Photon antibunching: Difference between revisions
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{{More citations needed|date=May 2008}} |
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[[File:Photon bunching.svg|thumb|Photon detections as a function of time for a) antibunching (e.g. light emitted from a single atom), b) random (e.g. a coherent state, laser beam), and c) bunching (chaotic light). τ<sub>c</sub> is the coherence time (the time scale of photon or intensity fluctuations).]] |
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'''Photon antibunching''' generally refers to a light field with photons more equally spaced than a coherent laser field,<ref>Anti-bunching and Entanglement - http://www.ucd.ie/speclab/UCDSOPAMS/peoplehtml/quantumoptics2006/lecture5.pdf</ref> a signature being |
'''Photon antibunching''' generally refers to a light field with photons more equally spaced than a coherent laser field,<ref>Anti-bunching and Entanglement - https://web.archive.org/web/20110615173635/http://www.ucd.ie/speclab/UCDSOPAMS/peoplehtml/quantumoptics2006/lecture5.pdf</ref> 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 [[Poisson distribution|Poissonian]] statistics yielding random photon spacing; while a [[Black-body radiation|thermal light]] field has [[super-Poissonian]] statistics and yields bunched photon spacing. In the thermal [[Hanbury Brown and Twiss effect|(bunched) case]], the number of fluctuations is larger than a coherent state; for an antibunched source they are smaller.<ref>{{cite journal | last = Paul | first = H | year = 1982 | title = Photon antibunching | journal = Reviews of Modern Physics | volume = 54 | pages = 1061–1102 | doi = 10.1103/RevModPhys.54.1061 | bibcode=1982RvMP...54.1061P | issue = 4}}</ref> |
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==Explanation== |
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The variance of the photon number distribution is |
The variance of the photon number distribution is |
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</math> |
</math> |
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Then we see that sub-Poisson photon statistics, one definition of photon antibunching, is given by <math> |
Then we see that sub-Poisson photon statistics, one definition of photon antibunching{{clarify|date=December 2022}}, is given by <math> |
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g^{(2)}(0) < 1</math>. We can equivalently express antibunching by <math>Q< 0</math> where the [[Mandel Q |
g^{(2)}(0) < 1</math>. We can equivalently express antibunching by <math>Q< 0</math> where the [[Mandel Q parameter]] is defined as |
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: <math> |
: <math> |
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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 <math>g^{(2)}(0)</math>. 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). |
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 <math>g^{(2)}(0)</math>. 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). |
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Photon antibunching by this definition was first observed by [[H. Jeff Kimble|Kimble]], [[Leonard Mandel|Mandel]], and Dagenais in [[resonance fluorescence]]. A driven atom cannot emit two photons at once, and so in this case <math>g^{(2)}(0)= |
Photon antibunching by this definition was first proposed by Carmichael and Walls<ref>H. J. Carmichael and D. F. Walls, A Quantum-Mechanical Master Equation Treatment of the Dynamical Stark Effect, J. Phys. B: Atom. Mol. Phys. 9, 1199 (1976).</ref> and first observed by [[H. Jeff Kimble|Kimble]], [[Leonard Mandel|Mandel]], and Dagenais in [[resonance fluorescence]]. A driven atom cannot emit two photons at once, and so in this case <math>g^{(2)}(0)=0</math>. 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. |
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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]] to the time dependent intensity [[Degree of coherence|correlation function]] |
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]] to the time dependent intensity [[Degree of coherence|correlation function]] |
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</math> |
</math> |
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It can be shown that for a classical positive definite probability distribution to exist (i.e. for the field to be classical) <math>g^{(2)}(\tau) \leq g^{(2)}(0)</math>.<ref>{{cite journal | |
It can be shown that for a classical positive definite probability distribution to exist (i.e. for the field to be classical) <math>g^{(2)}(\tau) \leq g^{(2)}(0)</math>.<ref>{{cite journal | last1 = Zou | first1 = X T | last2 = Mandel | first2 = L | year = 1990 | title = Photon-antibunching and sub-Poissonian photon statistics | journal = Phys. Rev. A | volume = 41 | pages = 475–476 | doi = 10.1103/PhysRevA.41.475 | issue = 1 | pmid=9902890| bibcode = 1990PhRvA..41..475Z }}</ref> Hence a rise in the second order intensity correlation function at early times is also nonclassical. This initial rise is photon antibunching. |
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Another way of looking at this time dependent correlation function, inspired by quantum trajectory theory is |
Another way of looking at this time dependent correlation function, inspired by quantum trajectory theory is |
