Operators' s-parameterized ordering and its classical correspondence in quantum optics theory
Fan Hong-Yi(范洪义)a), Yuan Hong-Chun(袁洪春)a)†, and Hu Li-Yun(胡利云)b)
a Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China; b College of Physics and Communication Electronics, Jiangxi Normal University, Nanchang 330022, China
Abstract In reference to the Weyl ordering , where X and P are coordinate and momentum operator, respectively, this paper examines operators' s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence and its complementary relation , where Hm,n is the two-variable Hermite polynomial, are bosonic annihilation and creation operators respectively, s is a complex parameter. The s'-ordered operator power-series expansion of s-ordered operator in terms of the two-variable Hermite polynomial is also derived. Application of operators' s-ordering formula in studying displaced-squeezed chaotic field is discussed.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10874174).
Cite this article:
Fan Hong-Yi(范洪义), Yuan Hong-Chun(袁洪春), and Hu Li-Yun(胡利云) Operators' s-parameterized ordering and its classical correspondence in quantum optics theory 2010 Chin. Phys. B 19 104204
[1]
Mandel L and Wolf E 1995 Optical Coherence and Quan-tum Optics (Cambridge: Cambridge University Press)
[2]
Scully M O and Zubairy M S 1997 Quamtum Optics(Cambridge: Cambridge University Press)
[3]
Orszag M 2000 Quantum Optics (Berlin: Springer-Verlag)
[4]
Fan H Y and Lu C H 2009 Opt. Commun. 282 4741
[5]
Cahill K E and Glauber R J 1969 Phys. Rev. 177 1857
[6]
Cahill K E and Glauber R J 1969 Phys. Rev. 177 1882
[7]
Fan H Y 2010 Chin. Phys. B 19 050303
[8]
Fan H Y, Hu L Y and Yuan H C 2010 Chin. Phys. B 19 060305
[9]
Weyl H 1927 Z. Phys. 46 1
[10]
Weyl H 1953 The Classical Groups (Princeton: Princeton University Press)
[11]
Wigner E P 1932 Phys. Rev. 40 749
[12]
Schleich W P 2001 Quantum Optics in Phase Space (New York: Wiley-VCH)
[13]
Klauder J R and Skargerstam B S 1985 Coherent States(Singapore: World Scienti c)
[14]
Glauber R J 1963 Phys. Rev. 131 2766
[15]
Erdelyi A 1953 Higher Transcendental Functions(McGraw-Hill: The Batemann Manuscript Project)
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
, where X and P are coordinate and momentum operator, respectively, this paper examines operators' s-parameterized ordering and its classical correspondence, finds the fundamental function-operator correspondence 
and its complementary relation 
, where Hm,n is the two-variable Hermite polynomial, 
are bosonic annihilation and creation operators respectively, s is a complex parameter. The s'-ordered operator power-series expansion of s-ordered operator 
in terms of the two-variable Hermite polynomial is also derived. Application of operators' s-ordering formula in studying displaced-squeezed chaotic field is discussed.