their consciousness into another person or being anywhere in the universe using "Ancient communication stones". It is not known how these stones operate, but the technology explained in the show usually revolves around wormholes for instant teleportation, faster-than-light, space-warping travel, and sometimes around quantum multiverses.

In Robert A. Heinlein's Time for the Stars, twin telepathy was used to maintain communication with a distant spaceship.

Peter F. Hamilton's Void Trilogy features psychic links between the multiple bodies simultaneously occupied by some characters.

In Brandon Sanderson's Skyward series, characters are able to use "Cytonics" to communicate instantaneously over any distance by sending messages via an inter-dimensional reality called "nowhere".

Other devices

Similar devices are present in the works of numerous others, such as Frank Herbert and Philip Pullman, who called his a lodestone resonator.

Anne McCaffrey's Crystal Singer series posited an instantaneous communication device powered by rare "Black Crystal" from the planet Ballybran. Black Crystals cut from the same mineral deposit could be "tuned" to sympathetically vibrate with each other instantly, even when separated by interstellar distances, allowing instantaneous telephone-like voice and data communication. Similarly, in Gregory Keyes' series The Age of Unreason, "aetherschreibers" use two-halves of a single "chime" to communicate, aided by scientific alchemy. While the speed of communication is important, so is the fact that the messages cannot be overheard except by listeners with a piece of the same original crystal.

Stephen R. Donaldson, in his Gap cycle, proposed a similar system, Symbiotic Crystalline Resonance Transmission, clearly ansible-type technology but very difficult to produce and limited to text messages.

In "With Folded Hands" (1947) and The Humanoids (1949), by Jack Williamson, instant communication and power transfer through interstellar space is possible with rhodomagnetic energy.

In Ivan Yefremov's 1957 novel Andromeda Nebula, a device for instant transfer of information and matter is made real by using "bipolar mathematics" to explore use of anti-gravitational shadow vectors through a zero field and the antispace, which enables them to make contact with the planet of Epsilon Tucanae.

In Edmond Hamilton's The Star Kings (1949), the discovery of an unknown form of electromagnetic radiation called sub-spectrum rays moves faster than light. The fastest of these are those of the Minus-42nd Octave, which allows for real time telestereo communication with anyone within the galaxy.

In Cordwainer Smith's Instrumentality novels and stories, interplanetary and interstellar communication is normally relayed from planet to planet, presumably at superluminal speed for each stage (at least between solar systems) but with a cumulative delay. For urgent communication there is the "instant message", which is effectively instantaneous but very expensive.

In Howard Taylor's web comic series Schlock Mercenary, superluminal communication is performed via the hypernet, a galaxy-spanning analogue to the Internet. Through the hypernet, communications and data are routed through nanoscopic wormholes, using conventional electromagnetic signals.

Superluminal motion

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Superluminal_motion

Superluminal motion

In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, BL Lac objects, quasars, blazars and recently also in some galactic sources called microquasars. Bursts of energy moving out along the relativistic jets emitted from these objects can have a proper motion that appears greater than the speed of light. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities. Light echoes can also produce apparent superluminal motion.

Explanation

Superluminal motion occurs as a special case of a more general phenomenon arising from the difference between the apparent speed of distant objects moving across the sky and their actual speed as measured at the source.

In tracking the movement of such objects across the sky, a naive calculation of their speed can be derived by a simple distance divided by time calculation. If the distance of the object from the Earth is known, the angular speed of the object can be measured, and the speed can be naively calculated via:

apparent speed = distance to object × angular speed.

This calculation does not yield the actual speed of the object, as it fails to account for the fact that the speed of light is finite. When measuring the movement of distant objects across the sky, there is a large time delay between what has been observed and what has occurred, due to the large distance the light from the distant object has to travel to reach us. The error in the above naive calculation comes from the fact that when an object has a component of velocity directed towards the Earth, as the object moves closer to the Earth that time delay becomes smaller. This means that the apparent speed as calculated above is greater than the actual speed. Correspondingly, if the object is moving away from the Earth, the above calculation underestimates the actual speed.

