Hanbury-Brown and Twiss effect
Encyclopedia
The Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation
and anti-correlation effects in the intensities
received by two detectors from a beam of particles. HBT effects can generally be attributed to the dual wave-particle nature of the beam, and the results of a given experiment depend on whether the beam is composed of fermion
s or boson
s. Devices which use the effect are commonly called intensity interferometer
s and were originally used in astronomy
, although they are also heavily used in the field of quantum optics
.
and Richard Q. Twiss
published A test of a new type of stellar interferometer on Sirius, in which two photomultiplier
tubes (PMTs), separated by about 6 meters, were aimed at the star Sirius. Light was collected into the PMTs using mirrors from searchlights. An interference effect was observed between the two intensities, revealing a positive correlation between the two signals, despite the fact that no phase
information was collected. Hanbury Brown and Twiss used the interference signal to determine the apparent angular size of Sirius, claiming excellent resolution.
Also, in the field of particle physics, Goldhaber et al. performed an experiment in 1959 in Berkeley and found an unexpected angular correlation among identical pions, in order to discover the ρ0 resonance (by means of
) [Phys.Rev.Lett.3,181(1959)]. From then on, the HBT technique started to be used in particular by the heavy-ion community to determine the space-time dimensions of the particle emission source for heavy ion collisions. For recent developments in this field, cf. for example the review article by Lisa [M.Lisa,et al., Ann.Rev.Nucl.Part.Sci 55, 357(2005), or, http://arxiv.org/abs/nucl-ex/0505014.
The original HBT result met with much skepticism in the physics
community. Although intensity interferometry
had been widely used in radio astronomy
where Maxwell's equations
are valid, at optical wavelengths the light would be quantised into a relatively small number of photon
s. Many physicists worried that the correlation was inconsistent with the laws of thermodynamics. Some even claimed that the effect violated the uncertainty principle
. Hanbury Brown
and Twiss
resolved the dispute in a neat series of papers (see References below) which demonstrated first that wave transmission in quantum optics had exactly the same mathematical form as Maxwell's equations albeit with an additional noise term due to quantisation at the detector, and secondly that according to Maxwell's equations, intensity interferometry should work. Others, such as Edward Mills Purcell
immediately supported the technique, pointing out that the clumping of bosons was simply a manifestation of an effect already known in statistical mechanics
. After a number of experiments, the whole physics community agreed that the observed effect was real.
The original experiment used the fact that two bosons tend to arrive at two separate detectors at the same time. Morgan and Mandel used a thermal photon
source to create a dim beam of photons and observed the tendency of the photons to arrive at the same time on a single detector. Both of these effects used the wave nature of light to create a correlation in arrival time - if a single photon beam is split into two beams, then the particle nature of light requires that each photon is only observed at a single detector, and so an anti-correlation was observed in 1986. Finally, bosons have a tendency to clump together, giving rise to Bose–Einstein correlations, while fermions due to the Pauli exclusion principle
, tend to spread apart leading to Fermi–Dirac (anti)correlations. Bose–Einstein correlations have been observed between pions, kaons and photons, and Fermi–Dirac (anti)correlations between protons, neutrons and electrons. For a general introduction in this field cf. the textbook on Bose–Einstein correlations by Richard M. Weiner
It must be noted, that a difference in repulsion of BECs in the "trap-and-free fall" analogy of the HBT effect affects comparison.
as a classical wave
. Suppose we have a single incident wave with frequency
on two detectors. Since the detectors are separated, say the second detector gets the signal delayed by a phase
of
. Since the intensity at a single detector is just the square of the wave amplitude, we have for the intensities at the two detectors
which makes the correlation
a constant plus a phase dependent component. Most modern schemes actually measure the correlation in intensity fluctuations at the two detectors, but it is not too difficult to see that if the intensities are correlated then the fluctuations
, where 
is the average intensity, ought to be correlated. In general
and since the average intensity at both detectors in this example is
,
so our constant vanishes. The average intensity is
because the time average of 
is 1/2.
An evaluation of a degree of the second-order coherence for complementary (anti-correlated) outputs of an interferometer leads to behaviour like "anti-bunching effect". For example a variation in reflectivity
(and thus also in transmittance) of beam splitter
, where
results in the negative correlation of fluctuations
i.e. a dip in the coherence function
.