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with <math>|\Psi_C\rangle</math> is the state conditioned on previous detection of a photon at time <math>\tau=0</math>. |
with <math>|\Psi_C\rangle</math> is the state conditioned on previous detection of a photon at time <math>\tau=0</math>. |
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== |
==Experiments== |
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Spatial antibunching has been observed in photon pairs produced by [[spontaneous parametric down-conversion]]. <ref>{{cite journal |last1=Nogueira |first1=W. A. T. |last2=Walborn |first2=S. P.|last3=P\'adua |first3=S.|last4=Monken |first4=C. H. |title=Experimental Observation of Spatial Antibunching of Photons |journal=Phys. Rev. Lett. |date=30 April 2001 |volume=86 |issue=18 |pages=4009–4012 |doi=10.1103/PhysRevLett.86.4009|pmid=11328082 |arxiv=quant-ph/0206039 |bibcode=2001PhRvL..86.4009N |s2cid=25655506 }}</ref><ref>{{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 }}</ref> |
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{{reflist|4}}Chandra, Naresh, and Hari Prakash. "Anticorrelation in two-photon attenuated laser beam." Physical Review A 1.6 (1970): 1696. |
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== See also == |
== See also == |
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* [[Hanbury Brown and Twiss effect]] |
* [[Hanbury Brown and Twiss effect]] |
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* [[Squeezed coherent state]] |
* [[Squeezed coherent state]] |
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== Sources == |
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⚫ | * <small>Article based on text from [https://web.archive.org/web/20080603152249/http://qwiki.stanford.edu/wiki/Main_Page Qwiki], reproduced under the [[GNU Free Documentation License]]: see [https://web.archive.org/web/20080317040903/http://qwiki.stanford.edu/wiki/Photon_Antibunching Photon Antibunching]</small> |
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<references /> |
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==External links== |
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*[https://www.becker-hickl.com/applications/antibunching-experiments/ Photon antibunching] (Becker & Hickl GmbH, web page) |
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[[Category:Quantum optics]] |
[[Category:Quantum optics]] |
Latest revision as of 08:01, 25 June 2024
This article needs additional citations for verification. (May 2008) |
Photon antibunching generally refers to a light field with photons more equally spaced than a coherent laser field,[1] 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.[2]
Explanation
[edit]The variance of the photon number distribution is
Using commutation relations, this can be written as
This can be written as
The second-order intensity correlation function (for zero delay time) is defined as
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
Then we see that sub-Poisson photon statistics, one definition of photon antibunching[clarification needed], is given by . We can equivalently express antibunching by where the Mandel Q parameter is defined as
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 . 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[3] and first observed by Kimble, Mandel, and Dagenais in resonance fluorescence. A driven atom cannot emit two photons at once, and so in this case . 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 to the time dependent intensity correlation function
It can be shown that for a classical positive definite probability distribution to exist (i.e. for the field to be classical) .[4] 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
where
with is the state conditioned on previous detection of a photon at time .
Experiments
[edit]Spatial antibunching has been observed in photon pairs produced by spontaneous parametric down-conversion. [5][6]
See also
[edit]- Correlation does not imply causation
- Degree of coherence
- Fock state
- Hong–Ou–Mandel effect
- Hanbury Brown and Twiss effect
- Squeezed coherent state
Sources
[edit]- Article based on text from Qwiki, reproduced under the GNU Free Documentation License: see Photon Antibunching
References
[edit]- ^ Anti-bunching and Entanglement - https://web.archive.org/web/20110615173635/http://www.ucd.ie/speclab/UCDSOPAMS/peoplehtml/quantumoptics2006/lecture5.pdf
- ^ Paul, H (1982). "Photon antibunching". Reviews of Modern Physics. 54 (4): 1061–1102. Bibcode:1982RvMP...54.1061P. doi:10.1103/RevModPhys.54.1061.
- ^ H. J. Carmichael and D. F. Walls, A Quantum-Mechanical Master Equation Treatment of the Dynamical Stark Effect, J. Phys. B: Atom. Mol. Phys. 9, 1199 (1976).
- ^ Zou, X T; Mandel, L (1990). "Photon-antibunching and sub-Poissonian photon statistics". Phys. Rev. A. 41 (1): 475–476. Bibcode:1990PhRvA..41..475Z. doi:10.1103/PhysRevA.41.475. PMID 9902890.
- ^ Nogueira, W. A. T.; Walborn, S. P.; P\'adua, S.; Monken, C. H. (30 April 2001). "Experimental Observation of Spatial Antibunching of Photons". Phys. Rev. Lett. 86 (18): 4009–4012. arXiv:quant-ph/0206039. Bibcode:2001PhRvL..86.4009N. doi:10.1103/PhysRevLett.86.4009. PMID 11328082. S2CID 25655506.
- ^ Nogueira, W. A. T.; Walborn, S. P.; P\'adua, S.; Monken, C. H. (30 January 2004). "Generation of a Two-Photon Singlet Beam". Phys. Rev. Lett. 92 (4): 043602. arXiv:quant-ph/0503117. Bibcode:2004PhRvL..92d3602N. doi:10.1103/PhysRevLett.92.043602. PMID 14995372. S2CID 25022990.
External links
[edit]- Photon antibunching (Becker & Hickl GmbH, web page)