This effect in itself does not generally lead to superluminal motion being observed. But when the actual speed of the object is close to the speed of light, the apparent speed can be observed as greater than the speed of light, as a result of the above effect. As the actual speed of the object approaches the speed of light, the effect is most pronounced as the component of the velocity towards the Earth increases. This means that in most cases, 'superluminal' objects are travelling almost directly towards the Earth. However it is not strictly necessary for this to be the case, and superluminal motion can still be observed in objects with appreciable velocities not directed towards the Earth.

Superluminal motion is most often observed in two opposing jets emanating from the core of a star or black hole. In this case, one jet is moving away from and one towards the Earth. If Doppler shifts are observed in both sources, the velocity and the distance can be determined independently of other observations.

Some contrary evidence

As early as 1983, at the "superluminal workshop" held at Jodrell Bank Observatory, referring to the seven then-known superluminal jets,

Schilizzi ... presented maps of arc-second resolution [showing the large-scale outer jets] ... which ... have revealed outer double structure in all but one (3C 273) of the known superluminal sources. An embarrassment is that the average projected size [on the sky] of the outer structure is no smaller than that of the normal radio-source population.

In other words, the jets are evidently not, on average, close to the Earth's line-of-sight. (Their apparent length would appear much shorter if they were.)

In 1993, Thomson et al. suggested that the (outer) jet of the quasar 3C 273 is nearly collinear to the Earth's line-of-sight. Superluminal motion of up to ~9.6c has been observed along the (inner) jet of this quasar.

Superluminal motion of up to 6c has been observed in the inner parts of the jet of M87. To explain this in terms of the "narrow-angle" model, the jet must be no more than 19° from the Earth's line-of-sight. But evidence suggests that the jet is in fact at about 43° to the Earth's line-of-sight. The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded.

Suggestions of turbulence and/or "wide cones" in the inner parts of the jets have been put forward to try to counter such problems, and there seems to be some evidence for this.

Signal velocity

The model identifies a difference between the information carried by the wave at its signal velocity c, and the information about the wave front's apparent rate of change of position. If a light pulse is envisaged in a wave guide (glass tube) moving across an observer's field of view, the pulse can only move at c through the guide. If that pulse is also directed towards the observer, he will receive that wave information, at c. If the wave guide is moved in the same direction as the pulse, the information on its position, passed to the observer as lateral emissions from the pulse, changes. He may see the rate of change of position as apparently representing motion faster than c when calculated, like the edge of a shadow across a curved surface. This is a different signal, containing different information, to the pulse and does not break the second postulate of special relativity. c is strictly maintained in all local fields.

Derivation of the apparent velocity

A relativistic jet coming out of the center of an active galactic nucleus is moving along AB with a velocity v, and is observed from the point O. At time ${\displaystyle t_1}$ a light ray leaves the jet from point A and another ray leaves at time ${\displaystyle t_2=t_1+\delta t}$ from point B. An observer at O receives the rays at time ${\displaystyle t_1^{\mathrm{\prime }}}$ and ${\displaystyle t_2^{\mathrm{\prime }}}$ respectively. The angle ${\displaystyle \varphi }$ is small enough that the two distances marked ${\displaystyle D_L}$ can be considered equal.

${\displaystyle AB=v\delta t}$

${\displaystyle AC=v\delta t\cos \theta }$

${\displaystyle BC=v\delta t\sin \theta }$

${\displaystyle t_2-t_1=\delta t}$

${\displaystyle t_1^{\prime }=t_1+\frac{D_L+v\delta t\cos \theta }{c}}$

${\displaystyle t_2^{\prime }=t_2+\frac{D_L}{c}}$

${\displaystyle \delta t^{\prime }=t_2^{\prime }-t_1^{\prime }=t_2-t_1-\frac{v\delta t\cos \theta }{c}=\delta t-\frac{v\delta t\cos \theta }{c}=\delta t(1-\beta \cos \theta )}$, where ${\displaystyle \beta =v/c}$

${\displaystyle \delta t=\frac{\delta t^{\prime }}{1-\beta \cos \theta }}$

${\displaystyle BC=D_L\sin \varphi \approx \varphi D_L=v\delta t\sin \theta \Rightarrow \varphi D_L=v\sin \theta \frac{\delta t^{\prime }}{1-\beta \cos \theta }}$