) effect can be entirely described by classical optics. The quantum description of the effect is less intuitive: if one supposes that a thermal or chaotic light source such as a star randomly emits photons, then it is not obvious how the photons "know" that they should arrive at a detector in a correlated (bunched) way. A simple argument suggested by Ugo Fano
[Fano, 1961] captures the essence of the quantum explanation. Consider two points
and 
in a source which emit photons detected by two detectors 
and 
as in the diagram. A joint detection takes place when the photon emitted by 
is detected by 
and the photon emitted by 
is detected by 
(red arrows) or when 
's photon is detected by 
and 
's by 
(green arrows). The quantum mechanical probability amplitudes for these two possibilities are denoted by
and
respectively. If the photons are indistinguishable, the two amplitudes interfere constructively to give a joint detection probability greater than that for two independent events. The sum over all possible pairs 
,
in the source washes out the interference unless the distance 
is sufficiently small.
Fano's explanation nicely illustrates the necessity of considering two particle amplitudes, which are not as intuitive as the more familiar single particle amplitudes used to interpret most interference effects. This may help to explain why some physicists in the 1950s had difficulty accepting the Hanbury Brown Twiss result. But the quantum approach is more than just a fancy way to reproduce the classical result: if the photons are replaced by identical fermions such as electrons, the antisymmetry of wavefunctions under exchange of particles renders the interference destructive, leading to zero joint detection probability for small detector separations. This effect is referred to as antibunching of fermions [Henny, 1999]. The above treatment also explains photon antibunching [Kimble, 1977]: if the source consists of a single atom which can only emit one photon at a time, simultaneous detection in two closely spaced detectors is clearly impossible. Antibunching, whether of bosons or of fermions, has no classical wave analog.
From the point of view of the field of quantum optics, the HBT effect was important to lead physicists (among them Roy J. Glauber
and Leonard Mandel
) to apply quantum electrodynamics to new situations, many of which had never been experimentally studied, and in which classical and quantum predictions differ.
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
and anti-correlation effects in the intensities
Intensity (physics)
In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...
received by two detectors from a beam of particles. HBT effects can generally be attributed to the dual wave-particle nature of the beam, and the results of a given experiment depend on whether the beam is composed of fermion
Fermion
In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....
s or boson
Boson
In particle physics, bosons are subatomic particles that obey Bose–Einstein statistics. Several bosons can occupy the same quantum state. The word boson derives from the name of Satyendra Nath Bose....
s. Devices which use the effect are commonly called intensity interferometer
Intensity interferometer
An intensity interferometer is the name given to devices that use the Hanbury-Brown and Twiss effect. In astronomy, the most common use of such an astronomical interferometer is to determine the apparent angular diameter of a radio source or star...
s and were originally used in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, although they are also heavily used in the field of quantum optics
Quantum optics
Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...
.
History
In 1956, Robert Hanbury BrownRobert Hanbury Brown
Robert Hanbury Brown, AC FRS was a British astronomer and physicist born in Aruvankadu, India. He made notable contributions to the development of radar and he later conducted pioneering work in the field of radio astronomy...
and Richard Q. Twiss
Richard Q. Twiss
Richard Q. Twiss is famous for his work on the Hanbury-Brown and Twiss effect with Robert Hanbury Brown. This led to the development of the Hanbury Brown-Twiss intensity interferometer in the UK in 1954. Their work was controversial as it appeared to contradict the established beliefs about...
published A test of a new type of stellar interferometer on Sirius, in which two photomultiplier
Photomultiplier
Photomultiplier tubes , members of the class of vacuum tubes, and more specifically phototubes, are extremely sensitive detectors of light in the ultraviolet, visible, and near-infrared ranges of the electromagnetic spectrum...
tubes (PMTs), separated by about 6 meters, were aimed at the star Sirius. Light was collected into the PMTs using mirrors from searchlights. An interference effect was observed between the two intensities, revealing a positive correlation between the two signals, despite the fact that no phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
information was collected. Hanbury Brown and Twiss used the interference signal to determine the apparent angular size of Sirius, claiming excellent resolution.
