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Photon antibunching generally refers to a light field with photons more equally spaced than a coherent laser field, a signature being a measured two-time correlation suppressed below that of a coherent laser field. More specifically, it can refer to sub-Poissonian photon statistics, that is a photon number distribution for which the variance is less than the mean. A coherent state, as output by a laser far above threshold, has Poissonian statistics yielding random photon spacing; while a thermal light field has super-Poissonian statistics and yields bunched photon spacing. In the thermal (bunched) case, the number of fluctuations is larger than a coherent state; for an antibunched source they are smaller.


Explanation

The variance of the photon number distribution is : V_n=\langle \Delta n^2\rangle=\langle n^2\rangle-\langle n\rangle^2= \left\langle \left(a^a\right)^2\right\rangle-\langle a^a\rangle ^2. Using commutation relations, this can be written as : V_n=\langle )^2a^2 \rangle+\langle a^a\rangle-\langle a^a\rangle ^2. This can be written as : V_n-\langle n\rangle=\langle (a^\dagger)^2 a^2\rangle -\langle a^a\rangle^2. The second-order intensity
correlation function A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables ...
(for zero delay time) is defined as : g^(0)=. This quantity is basically the probability of detecting two simultaneous photons, normalized by the probability of detecting two photons at once for a random photon source. Here and after we assume stationary counting statistics. Then we have : (V_n-\langle n\rangle) =g^(0)-1. Then we see that sub-Poisson photon statistics, one definition of photon antibunching, is given by g^(0) < 1. We can equivalently express antibunching by Q< 0 where the Mandel Q parameter is defined as : Q\equiv \frac-1. If the field had a classical stochastic process underlying it, say a positive definite probability distribution for photon number, the variance would have to be greater than or equal to the mean. This can be shown by an application of the Cauchy–Schwarz inequality to the definition of g^(0). Sub-Poissonian fields violate this, and hence are nonclassical in the sense that there can be no underlying positive definite probability distribution for photon number (or intensity). Photon antibunching by this definition was first proposed by Carmichael and Walls and first observed by Kimble, Mandel, and Dagenais in
resonance fluorescence Resonance fluorescence is the process in which a two-level atom system interacts with the quantum electromagnetic field if the field is driven at a frequency near to the natural frequency Natural frequency, measured in terms of '' eigenfreque ...
. A driven atom cannot emit two photons at once, and so in this case g^(0)=0. An experiment with more precision that did not require subtraction of a background count rate was done for a single atom in an ion trap by Walther et al. A more general definition for photon antibunching concerns the slope of the correlation function away from zero time delay. It can also be shown by an application of the
Cauchy–Schwarz inequality The Cauchy–Schwarz inequality (also called Cauchy–Bunyakovsky–Schwarz inequality) is an upper bound on the absolute value of the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is ...
to the time dependent intensity
correlation function A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables ...
: g^(\tau)=. It can be shown that for a classical positive definite probability distribution to exist (i.e. for the field to be classical) g^(\tau) \leq g^(0). Hence a rise in the second order intensity correlation function at early times is also nonclassical. This initial rise is photon antibunching. Another way of looking at this time dependent correlation function, inspired by quantum trajectory theory is : g^(\tau)= where : \langle O \rangle_C \equiv \langle \Psi_C , O, \Psi_C\rangle. with , \Psi_C\rangle is the state conditioned on previous detection of a photon at time \tau=0.


Experiments

Spatial antibunching has been observed in photon pairs produced by
spontaneous parametric down-conversion Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence or parametric scattering) is a nonlinear instant optical process that converts one photon of higher energy (namely, a ''pump'' photon) into a pair of photons (name ...
. {{cite journal , last1=Nogueira , first1=W. A. T. , last2=Walborn , first2=S. P. , last3=P\'adua , first3=S., last4=Monken , first4=C. H. , title=Generation of a Two-Photon Singlet Beam , journal=Phys. Rev. Lett. , date=30 January 2004 , volume=92 , issue=4 , page=043602 , doi=10.1103/PhysRevLett.92.043602, pmid=14995372 , arxiv=quant-ph/0503117 , bibcode=2004PhRvL..92d3602N , s2cid=25022990


See also

*
Degree of coherence In quantum optics, correlation functions are used to characterize the statistical and Coherence (physics), coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or ...
*
Fock state In quantum mechanics, a Fock state or number state is a quantum state that is an element of a Fock space with a well-defined number of particles (or quanta). These states are named after the Soviet physicist Vladimir Fock. Fock states play an im ...
* Hong–Ou–Mandel effect *
Hanbury Brown and Twiss effect In physics, the Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation and anti-correlation effects in the intensity (physics), intensities received by two detectors from a beam of particles. HBT effects can generally be attribut ...
*
Squeezed coherent state In physics, a squeezed coherent state is a quantum state that is usually described by two non-commuting observables having continuous spectra of eigenvalues. Examples are position x and momentum p of a particle, and the (dimension-less) electr ...


Sources

* Article based on text fro
Qwiki
reproduced under the
GNU Free Documentation License The GNU Free Documentation License (GNU FDL or GFDL) is a copyleft license for free documentation, designed by the Free Software Foundation (FSF) for the GNU Project. It is similar to the GNU General Public License, giving readers the rights ...
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Photon Antibunching
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References


External links


Photon antibunching
(Becker & Hickl GmbH, web page) Quantum optics