Apparent transverse velocity along ${\displaystyle CB}$, ${\displaystyle v_{\text{T}}=\frac{\varphi D_L}{\delta t^{\prime }}=\frac{v\sin \theta }{1-\beta \cos \theta }}$

${\displaystyle {\beta }_{\text{T}}=\frac{v_{\text{T}}}{c}=\frac{\beta \sin \theta }{1-\beta \cos \theta }.}$

The apparent transverse velocity is maximal for angle (${\displaystyle 0<\beta <1}$ is used)

${\displaystyle \frac{\mathrm{\partial }{\beta }_{\text{T}}}{\mathrm{\partial }\theta }=\frac{\mathrm{\partial }}{\mathrm{\partial }\theta }\left[\frac{\beta \sin \theta }{1-\beta \cos \theta }\right]=\frac{\beta \cos \theta }{1-\beta \cos \theta }-\frac{(\beta \sin \theta {)}^2}{(1-\beta \cos \theta {)}^2}=0}$

${\displaystyle \Rightarrow \beta \cos \theta (1-\beta \cos \theta {)}^2=(1-\beta \cos \theta )(\beta \sin \theta {)}^2}$

${\displaystyle \Rightarrow \beta \cos \theta (1-\beta \cos \theta )=(\beta \sin \theta {)}^2\Rightarrow \beta \cos \theta -{\beta }^2{\cos }^2\theta ={\beta }^2{\sin }^2\theta \Rightarrow \cos {\theta }_{\text{max}}=\beta }$

${\displaystyle \Rightarrow \sin {\theta }_{\text{max}}=\sqrt{1-{\cos }^2{\theta }_{\text{max}}}=\sqrt{1-{\beta }^2}=\frac{1}{\gamma }}$, where ${\displaystyle \gamma =\frac{1}{\sqrt{1-{\beta }^2}}}$

${\displaystyle \therefore {\beta }_{\text{T}}^{\text{max}}=\frac{\beta \sin {\theta }_{\text{max}}}{1-\beta \cos {\theta }_{\text{max}}}=\frac{\beta /\gamma }{1-{\beta }^2}=\beta \gamma }$

If ${\displaystyle \gamma \gg 1}$ (i.e. when velocity of jet is close to the velocity of light) then ${\displaystyle {\beta }_{\text{T}}^{\text{max}}>1}$ despite the fact that ${\displaystyle \beta <1}$. And of course ${\displaystyle {\beta }_{\text{T}}>1}$ means that the apparent transverse velocity along ${\displaystyle CB}$, the only velocity on the sky that can be measured, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal.

History

The apparent superluminal motion in the faint nebula surrounding Nova Persei was first observed in 1901 by Charles Dillon Perrine. “Mr. Perrine’s photograph of November 7th and 8th, 1901, secured with the Crossley Reflector, led to the remarkable discovery that the masses of nebulosity were apparently in motion, with a speed perhaps several hundred times as great as hitherto observed.” “Using the 36-in. telescope (Crossley), he discovered the apparent superluminal motion of the expanding light bubble around Nova Persei (1901). Thought to be a nebula, the visual appearance was actually caused by light from the nova event reflected from the surrounding interstellar medium as the light moved outward from the star. Perrine studied this phenomenon using photographic, spectroscopic, and polarization techniques.”

Superluminal motion was first observed in 1902 by Jacobus Kapteyn in the ejecta of the nova GK Persei, which had exploded in 1901. His discovery was published in the German journal Astronomische Nachrichten, and received little attention from English-speaking astronomers until many decades later.

In 1966, Martin Rees pointed out that "an object moving relativistically in suitable directions may appear to a distant observer to have a transverse velocity much greater than the velocity of light". In 1969 and 1970 such sources were found as very distant astronomical radio sources, such as radio galaxies and quasars, and were called superluminal sources. The discovery was the result of a new technique called Very Long Baseline Interferometry, which allowed astronomers to set limits to the angular size of components and to determine positions to better than milli-arcseconds, and in particular to determine the change in positions on the sky, called proper motions, in a timespan of typically years. The apparent velocity is obtained by multiplying the observed proper motion by the distance, which could be up to 6 times the speed of light.

