MOMENT HIERARCHIES AND CUMULANTS IN QUANTUM OPTICS

被引:43
作者
SCHACK, R [1 ]
SCHENZLE, A [1 ]
机构
[1] MAX PLANCK INST QUANTUM OPT, W-8046 GARCHING, GERMANY
来源
PHYSICAL REVIEW A | 1990年 / 41卷 / 07期
关键词
D O I
10.1103/PhysRevA.41.3847
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Nonlinear problems in quantum optics can be described by an infinite hierarchy of ordinary differential equations for the moments. We discuss different truncation schemes involving cumulants. For illustration the method is applied to second-harmonic generation. We prove that all but second-order cumulants are equal for any quasiprobability distribution Ps, especially for the P, Q, and W functions. © 1990 The American Physical Society.
引用
收藏
页码:3847 / 3852
页数:6
相关论文
共 18 条
[1]  
[Anonymous], 1984, SPRINGER SERIES SYNE
[2]   PHOTON STATISTICS OF A BISTABLE ABSORBER [J].
BONIFACIO, R ;
GRONCHI, M ;
LUGIATO, LA .
PHYSICAL REVIEW A, 1978, 18 (05) :2266-2279
[3]   BIFURCATIONS AND THE POSITIVE P-REPRESENTATION [J].
DORFLE, M ;
SCHENZLE, A .
ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1986, 65 (01) :113-131
[4]   GENERALIZED P-REPRESENTATIONS IN QUANTUM OPTICS [J].
DRUMMOND, PD ;
GARDINER, CW .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1980, 13 (07) :2353-2368
[5]   NONEQUILIBRIUM TRANSITIONS IN SUB-2ND HARMONIC-GENERATION .2. QUANTUM-THEORY [J].
DRUMMOND, PD ;
MCNEIL, KJ ;
WALLS, DF .
OPTICA ACTA, 1981, 28 (02) :211-225
[6]   CARLEMAN IMBEDDING OF MULTIPLICATIVE STOCHASTIC-PROCESSES [J].
GRAHAM, R ;
SCHENZLE, A .
PHYSICAL REVIEW A, 1982, 25 (03) :1731-1754
[7]   SHELL EFFECTS IN THE MASS-TRANSPORT DURING HEAVY-ION COLLISIONS [J].
GROSSMANN, S .
ZEITSCHRIFT FUR PHYSIK A-HADRONS AND NUCLEI, 1980, 296 (03) :251-262
[8]   On a property of Gauss's law [J].
Marcinkiewicz, J .
MATHEMATISCHE ZEITSCHRIFT, 1939, 44 :612-618
[9]   SERIES EXPANSION OF DISTRIBUTION FUNCTIONS IN MULTICOMPONENT FLUID SYSTEMS [J].
MEERON, E .
JOURNAL OF CHEMICAL PHYSICS, 1957, 27 (06) :1238-1246
[10]   ANALYTICAL THEORIES OF TURBULENCE [J].
ORSZAG, SA .
JOURNAL OF FLUID MECHANICS, 1970, 41 :363-&