Schwinger limit

Last updated
A Feynman diagram (box diagram) for photon-photon scattering; one photon scatters from the transient vacuum charge fluctuations of the other. Photon-photon scattering.svg
A Feynman diagram (box diagram) for photon–photon scattering; one photon scatters from the transient vacuum charge fluctuations of the other.

In quantum electrodynamics (QED), the Schwinger limit is a scale above which the electromagnetic field is expected to become nonlinear. The limit was first derived in one of QED's earliest theoretical successes by Fritz Sauter in 1931 [1] and discussed further by Werner Heisenberg and his student Hans Heinrich Euler. [2] The limit, however, is commonly named in the literature [3] for Julian Schwinger, who derived the leading nonlinear corrections to the fields and calculated the rate of electron–positron pair production in a strong electric field. [4] The limit is typically reported as a maximum electric field or magnetic field before nonlinearity for the vacuum of

where me is the mass of the electron, c is the speed of light in vacuum, qe is the elementary charge, and ħ is the reduced Planck constant. These are enormous field strengths. Such an electric field is capable of accelerating a proton from rest to the maximum energy attained by protons at the Large Hadron Collider in only approximately 5 micrometers. The magnetic field is associated with birefringence of the vacuum and is exceeded on magnetars.

In vacuum, the classical Maxwell's equations are perfectly linear differential equations. This implies – by the superposition principle – that the sum of any two solutions to Maxwell's equations is another solution to Maxwell's equations. For example, two intersecting beams of light should simply add together their electric fields and pass right through each other. Thus Maxwell's equations predict the impossibility of any but trivial elastic photon–photon scattering. In QED, however, non-elastic photon–photon scattering becomes possible when the combined energy is large enough to create virtual electron–positron pairs spontaneously, illustrated by the Feynman diagram in the adjacent figure. This creates nonlinear effects that are approximately described by Euler and Heisenberg's nonlinear variant of Maxwell's equations.

A single plane wave is insufficient to cause nonlinear effects, even in QED. [4] The basic reason for this is that a single plane wave of a given energy may always be viewed in a different reference frame, where it has less energy (the same is the case for a single photon). A single wave or photon does not have a center-of-momentum frame where its energy must be at minimal value. However, two waves or two photons not traveling in the same direction always have a minimum combined energy in their center-of-momentum frame, and it is this energy and the electric field strengths associated with it, which determine particle–antiparticle creation, and associated scattering phenomena.

Photon–photon scattering and other effects of nonlinear optics in vacuum is an active area of experimental research, with current or planned technology beginning to approach the Schwinger limit. [5] It has already been observed through inelastic channels in SLAC Experiment 144. [6] [7] However, the direct effects in elastic scattering have not been observed. As of 2012, the best constraint on the elastic photon–photon scattering cross section belonged to PVLAS, which reported an upper limit far above the level predicted by the Standard Model. [8]

Proposals were made to measure elastic light-by-light scattering using the strong electromagnetic fields of the hadrons collided at the LHC. [9] In 2019, the ATLAS experiment at the LHC announced the first definitive observation of photon–photon scattering, observed in lead ion collisions that produced fields as large as 1025 V/m, well in excess of the Schwinger limit. [10] Observation of a cross section larger or smaller than that predicted by the Standard Model could signify new physics such as axions, the search of which is the primary goal of PVLAS and several similar experiments. ATLAS observed more events than expected, potentially evidence that the cross section is larger than predicted by the Standard Model, but the excess is not yet statistically significant. [11]

The planned, funded ELI–Ultra High Field Facility, which will study light at the intensity frontier, is likely to remain well below the Schwinger limit [12] although it may still be possible to observe some nonlinear optical effects. [13] The Station of Extreme Light (SEL) is another laser facility under construction which should be powerful enough to observe the effect. [14] Such an experiment, in which ultra-intense light causes pair production, has been described in the popular media as creating a "hernia" in spacetime. [15]

See also

Related Research Articles

<span class="mw-page-title-main">Quantum electrodynamics</span> Quantum field theory of electromagnetism

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.

<span class="mw-page-title-main">Zero-point energy</span> Lowest possible energy of a quantum system or field

Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. Therefore, even at absolute zero, atoms and molecules retain some vibrational motion. Apart from atoms and molecules, the empty space of the vacuum also has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions, and force fields, whose quanta are bosons. All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics since some systems can detect the existence of this energy. However, this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein's theory of special relativity.