In the introduction to a workshop on superluminal radio sources, Pearson and Zensus reported

The first indications of changes in the structure of some sources were obtained by an American-Australian team in a series of transpacific VLBI observations between 1968 and 1970 (Gubbay et al. 1969). Following the early experiments, they had realised the potential of the NASA tracking antennas for VLBI measurements and set up an interferometer operating between California and Australia. The change in the source visibility that they measured for 3C 279, combined with changes in total flux density, indicated that a component first seen in 1969 had reached a diameter of about 1 milliarcsecond, implying expansion at an apparent velocity of at least twice the speed of light. Aware of Rees's model, (Moffet et al. 1972) concluded that their measurement presented evidence for relativistic expansion of this component. This interpretation, although by no means unique, was later confirmed, and in hindsight it seems fair to say that their experiment was the first interferometric measurement of superluminal expansion.

In 1994, a galactic speed record was obtained with the discovery of a superluminal source in the Milky Way, the cosmic x-ray source GRS 1915+105. The expansion occurred on a much shorter timescale. Several separate blobs were seen to expand in pairs within weeks by typically 0.5 arcsec. Because of the analogy with quasars, this source was called a microquasar.

Dynamic nuclear polarization

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Dynamic_nuclear_polarization

Dynamic nuclear polarization (DNP) is one of several hyperpolarization methods developed to enhance the sensitivity of nuclear magnetic resonance (NMR) spectroscopy. While an essential analytical tool with applications in several fields, NMR’s low sensitivity poses major limitations to analyzing samples with low concentrations and limited masses and volumes. This low sensitivity is due to the relatively low nuclear gyromagnetic ratios (γ_n) of NMR active nuclei (¹H, ¹³C, ¹⁵N, etc.) as well as the low natural abundance of certain nuclei. Several techniques have been developed to address this limitation, including hardware adjustments to NMR instruments and equipment (e.g., NMR tubes), improvements to data processing methods, and polarization transfer methods to NMR active nuclei in a sample—under which DNP falls.

Overhauser et al. were the first to hypothesize and describe the DNP effect in 1953; later that year, Carver and Slichter  observed the effect in experiments using metallic lithium. DNP involves transferring the polarization of electron spins to neighboring nuclear spins using microwave irradiation at or near electron paramagnetic resonance (EPR) transitions. It is based on two fundamental concepts: first, that the electronic gyromagnetic moment (γ_e) is several orders of magnitude larger than γ_n (about 658 times more; see below), and second, that the relaxation of electron spins is much faster than nuclear spins.

${\displaystyle \frac{P_e}{P_n}\approx \frac{{\gamma }_e}{{\gamma }_n}\approx \frac{1.760859644\times {10}^{11}{s}^{-}1}{2.675221900\times {10}^8{s}^{-}1}\approx 658}$,

where

${\displaystyle P=\tanh (\frac{\gamma \hslash B_0}{2k_{B}T})\approx \frac{\gamma \hslash B_0}{2k_{B}T}}$

is the Boltzmann equilibrium spin polarization. Note that the alignment of electron spins at a given magnetic field and temperature is described by the Boltzmann distribution under thermal equilibrium. A larger gyromagnetic moment corresponds to a larger Boltzmann distribution of populations in spin states; through DNP, the larger population distribution in the electronic spin reservoir is transferred to the neighboring nuclear spin reservoir, leading to stronger NMR signal intensities. The larger γ and faster relaxation of electron spins also help shorten T₁ relaxation times of nearby nuclei, corresponding to stronger signal intensities.

Under ideal conditions (full saturation of electron spins and dipolar coupling without leakage to nuclear spins), the NMR signal enhancement for protons can at most be 659. This corresponds to a time-saving factor of 434,000 for a solution-phase NMR experiment. In general, the DNP enhancement parameter η is defined as:

${\displaystyle \eta =\frac{I-I_0}{I_0}}$

where I is the signal intensity of the nuclear spins when the electron spins are saturated and I₀ is the signal intensity of the nuclear spins when the electron spins are in equilibrium.