Also, in the field of particle physics, Goldhaber et al. performed an experiment in 1959 in Berkeley and found an unexpected angular correlation among identical pions, in order to discover the ρ0 resonance (by means of
) [Phys.Rev.Lett.3,181(1959)]. From then on, the HBT technique started to be used in particular by the heavy-ion community to determine the space-time dimensions of the particle emission source for heavy ion collisions. For recent developments in this field, cf. for example the review article by Lisa [M.Lisa,et al., Ann.Rev.Nucl.Part.Sci 55, 357(2005), or, http://arxiv.org/abs/nucl-ex/0505014.The original HBT result met with much skepticism in the physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
community. Although intensity interferometry
Intensity interferometer
An intensity interferometer is the name given to devices that use the Hanbury-Brown and Twiss effect. In astronomy, the most common use of such an astronomical interferometer is to determine the apparent angular diameter of a radio source or star...
had been widely used in radio astronomy
Radio astronomy
Radio astronomy is a subfield of astronomy that studies celestial objects at radio frequencies. The initial detection of radio waves from an astronomical object was made in the 1930s, when Karl Jansky observed radiation coming from the Milky Way. Subsequent observations have identified a number of...
where Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
are valid, at optical wavelengths the light would be quantised into a relatively small number of photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
s. Many physicists worried that the correlation was inconsistent with the laws of thermodynamics. Some even claimed that the effect violated the uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
. Hanbury Brown
Robert Hanbury Brown
Robert Hanbury Brown, AC FRS was a British astronomer and physicist born in Aruvankadu, India. He made notable contributions to the development of radar and he later conducted pioneering work in the field of radio astronomy...
and Twiss
Richard Q. Twiss
Richard Q. Twiss is famous for his work on the Hanbury-Brown and Twiss effect with Robert Hanbury Brown. This led to the development of the Hanbury Brown-Twiss intensity interferometer in the UK in 1954. Their work was controversial as it appeared to contradict the established beliefs about...
resolved the dispute in a neat series of papers (see References below) which demonstrated first that wave transmission in quantum optics had exactly the same mathematical form as Maxwell's equations albeit with an additional noise term due to quantisation at the detector, and secondly that according to Maxwell's equations, intensity interferometry should work. Others, such as Edward Mills Purcell
Edward Mills Purcell
Edward Mills Purcell was an American physicist who shared the 1952 Nobel Prize for Physics for his independent discovery of nuclear magnetic resonance in liquids and in solids. Nuclear magnetic resonance has become widely used to study the molecular structure of pure materials and the...
immediately supported the technique, pointing out that the clumping of bosons was simply a manifestation of an effect already known in statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
. After a number of experiments, the whole physics community agreed that the observed effect was real.
The original experiment used the fact that two bosons tend to arrive at two separate detectors at the same time. Morgan and Mandel used a thermal photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
source to create a dim beam of photons and observed the tendency of the photons to arrive at the same time on a single detector. Both of these effects used the wave nature of light to create a correlation in arrival time - if a single photon beam is split into two beams, then the particle nature of light requires that each photon is only observed at a single detector, and so an anti-correlation was observed in 1986. Finally, bosons have a tendency to clump together, giving rise to Bose–Einstein correlations, while fermions due to the Pauli exclusion principle
Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles...
, tend to spread apart leading to Fermi–Dirac (anti)correlations. Bose–Einstein correlations have been observed between pions, kaons and photons, and Fermi–Dirac (anti)correlations between protons, neutrons and electrons. For a general introduction in this field cf. the textbook on Bose–Einstein correlations by Richard M. Weiner
Richard M. Weiner
Richard M. Weiner is a professor of theoretical physics at the University of Marburg in Marburg, Germany and an associate of the Laboratoire de Physique Théorique at Paris-Sud 11 University in Orsay, France.-Biography:...
It must be noted, that a difference in repulsion of BECs in the "trap-and-free fall" analogy of the HBT effect affects comparison.