<span class="mw-page-title-main">Spontaneous parametric down-conversion</span> Optical process

Spontaneous parametric down-conversion is a nonlinear instant optical process that converts one photon of higher energy, into a pair of photons of lower energy, in accordance with the law of conservation of energy and law of conservation of momentum. It is an important process in quantum optics, for the generation of entangled photon pairs, and of single photons.

<span class="mw-page-title-main">Rydberg atom</span> Excited atomic quantum state with high principal quantum number (n)

A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number, n. The higher the value of n, the farther the electron is from the nucleus, on average. Rydberg atoms have a number of peculiar properties including an exaggerated response to electric and magnetic fields, long decay periods and electron wavefunctions that approximate, under some conditions, classical orbits of electrons about the nuclei. The core electrons shield the outer electron from the electric field of the nucleus such that, from a distance, the electric potential looks identical to that experienced by the electron in a hydrogen atom.

In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs that change the distribution of charges and currents that generated the original electromagnetic field. It is also sometimes referred to as the self-energy of the gauge boson (photon).

<span class="mw-page-title-main">Two-photon physics</span> Branch of particle physics concerning interactions between two photons

Two-photon physics, also called gamma–gamma physics, is a branch of particle physics that describes the interactions between two photons. Normally, beams of light pass through each other unperturbed. Inside an optical material, and if the intensity of the beams is high enough, the beams may affect each other through a variety of non-linear effects. In pure vacuum, some weak scattering of light by light exists as well. Also, above some threshold of this center-of-mass energy of the system of the two photons, matter can be created.

<span class="mw-page-title-main">History of quantum field theory</span>

In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, leading to the introduction of renormalized quantum electrodynamics (QED). The field theory behind QED was so accurate and successful in predictions that efforts were made to apply the same basic concepts for the other forces of nature. Beginning in 1954, the parallel was found by way of gauge theory, leading by the late 1970s, to quantum field models of strong nuclear force and weak nuclear force, united in the modern Standard Model of particle physics.

<span class="mw-page-title-main">Optical parametric oscillator</span>

An optical parametric oscillator (OPO) is a parametric oscillator that oscillates at optical frequencies. It converts an input laser wave with frequency into two output waves of lower frequency by means of second-order nonlinear optical interaction. The sum of the output waves' frequencies is equal to the input wave frequency: . For historical reasons, the two output waves are called "signal" and "idler", where the output wave with higher frequency is the "signal". A special case is the degenerate OPO, when the output frequency is one-half the pump frequency, , which can result in half-harmonic generation when signal and idler have the same polarization.

<span class="mw-page-title-main">Schwinger effect</span> Decay of strong electromagnetic fields into particles

The Schwinger effect is a predicted physical phenomenon whereby matter is created by a strong electric field. It is also referred to as the Sauter–Schwinger effect, Schwinger mechanism, or Schwinger pair production. It is a prediction of quantum electrodynamics (QED) in which electron–positron pairs are spontaneously created in the presence of an electric field, thereby causing the decay of the electric field. The effect was originally proposed by Fritz Sauter in 1931 and further important work was carried out by Werner Heisenberg and Hans Heinrich Euler in 1936, though it was not until 1951 that Julian Schwinger gave a complete theoretical description.

In quantum optics, a NOON state or N00N state is a quantum-mechanical many-body entangled state:

PVLAS aims to carry out a test of quantum electrodynamics and possibly detect dark matter at the Department of Physics and National Institute of Nuclear Physics in Ferrara, Italy. It searches for vacuum polarization causing nonlinear optical behavior in magnetic fields. Experiments began in 2001 at the INFN Laboratory in Legnaro and continue today with new equipment.

Delbrück scattering, the deflection of high-energy photons in the Coulomb field of nuclei as a consequence of vacuum polarization, was observed in 1975. The related process of the scattering of light by light, also a consequence of vacuum polarization, was not observed until 1998. In both cases, it is a process described by quantum electrodynamics.

Discovered only as recently as 2006 by C.D. Stanciu and F. Hansteen and published in Physical Review Letters, this effect is generally called all-optical magnetization reversal. This magnetization reversal technique refers to a method of reversing magnetization in a magnet simply by circularly polarized light and where the magnetization direction is controlled by the light helicity. In particular, the direction of the angular momentum of the photons would set the magnetization direction without the need of an external magnetic field. In fact, this process could be seen as similar to magnetization reversal by spin injection. The only difference is that now, the angular momentum is supplied by the circularly polarized photons instead of the polarized electrons.