Common polarizing agents (PAs) used in DNP experiments.

DNP methods typically fall under one of two categories: continuous wave DNP (CW-DNP) and pulsed DNP. As their names suggest, these methods differ in whether the sample is continuously irradiated or pulsed with microwaves. When electron spin polarization deviates from its thermal equilibrium value, polarization transfers between electrons and nuclei can occur spontaneously through electron-nuclear cross relaxation or spin-state mixing among electrons and nuclei. For example, polarization transfer is spontaneous after a homolysis chemical reaction. On the other hand, when the electron spin system is in a thermal equilibrium, the polarization transfer requires continuous microwave irradiation at a frequency close to the corresponding EPR frequency. It is also possible that electrons are aligned to a higher degree of order by other preparations of electron spin order such as chemical reactions (known as chemical-induced DNP or CIDNP), optical pumping, and spin injection. A polarizing agent (PA)—either an endogenous or exogenous paramagnetic system to the sample—is required as part of the DNP experimental setup. Typically, PAs are stable free radicals that are dissolved in solution or doped in solids; they provide a source of unpaired electrons that can be polarized by microwave radiation near the EPR transitions. DNP can also be induced using unpaired electrons produced by radiation damage in solids. Some common PAs are shown.

Described below are the four different mechanisms by which the DNP effect operates: the Overhauser effect (OE), the solid effect (SE), the cross effect (CE), and thermal mixing (TM). The DNP effect is present in solids and liquids and has been utilized successfully in solid-state and solution-phase NMR experiments. For solution-phase NMR experiments, only the OE mechanism is relevant, whereas for solid-state NMR any of the four mechanisms can be employed depending on the specific experimental conditions utilized.

The first DNP experiments were performed in the early 1950s at low magnetic fields  but until recently the technique was of limited applicability for high-frequency, high-field NMR spectroscopy because of the lack of microwave (or terahertz) sources operating at the appropriate frequency. Today, such sources are available as turn-key instruments, making DNP a valuable and indispensable method especially in the field of structure determination by high-resolution solid-state NMR spectroscopy.

Mechanisms

Overhauser effect

DNP was first realized using the concept of the Overhauser effect, which is the perturbation of nuclear spin level populations observed in metals and free radicals when electron spin transitions are saturated by microwave irradiation. This effect relies on stochastic interactions between an electron and a nucleus. The "dynamic" initially meant to highlight the time-dependent and random interactions in this polarization transfer process.

The DNP phenomenon was theoretically predicted by Albert Overhauser in 1953  and initially drew some criticism from Norman Ramsey, Felix Bloch, and other renowned physicists of the time on the grounds of being "thermodynamically improbable". The experimental confirmation by Carver and Slichter as well as an apologetic letter from Ramsey both reached Overhauser in the same year.

The so-called electron-nucleus cross-relaxation, which is responsible for the DNP phenomenon is caused by rotational and translational modulation of the electron-nucleus hyperfine coupling. The theory of this process is based essentially on the second-order time-dependent perturbation theory solution of the von Neumann equation for the spin density matrix.

While the Overhauser effect relies on time-dependent electron-nuclear interactions, the remaining polarizing mechanisms rely on time-independent electron-nuclear and electron-electron interactions.

Solid effect

The simplest spin system exhibiting the SE DNP mechanism is an electron-nucleus spin pair. The Hamiltonian of the system can be written as:

${\displaystyle H_0={\omega }_e{S}_z+{\omega }_{\mathrm{n}}{I}_z+A{S}_z{I}_z+B{S}_z{I}_x}$

These terms are referring respectively to the electron and nucleus Zeeman interaction with the external magnetic field, and the hyperfine interaction. S and I are the electron and nuclear spin operators in the Zeeman basis (spin 1⁄2 considered for simplicity), ω_e and ω_n are the electron and nuclear Larmor frequencies, and A and B are the secular and pseudo-secular parts of the hyperfine interaction. For simplicity we will only consider the case of |A|,|B|<<|ω_n|. In such a case A has little effect on the evolution of the spin system. During DNP a MW irradiation is applied at a frequency ω_MW and intensity ω₁, resulting in a rotating frame Hamiltonian given by

