Bose-Einstein Correlations

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Bose-Einstein correlations are correlations between identical bosons , named after the physicists Satyendranath Bose and Albert Einstein . They find important applications in astronomy , optics , nuclear and particle physics .

Intensity interferometry and Bose-Einstein correlations

In optics, the interference of two light beams is called coherent if the phase difference of the corresponding waves is constant. The coherent superposition of wave amplitudes is called first order interference, in contrast to the superposition of intensities, which is called intensity interference , Hanbury-Brown and Twiss (HBT) interference or second order interference. Accordingly, a distinction is made between first-order coherence and second-order coherence, which is also called quantum coherence . Amplitude interferometry is used in optics to determine lengths, surface irregularities and refraction coefficients. The intensity interference, besides ensuring better stability, has the additional property that it also enables the determination of the quantum coherence of sources.

The interference of two (or more) waves leads to a correlation between these waves. In particle physics, each particle corresponds to a wave. This leads to interferences and correlations of two (or more) particles, which are described by second (or higher) order correlation functions. With identical particles, these correlations have specific properties. A distinction is made here between Bose-Einstein correlations, which occur with bosons, and Fermi-Dirac correlations, which relate to fermions. In the case of Bose-Einstein correlations (BEK), the particles are bundled and in the case of Fermi-Dirac correlations, they are anti-bundled. Another difference between Bose-Einstein and Fermi-Dirac correlations is that quantum coherence is only possible with BEK.

Bose-Einstein Correlations and Quantum Coherence

The term quantum coherence goes back to Roy Glauber and was initially used for lasers and measles , but soon found important applications in other areas of physics, e.g. B. Bose-Einstein condensation . As the name suggests, both Bose-Einstein correlations and Bose-Einstein condensation are consequences of the Bose-Einstein statistics and therefore refer not only to photons, but to bosons in general. Bose-Einstein condensation leads, among other things, to superconductivity and superfluidity, and Bose-Einstein correlations are also noticed in hadrons.

Almost simultaneously with the invention of intensity interferometry by Hanbury-Brown and Twiss (HBT) in optics, Gerson Goldhaber , Sulamith Goldhaber, Wonyong Lee and Abraham Pais (GGLP) discovered in proton-antiproton annihilation processes that the identically charged pion pairs produced, were bundled, while pairs of pions with opposite charges did not show this phenomenon. They interpreted this effect as a consequence of Bose-Einstein statistics. It was later recognized that the HBT effect is also a Bose-Einstein correlation effect, namely of photons.

Bose-Einstein correlations in sub-nuclear physics are described in quantum statistics with the help of the formalism of classical currents and coherent states. Since the 1980s, BEKs have become an important topic in high energy physics and conferences are held that deal exclusively with this. One of the reasons for this interest is the fact that until now BEK is the only method for measuring dimensions and lifetimes of sources of elementary particles. So they find important applications u. a. in the investigation of quark matter, because the formation of this phase of matter requires a critical energy density. In order to determine this one has to know the volume or the expansion of the fireball in which one expects this matter to arise. The corresponding size can be measured with the help of intensity interferometry. In addition, a phase of matter means a quasi-stable state, i.e. That is, a state that lives longer than the duration of the collision in which this state occurs. This means that one has to know the lifetime of the source to prove the stability, which in turn is only possible by measuring BEK.

Quantum Coherence in Strong Interactions

BEK can also be used to determine quantum coherence in strong interactions. The most convincing evidence of coherence in BEK is based on the measurement of higher order correlations. This experiment is also distinguished by the fact that it tests the predictions of quantum statistics through an, albeit unintentional, attempt at falsification.

Quantum statistics have also made a surprising heuristic finding possible in connection with the principle of identity of elementary particles.

Bose-Einstein correlations and the principle of identity of elementary particles

In processes in which the number of particles remains constant, the system can be described by a wave function. This first quantization method was also originally used in the interpretation of Bose-Einstein (and Fermi-Dirac) correlations. In processes that take place at high energies, however, particles are generated and absorbed and this makes the application of field theoretical methods necessary (second quantization). Quantum optics uses this more general method to describe quantum coherence, lasers and condensates. Another phenomenon discovered by this method are Bose-Einstein correlations between particles and antiparticles .

The wave function of two identical particles is symmetric or antisymmetric , depending on whether you are looking at identical bosons or identical fermions. In the case of non-identical particles there is no permutation symmetry and within the framework of the wave function formalism there are also no Bose-Einstein or Fermi-Dirac correlations between these particles. This also refers to the special case of a pair consisting of a particle and an antiparticle, for example a positive and a negative pion . In this case, however, one must take into account that the two charged pions can annihilate and transform into a pair of neutral pions (or photons), i.e. a pair of identical particles. The method of second quantization comes into play and we have a new type of Bose-Einstein correlation, the one between positive and negative pions, which is, however, weaker than that between two identically charged pions. On the other hand, there is no Bose-Einstein correlation between a charged and a neutral pion, as if a positive and a negative pion were “less different” than a charged and a neutral pion. In addition, it is found that correlations between two neutral pions are stronger than those between identically charged pions, as if the neutral pions were “more identical” than the charged ones. These surprising and sensational results prove the superiority of the second quantization. They also prove that the analogy between optical and particle interferometry has its limits and that Bose-Einstein correlations between identically charged pions are different from corresponding correlations between photons, a topic that has led to misunderstandings in the literature and has been clarified in.

