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454:{\displaystyle Q={\frac {\left\langle (\Delta {\hat {n}})^{2}\right\rangle -\langle {\hat {n}}\rangle }{\langle {\hat {n}}\rangle }}={\frac {\langle {\hat {n}}^{(2)}\rangle -\langle {\hat {n}}\rangle ^{2}}{\langle {\hat {n}}\rangle }}-1=\langle {\hat {n}}\rangle \left(g^{(2)}(0)-1\right)}
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194:. It is a convenient way to characterize non-classical states with negative values indicating a sub-Poissonian statistics, which have no classical analog. It is defined as the normalized variance of the boson distribution:
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Negative values of Q corresponds to state which variance of photon number is less than the mean (equivalent to sub-Poissonian statistics). In this case, the
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641:{\displaystyle -1\leq Q<0\Leftrightarrow 0\leq \langle (\Delta {\hat {n}})^{2}\rangle \leq \langle {\hat {n}}\rangle }
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729:. The resulting occupation distribution of the number state is characterized by a
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Mandel, L. (1979). "Sub-Poissonian photon statistics in resonance fluorescence".
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distribution cannot be interpreted as a classical probability distribution.
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is the normalized second-order correlation function as defined by
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measures the departure of the occupation number distribution from
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have a
Poissonian photon-number statistics for which
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may be too technical for most readers to understand
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867:"The Quantum Theory of Optical Coherence"
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166:Learn how and when to remove this message
148:Learn how and when to remove this message
132:, without removing the technical details.
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915:Optical Coherence and Quantum Optics
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758:{\displaystyle Q=\langle n\rangle }
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706:{\displaystyle \Delta n=0}
486:{\displaystyle {\hat {n}}}
892:10.1103/PhysRev.130.2529
865:Glauber, Roy J. (1963).
731:Bose–Einstein statistics
523:{\displaystyle g^{(2)}}
186:. It was introduced in
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673:{\displaystyle Q=-1}
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790:{\displaystyle Q=0}
538:Non-classical value
82:disambiguation page
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544:phase space
943:R. Loudon
801:References
733:for which
138:April 2014
94:April 2014
36:improve it
931:L. Mandel
901:0031-899X
844:0146-9592
753:⟩
747:⟨
692:Δ
665:−
636:⟩
630:^
621:⟨
618:≤
615:⟩
599:^
590:Δ
584:⟨
581:≤
575:⇔
563:≤
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478:^
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255:⟨
252:−
231:^
222:Δ
86:talk page
78:splitting
42:talk page
955:Category
852:19687850
727:Gaussian
717:Examples
248:⟩
215:⟨
935:E. Wolf
879:Bibcode
824:Bibcode
532:Glauber
493:is the
464:where
124:Please
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848:PMID
840:ISSN
721:For
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