${\displaystyle H=\mathrm{\Delta }{\omega }_e{S}_z+{\omega }_{\mathrm{n}}{I}_z+A{S}_z{I}_z+B{S}_z{I}_x+{\omega }_1{S}_x}$where ${\displaystyle \mathrm{\Delta }{\omega }_e={\omega }_e-{\omega }_{\mathrm{M}\mathrm{W}}}$

The MW irradiation can excite the electron single quantum transitions ("allowed transitions") when ω_MW is close to ω_e, resulting in a loss of the electron polarization. In addition, due to the small state mixing caused by the B term of the hyperfine interaction, it is possible to irradiate on the electron-nucleus zero quantum or double quantum ("forbidden") transitions around ω_MW = ω_e ± ω_n, resulting in polarization transfer between the electrons and the nuclei. The effective MW irradiation on these transitions is approximately given by Bω₁/2ω_n.

Static sample case

In a simple picture of an electron-nucleus two-spin system, the solid effect occurs when a transition involving an electron-nucleus mutual flip (called zero quantum or double quantum) is excited by a microwave irradiation, in the presence of relaxation. This kind of transition is in general weakly allowed, meaning that the transition moment for the above microwave excitation results from a second-order effect of the electron-nuclear interactions and thus requires stronger microwave power to be significant, and its intensity is decreased by an increase of the external magnetic field B₀. As a result, the DNP enhancement from the solid effect scales as B₀⁻² when all the relaxation parameters are kept constant. Once this transition is excited and the relaxation is acting, the magnetization is spread over the "bulk" nuclei (the major part of the detected nuclei in an NMR experiment) via the nuclear dipole network. This polarizing mechanism is optimal when the exciting microwave frequency shifts up or down by the nuclear Larmor frequency from the electron Larmor frequency in the discussed two-spin system. The direction of frequency shifts corresponds to the sign of DNP enhancements. Solid effect exist in most cases but is more easily observed if the linewidth of the EPR spectrum of involved unpaired electrons is smaller than the nuclear Larmor frequency of the corresponding nuclei.

Magic angle spinning case

In the case of magic angle spinning DNP (MAS-DNP), the mechanism is different but to understand it, a two spins system can still be used. The polarization process of the nucleus still occurs when the microwave irradiation excites the double quantum or zero quantum transition, but due to the fact that the sample is spinning, this condition is only met for a short time at each rotor cycle (which makes it periodical). The DNP process in that case happens step by step and not continuously as in the static case.

Cross effect

Static case

The cross effect requires two unpaired electrons as the source of high polarization. Without special condition, such a three spins system can only generate a solid effect type of polarization. However, when the resonance frequency of each electron is separated by the nuclear Larmor frequency, and when the two electrons are dipolar coupled, another mechanism occurs: the cross-effect. In that case, the DNP process is the result of irradiation of an allowed transition (called single quantum) as a result the strength of microwave irradiation is less demanded than that in the solid effect. In practice, the correct EPR frequency separation is accomplished through random orientation of paramagnetic species with g-anisotropy. Since the "frequency" distance between the two electrons should be equal to the Larmor frequency of the targeted nucleus, cross-effect can only occur if the inhomogeneously broadened EPR lineshape has a linewidth broader than the nuclear Larmor frequency. Therefore, as this linewidth is proportional to external magnetic field B₀, the overall DNP efficiency (or the enhancement of nuclear polarization) scales as B₀⁻¹. This remains true as long as the relaxation times remain constant. Usually going to higher field leads to longer nuclear relaxation times and this may partially compensate for the line broadening reduction. In practice, in a glassy sample, the probability of having two dipolarly coupled electrons separated by the Larmor frequency is very scarce. Nonetheless, this mechanism is so efficient that it can be experimentally observed alone or in addition to the solid-effect.