Individual evidence

  1. ^ Richard M. Weiner: Introduction to Bose-Einstein Correlations and Subatomic Interferometry. John Wiley, 2000, ISBN 0-471-96922-2 .
  2. ↑ Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 .
  3. ↑ The correlation function of the n-th order is the transition amplitude between n-particle states.
  4. ↑ In the present article, the abbreviation BEK refers exclusively to Bose-Einstein correlations and not, as is common in the literature, to Bose-Einstein condensates.
  5. ^ Roy J. Glauber : Coherent and Incoherent States of the Radiation Field . In: Physical Review . tape  131 , no. 6 , 1963, pp. 2766-2788 , doi : 10.1103 / PhysRev.131.2766 .
  6. ↑ Gerson Goldhaber, Sulamith Goldhaber, Wonyong Lee, Abraham Pais: Influence of Bose-Einstein Statistics on the Antiproton-Proton Annihilation Process . In: Physical Review . tape 120 , no. 1 , 1960, p. 300–312 , doi : 10.1103 / PhysRev.120.300 (reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , pp. 3.).
  7. ↑ VG Grishin, GI Kopylov, MI Podgoretskiĭ: In: Sov. J. Nucl. Phys. 13, 1971, p. 638. Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , p. 16.
  8. ↑ The fact that it took so long to recognize this connection is partly due to the fact that in HBT interferometry correlations between distances are measured, while GGLP refers to correlations between pulses.
  9. ^ IV Andreev, RM Weiner: Space-time aspects of Bose-Einstein correlations and quantum statistics . In: Physics Letters B . tape 253 , no. 3-4 , 1991, pp. 416-420 , doi : 10.1016 / 0370-2693 (91) 91743-F (Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471- 96979-6 , p. 312.).
  10. ^ IV Andreev, M. Plümer, RM Weiner: In: Int. J. Mod. Phys. 8A, 1993, p. 4577. Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , p. 352.
  11. ↑ GI Kopylov, MI Podgoretskiĭ: In: Sov. J. Nucl. Phys. 18, 1974, p. 336. Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , p. 336.
  12. ↑ GN Fowler, RM Weiner: Effects of classical fields in meson correlations . In: Physical Review D . tape 17 , no. 11 , 1978, p. 3118–3123 , doi : 10.1103 / PhysRevD.17.3118 (Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , pp. 78.).
  13. ↑ M. Gyulassy, SK Kauffmann, Lance W. Wilson: Pion interferometry of nuclear collisions. I. Theory . In: Physical Review C . tape 20 , no. 6 , 1979, pp. 2267–2292 , doi : 10.1103 / PhysRevC.20.2267 (Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , pp. 86.).
  14. ↑ The first meeting of this kind was Correlations and Multiparticle Production-CAMP, conference proceedings edited by M. Plümer, S. Raha, RM Weiner: World Scientific. 1990, ISBN 981-02-0331-4 .
  15. ↑ EV Shuryak: In: Sov. J. Nucl. Phys. 18, 1974, p. 667. Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , p. 32.
  16. ↑ GN Fowler, RM Weiner: Possible evidence for coherence of hadronic fields from Bose-Einstein correlation experiments . In: Physics Letters B . tape 70 , no. 2 , 1977, p. 201-203 , doi : 10.1016 / 0370-2693 (77) 90520-2 .
  17. ↑ M. Plümer, LV Razumov, RM Weiner: Evidence for quantum statistical coherence from experimental data on higher order Bose-Einstein correlations . In: Physics Letters B . tape 286 , no. 3-4 , 1992, pp. 335-340 , doi : 10.1016 / 0370-2693 (92) 91784-7 (Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471- 96979-6 , p. 344.).
  18. ↑ N. Neumeister, T. Gajdosik, B. Buschbeck, H. Dibon, M. Markytan, D. Weselka, C.-E. Wulz, G. Bocquet, A. Norton, V. Karimäki, R. Kinnunen, M. Pimiä, J. Tuominiemi, C. Albajar, J.-P. Revol, P. Sphicas, K. Sumorok, CH Tan, S. Tether: Higher order Bose-Einstein correlations in p collisions at √ s = 630 and 900 GeV . In: Physics Letters B . tape 275 , no. 1-2 , 1992, pp. 186-194 (Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , p. 332.).
  19. ^ A b IV Andreev, M. Plümer, RM Weiner: Surprises from Bose-Einstein correlations . In: Physical Review Letters . tape 67 , no. 25 , 1991, pp. 3475–3478 , doi : 10.1103 / PhysRevLett.67.3475 (reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471-96979-6 , pp. 326.).
  20. ↑ Leonid V. Razumov, RM Weiner: Quantum field theory of Bose-Einstein correlations . In: Physics Letters B . tape 348 , no. 1-2 , January 19, 1995, pp. 133–140 , doi : 10.1016 / 0370-2693 (95) 00119-6 (Reprinted in: Richard M. Weiner Bose-Einstein Correlations in Particle and Nuclear Physics. A Collection of Reprints, John Wiley, 1997, ISBN 0-471- 96979-6 , p. 452.).
  21. ^ MG Bowler: On surprises from Bose-Einstein correlations . In: Physics Letters B . tape 276 , no. 1-2 , 1992, pp. 237-241 , doi : 10.1016 / 0370-2693 (92) 90570-T .
  22. ↑ RM Weiner: Boson interferometry in high-energy physics . In: Physics Reports . tape 327 , no. 5 , 2000, pp. 249-346 , doi : 10.1016 / S0370-1573 (99) 00114-3 .