In physics, the Euler–Heisenberg Lagrangian describes the non-linear dynamics of electromagnetic fields in vacuum. It was first obtained by Werner Heisenberg and Hans Heinrich Euler in 1936. By treating the vacuum as a medium, it predicts rates of quantum electrodynamics (QED) light interaction processes.

<span class="mw-page-title-main">Breit–Wheeler process</span> Electron-positron production from two photons

The Breit–Wheeler process or Breit–Wheeler pair production is a proposed physical process in which a positron–electron pair is created from the collision of two photons. It is the simplest mechanism by which pure light can be potentially transformed into matter. The process can take the form γ γ′ → e+ e where γ and γ′ are two light quanta.

<span class="mw-page-title-main">Light-front quantization applications</span> Quantization procedure in quantum field theory

The light-front quantization of quantum field theories provides a useful alternative to ordinary equal-time quantization. In particular, it can lead to a relativistic description of bound systems in terms of quantum-mechanical wave functions. The quantization is based on the choice of light-front coordinates, where plays the role of time and the corresponding spatial coordinate is . Here, is the ordinary time, is a Cartesian coordinate, and is the speed of light. The other two Cartesian coordinates, and , are untouched and often called transverse or perpendicular, denoted by symbols of the type . The choice of the frame of reference where the time and -axis are defined can be left unspecified in an exactly soluble relativistic theory, but in practical calculations some choices may be more suitable than others. The basic formalism is discussed elsewhere.

In quantum physics, light is in a squeezed state if its electric field strength Ԑ for some phases has a quantum uncertainty smaller than that of a coherent state. The term squeezing thus refers to a reduced quantum uncertainty. To obey Heisenberg's uncertainty relation, a squeezed state must also have phases at which the electric field uncertainty is anti-squeezed, i.e. larger than that of a coherent state. Since 2019, the gravitational-wave observatories LIGO and Virgo employ squeezed laser light, which has significantly increased the rate of observed gravitational-wave events.

Patrick Mora is a French theoretical plasma physicist who specializes in laser-plasma interactions. He was awarded the 2014 Hannes Alfvén Prize and 2019 Edward Teller Award for his contributions to the field of laser-plasma physics.

Sergei Vladimirovich Bulanov, is a Russian physicist. He received the 1983 State Prize of the USSR, the 2016 Hannes Alfvén Prize for "contributions to the development of large-scale next-step devices in high-temperature plasma physics research", and the Order of Rising Sun with Gold Rays and Rosette in 2020.

<span class="mw-page-title-main">Non-linear inverse Compton scattering</span> Electron-many photon scattering

Non-linear inverse Compton scattering (NICS), also known as non-linear Compton scattering and multiphoton Compton scattering, is the scattering of multiple low-energy photons, given by an intense electromagnetic field, in a high-energy photon during the interaction with a charged particle, in many cases an electron. This process is an inverted variant of Compton scattering since, contrary to it, the charged particle transfers its energy to the outgoing high-energy photon instead of receiving energy from an incoming high-energy photon. Furthermore, differently from Compton scattering, this process is explicitly non-linear because the conditions for multiphoton absorption by the charged particle are reached in the presence of a very intense electromagnetic field, for example, the one produced by high-intensity lasers.

