aqora

New approach for anti-normally and normally ordering bosonic-operator functions in quantum optics

Shi-Min Xu, Yunhai Zhang, Xing-Lei Xu +2 more

In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f ( λ + ν ) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.In this paper, we provide a new kind of operator formula for anti-normally and normally ordering bosonic-operator functions in quantum optics, which can help us arrange a bosonic-operator function f ( λ + ν ) in its anti-normal and normal ordering conveniently. Furthermore, mutual transformation formulas between anti-normal ordering and normal ordering, which have good universality, are derived too. Based on these operator formulas, some new differential relations and some useful mathematical integral formulas are easily derived without really performing these integrations.

Chinese Physics BNov 29, 20167 citations

Deriving some quantum optical identities using the general ordering theorem

Farid Farid, Shahandeh, Mohammad +4 more

中国物理B：英文版Jan 1, 20120 citations

Ordered operator expansions by comparison

Wolfgang Witschel

Ordered operator expansions for operators forming physically important low-dimensional Lie algebras are derived in a simple unified way. Starting with the Zassenhaus formula for the disentangling of exponential operators, series expansions of both undisentangled and disentangled exponentials and comparison of the operator coefficients of equal powers of an ordering parameter alpha leads to ordered operator expansions. This 'comparison method' gives an alternative simple derivation of some already known formulae and a number of new formulae in the physical and chemical applications of the harmonic oscillator and for master equation problems with nearest-neighbour transition probabilities. The 'comparison method' cannot be applied to the angular momentum algebra directly. By a slight modification it can be used to derive from one matrix element or trace of J x k J y l J z n all possible combinations k, l, n by simply comparing powers of ordering parameters.Ordered operator expansions for operators forming physically important low-dimensional Lie algebras are derived in a simple unified way. Starting with the Zassenhaus formula for the disentangling of exponential operators, series expansions of both undisentangled and disentangled exponentials and comparison of the operator coefficients of equal powers of an ordering parameter alpha leads to ordered operator expansions. This 'comparison method' gives an alternative simple derivation of some already known formulae and a number of new formulae in the physical and chemical applications of the harmonic oscillator and for master equation problems with nearest-neighbour transition probabilities. The 'comparison method' cannot be applied to the angular momentum algebra directly. By a slight modification it can be used to derive from one matrix element or trace of J x k J y l J z n all possible combinations k, l, n by simply comparing powers of ordering parameters.

Journal of Physics A Mathematical and GeneralFeb 1, 197553 citations

Ordering of field operators and equations of motion in quantum optics

A. Lukš, Vlasta Peřinová

Czechoslovak Journal of PhysicsNov 1, 198712 citations

On arbitrary ordering of M-mode field operators in quantum optics

Jan Peřina, R. Horák

Optics CommunicationsMay 1, 19696 citations

Normally Ordering and Anti-normally Ordering Some Useful Operator Formulas in Quantum Optics Theory by Virture of the IWOP Technique

Xuefen Xu

By using the technique of integration within an ordered product(IWOP) of operators,which is proposed in Ref.[1],the paper derives the useful light-field operator formulas(in ACTA SINICA Quantum Optica,Vol.8(2002) p8-12 written by Chen Chang-yuan) in a convenient and easily be remembered way.Some other operator formulas about two-variable Hermite polynomials are also derived.

Acta Sinica Quantum OpticaJan 1, 20070 citations

Simple Approach to Deriving Some Operator Ordering Formulas in Quantum Optics

Related papers

Simple Approach to Deriving Some Operator Ordering Formulas in Quantum Optics

Related papers