Magic angle spinning case

As in the static case, the MAS-DNP mechanism of cross effect is deeply modified due to the time dependent energy level. By taking a simple three spin system, it has been demonstrated that the cross-effect mechanism is different in the Static and MAS case. The cross effect is the result of very fast multi-step process involving EPR single quantum transition, electron dipolar anti-crossing and cross effect degeneracy conditions. In the most simple case the MAS-DNP mechanism can be explained by the combination of a single quantum transition followed by the cross-effect degeneracy condition, or by the electron-dipolar anti-crossing followed by the cross-effect degeneracy condition.

This in turn change dramatically the CE dependence over the static magnetic field which does not scale like B₀⁻¹ and makes it much more efficient than the solid effect.

Thermal mixing

Thermal mixing is an energy exchange phenomenon between the electron spin ensemble and the nuclear spin, which can be thought of as using multiple electron spins to provide hyper-nuclear polarization. Note that the electron spin ensemble acts as a whole because of stronger inter-electron interactions. The strong interactions lead to a homogeneously broadened EPR lineshape of the involved paramagnetic species. The linewidth is optimized for polarization transfer from electrons to nuclei, when it is close to the nuclear Larmor frequency. The optimization is related to an embedded three-spin (electron-electron-nucleus) process that mutually flips the coupled three spins under the energy conservation (mainly) of the Zeeman interactions. Due to the inhomogeneous component of the associated EPR lineshape, the DNP enhancement by this mechanism also scales as B₀⁻¹.

DNP-NMR enhancement curves

¹H DNP-NMR enhancement curve for cellulose char heated for several hours at 350 °C. P_H – 1 is the relative polarization or intensity of the ¹H signal.

Many types of solid materials can exhibit more than one mechanism for DNP. Some examples are carbonaceous materials such bituminous coal and charcoal (wood or cellulose heated at high temperatures above their decomposition point which leaves a residual solid char). To separate out the mechanisms of DNP and to characterize the electron-nuclear interactions occurring in such solids a DNP enhancement curve can be made. A typical enhancement curve is obtained by measuring the maximum intensity of the NMR FID of the ¹H nuclei, for example, in the presence of continuous microwave irradiation as a function of the microwave frequency offset.

Carbonaceous materials such as cellulose char contain large numbers of stable free electrons delocalized in large polycyclic aromatic hydrocarbons. Such electrons can give large polarization enhancements to nearby protons via proton-proton spin-diffusion if they are not so close together that the electron-nuclear dipolar interaction does not broaden the proton resonance beyond detection. For small isolated clusters, the free electrons are fixed and give rise to solid-state enhancements (SS). The maximal proton solid-state enhancement is observed at microwave offsets of ω ≈ ω_e ± ω_H, where ω_e and ω_H are the electron and nuclear Larmor frequencies, respectively. For larger and more densely concentrated aromatic clusters, the free electrons can undergo rapid electron exchange interactions. These electrons give rise to an Overhauser enhancement centered at a microwave offset of ω_e – ω_H = 0. The cellulose char also exhibits electrons undergoing thermal mixing effects (TM). While the enhancement curve reveals the types electron-nuclear spin interactions in a material, it is not quantitative and the relative abundance of the different types of nuclei cannot be determined directly from the curve.

DNP-NMR

DNP can be performed to enhance NMR signals but also to introduce an inherent spatial dependence: the magnetization enhancement takes place in the vicinity of the irradiated electrons and propagates throughout the sample. Spatial selectivity can finally be obtained using magnetic resonance imaging (MRI) techniques, so that signals from similar parts can be separated based on their location in the sample. DNP has triggered enthusiasm in the NMR community because it can enhance sensitivity in solid-state NMR. In DNP, a large electronic spin polarization is transferred onto the nuclear spins of interest using a microwave source. There are two main DNP approaches for solids. If the material does not contain suitable unpaired electrons, exogenous DNP is applied: the material is impregnated by a solution containing a specific radical. When possible, endogenous DNP is performed using the electrons in transition metal ions (metal-ion dynamic nuclear polarization, MIDNP) or conduction electrons. The experiments usually need to be performed at low temperatures with magic angle spinning. It is important to note that DNP was only performed ex situ as it usually requires low temperature to lower electronic relaxation.