References

  1. F. Sauter (1931). "Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs". Zeitschrift für Physik. 69 (11–12) (82nd ed.) (published November 1931): 742–764. Bibcode:1931ZPhy...69..742S. doi:10.1007/BF01339461. ISSN   1434-6001. S2CID   122120733. Wikidata   Q60698281.
  2. Werner Heisenberg; Hans Heinrich Euler (1936). "Folgerungen aus der Diracschen Theorie des Positrons". Zeitschrift für Physik (in German). 98 (11–12) (98th ed.) (published November 1936): 714–732. Bibcode:1936ZPhy...98..714H. doi:10.1007/BF01343663. ISSN   1434-6001. S2CID   120354480. Wikidata   Q28794438. English translation
  3. Mark Buchanan (2006). "Thesis: Past the Schwinger limit". Nature Physics. 2 (11) (2nd ed.) (published November 2006): 721. Bibcode:2006NatPh...2..721B. doi: 10.1038/nphys448 . ISSN   1745-2473. S2CID   119831515. Wikidata   Q63918589.
  4. 1 2 J. Schwinger (1951). "On Gauge Invariance and Vacuum Polarization". Phys. Rev. 82 (5) (82nd ed.) (published June 1951): 664–679. Bibcode:1951PhRv...82..664S. doi:10.1103/PhysRev.82.664. ISSN   0031-899X. Zbl   0043.42201. Wikidata   Q21709192.
  5. Stepan S Bulanov; Timur Esirkepov; Alexander G. Thomas; James K Koga; Sergei V Bulanov (2010). "On the Schwinger limit attainability with extreme power lasers". Phys. Rev. Lett. 105 (22) (105th ed.) (published 24 November 2010): 220407. arXiv: 1007.4306 . doi:10.1103/PhysRevLett.105.220407. ISSN   0031-9007. PMID   21231373. S2CID   36857911. Wikidata   Q27447776.
  6. C. Bula; K. T. McDonald; E. J. Prebys; et al. (1996). "Observation of Nonlinear Effects in Compton Scattering". Phys. Rev. Lett. 76 (17) (76th ed.) (published 22 April 1996): 3116–3119. Bibcode:1996PhRvL..76.3116B. doi:10.1103/PhysRevLett.76.3116. ISSN   0031-9007. PMID   10060879. Wikidata   Q27450530.
  7. C. Bamber; S. J. Boege; T. Koffas; et al. (1999). "Studies of nonlinear QED in collisions of 46.6 GeV electrons with intense laser pulses". Phys. Rev. D. 60 (9) (60th ed.) (published 8 October 1999): 092004. Bibcode:1999PhRvD..60i2004B. doi:10.1103/PhysRevD.60.092004. ISSN   1550-7998. Wikidata   Q27441586.
  8. G. ZAVATTINI; U. GASTALDI; R. PENGO; G. RUOSO; F. DELLA VALLE; E. MILOTTI (20 June 2012). "Measuring the magnetic birefringence of vacuum: the PVLAS experiment". International Journal of Modern Physics A. 27 (15): 1260017. arXiv: 1201.2309 . doi:10.1142/S0217751X12600172. ISSN   0217-751X. Zbl   1247.81603. Wikidata   Q62555414.
  9. David d'Enterria; Gustavo G da Silveira (2013). "Observing Light-by-Light Scattering at the Large Hadron Collider". Phys. Rev. Lett. 111 (8) (111th ed.) (published 22 August 2013): 080405. arXiv: 1305.7142 . Bibcode:2013PhRvL.111h0405D. doi:10.1103/PhysRevLett.111.080405. ISSN   0031-9007. PMID   24010419. S2CID   43797550. Wikidata   Q85643997.
  10. ATLAS Collaboration (17 March 2019). "ATLAS observes light scattering off light".
  11. G. Aad; et al. (31 July 2019). "Observation of Light-by-Light Scattering in Ultraperipheral Pb+Pb Collisions with the ATLAS Detector". Physical Review Letters . 123 (5): 052001. arXiv: 1904.03536 . Bibcode:2019PhRvL.123e2001A. doi:10.1103/PhysRevLett.123.052001. PMID   31491300. S2CID   260811101.
  12. Heinzl, T. (2012). "Strong-Field QED and High Power Lasers" (PDF). International Journal of Modern Physics A. 27 (15). arXiv: 1111.5192 . Bibcode:2012IJMPA..2760010H. doi:10.1142/S0217751X1260010X. S2CID   119198507.
  13. Gagik Yu Kryuchkyan; Karen Z. Hatsagortsyan (2011). "Bragg Scattering of Light in Vacuum Structured by Strong Periodic Fields". Phys. Rev. Lett. 107 (5) (107th ed.) (published 27 July 2011): 053604. arXiv: 1102.4013 . Bibcode:2011PhRvL.107e3604K. doi:10.1103/PhysRevLett.107.053604. ISSN   0031-9007. PMID   21867070. S2CID   25991919. Wikidata   Q27347258.
  14. Berboucha, Meriame. "This Laser Could Rip Apart Empty Space". Forbes. Retrieved 2021-02-18.
  15. I. O'Neill (2011). "A Laser to Give the Universe a Hernia?". Discovery News. Archived from the original on November 3, 2011.