Wave mechanics
The HBT effect can in fact be predicted solely by treating the incident electromagnetic radiationElectromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
as a classical wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
. Suppose we have a single incident wave with frequency
on two detectors. Since the detectors are separated, say the second detector gets the signal delayed by a phasePhase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
of
. Since the intensity at a single detector is just the square of the wave amplitude, we have for the intensities at the two detectorswhich makes the correlation
a constant plus a phase dependent component. Most modern schemes actually measure the correlation in intensity fluctuations at the two detectors, but it is not too difficult to see that if the intensities are correlated then the fluctuations
, where is the average intensity, ought to be correlated. In generaland since the average intensity at both detectors in this example is
,so our constant vanishes. The average intensity is
because the time average of is 1/2.An evaluation of a degree of the second-order coherence for complementary (anti-correlated) outputs of an interferometer leads to behaviour like "anti-bunching effect". For example a variation in reflectivity
Reflectivity
In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...
(and thus also in transmittance) of beam splitter
Beam splitter
A beam splitter is an optical device that splits a beam of light in two. It is the crucial part of most interferometers.In its most common form, a rectangle, it is made from two triangular glass prisms which are glued together at their base using Canada balsam...
, where
results in the negative correlation of fluctuations
i.e. a dip in the coherence function
.Quantum interpretation
The above discussion makes it clear that the Hanbury Brown and Twiss (or photon bunchingPhoton bunching
In physics, photon bunching refers to the statistical tendency for photons to distribute themselves in bunches rather that at random . Thermal fields are examples of photon bunching. Their statistic can be observed as photons that arrive more simultaneously at detectors...
) effect can be entirely described by classical optics. The quantum description of the effect is less intuitive: if one supposes that a thermal or chaotic light source such as a star randomly emits photons, then it is not obvious how the photons "know" that they should arrive at a detector in a correlated (bunched) way. A simple argument suggested by Ugo Fano
Ugo Fano
Ugo Fano was an Italian American physicist, a leader in theoretical physics in the 20th century.- Biography :Ugo Fano was born into a wealthy Jewish family in Turin, Italy...
[Fano, 1961] captures the essence of the quantum explanation. Consider two points
and in a source which emit photons detected by two detectors and as in the diagram. A joint detection takes place when the photon emitted by is detected by and the photon emitted by is detected by (red arrows) or when 's photon is detected by and 's by (green arrows). The quantum mechanical probability amplitudes for these two possibilities are denoted by and respectively. If the photons are indistinguishable, the two amplitudes interfere constructively to give a joint detection probability greater than that for two independent events. The sum over all possible pairs , in the source washes out the interference unless the distance is sufficiently small. Fano's explanation nicely illustrates the necessity of considering two particle amplitudes, which are not as intuitive as the more familiar single particle amplitudes used to interpret most interference effects. This may help to explain why some physicists in the 1950s had difficulty accepting the Hanbury Brown Twiss result. But the quantum approach is more than just a fancy way to reproduce the classical result: if the photons are replaced by identical fermions such as electrons, the antisymmetry of wavefunctions under exchange of particles renders the interference destructive, leading to zero joint detection probability for small detector separations. This effect is referred to as antibunching of fermions [Henny, 1999]. The above treatment also explains photon antibunching [Kimble, 1977]: if the source consists of a single atom which can only emit one photon at a time, simultaneous detection in two closely spaced detectors is clearly impossible. Antibunching, whether of bosons or of fermions, has no classical wave analog.
From the point of view of the field of quantum optics, the HBT effect was important to lead physicists (among them Roy J. Glauber
Roy J. Glauber
Roy Jay Glauber is an American theoretical physicist. He is the Mallinckrodt Professor of Physics at Harvard University and Adjunct Professor of Optical Sciences at the University of Arizona...
and Leonard Mandel
Leonard Mandel
Leonard Mandel was the Lee DuBridge Professor Emeritus of Physics and Optics at the University of Rochester when he died at the age of 73 at his home in Pittsford, New York. He contributed immensely to theoretical and experimental optics...
) to apply quantum electrodynamics to new situations, many of which had never been experimentally studied, and in which classical and quantum predictions differ.
See also
- Timeline of electromagnetism and classical opticsTimeline of electromagnetism and classical opticsTimeline of electromagnetism and classical optics*424 BC Aristophanes "lens" is a glass globe filled with water....
- Degree of coherence
- Bose–Einstein correlations
External links
- http://adsabs.harvard.edu//full/seri/JApA./0015//0000015.000.html
- http://physicsweb.org/articles/world/15/10/6/1
- http://www.du.edu/~jcalvert/astro/starsiz.htm
- http://www.2physics.com/2010/11/hanbury-brown-and-twiss-interferometry.html