The optical equivalence theorem in quantum optics

Quantum optics

Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter.- History of quantum optics :...

 says that the expectation value of any normally ordered

Normal order

In quantum field theory a product of quantum fields, or equivalently their creation and annihilation operators, is usually said to be normal ordered when all creation operators are to the left of all annihilation operators in the product. The process of putting a product into normal order is...

 function of creation and annihilation operators

Creation and annihilation operators

Creation and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator lowers the number of particles in a given state by one...

,


can be found by replacing the operators by their eigenvalues and averaging over the resulting complex number

Complex number

A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...

, using the weighting function from the Glauber-Sudarshan P-representation, .

This theorem implies the formal equivalence between expectation values of normally ordered operators in quantum optics and the corresponding complex numbers in classical optics. The theorem was derived by George Sudarshan

George Sudarshan

Ennackal Chandy George Sudarshan , also E.C.G. Sudarshan, is a prominent Indian American physicist, author, and professor at The University of Texas at Austin.-Early life:...

in 1963.