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- Optical_equivalence_theorem abstract "The optical equivalence theorem in quantum optics asserts an equivalence between the expectation value of an operator in Hilbert space and the expectation value of its associated function in the phase space formulation with respect to a quasiprobability distribution. The theorem was first reported by George Sudarshan in 1963 for normally ordered operators and generalized later that decade to any ordering. Let Ω be an ordering of the non-commutative creation and annihilation operators, and let be an operator that is expressible as a power series in the creation and annihilation operators that satisfies the ordering Ω. Then the optical equivalence theorem is succinctly expressed asHere, α is understood to be the eigenvalue of the annihilation operator on a coherent state and is replaced formally in the power series expansion of g. The left side of the above equation is an expectation value in the Hilbert space whereas the right hand side is an expectation value with respect to the quasiprobability distribution. We may write each of these explicitly for better clarity. Let be the density operator and be the ordering reciprocal to Ω. The quasiprobability distribution associated with Ω is given, at least formally, byThe above framed equation becomesFor example, let Ω be the normal order. This means that g can be written in a power series of the following form:The quasiprobability distribution associated with the normal order is the Glauber-Sudarshan P representation. In these terms, we arrive atThis theorem implies the formal equivalence between expectation values of normally ordered operators in quantum optics and the corresponding complex numbers in classical optics.".
- Optical_equivalence_theorem wikiPageID "5906036".
- Optical_equivalence_theorem wikiPageRevisionID "499123044".
- Optical_equivalence_theorem hasPhotoCollection Optical_equivalence_theorem.
- Optical_equivalence_theorem subject Category:Physics_theorems.
- Optical_equivalence_theorem subject Category:Quantum_optics.
- Optical_equivalence_theorem type Abstraction100002137.
- Optical_equivalence_theorem type Communication100033020.
- Optical_equivalence_theorem type Message106598915.
- Optical_equivalence_theorem type PhysicsTheorems.
- Optical_equivalence_theorem type Proposition106750804.
- Optical_equivalence_theorem type Statement106722453.
- Optical_equivalence_theorem type Theorem106752293.
- Optical_equivalence_theorem comment "The optical equivalence theorem in quantum optics asserts an equivalence between the expectation value of an operator in Hilbert space and the expectation value of its associated function in the phase space formulation with respect to a quasiprobability distribution. The theorem was first reported by George Sudarshan in 1963 for normally ordered operators and generalized later that decade to any ordering.".
- Optical_equivalence_theorem label "Optical equivalence theorem".
- Optical_equivalence_theorem sameAs m.0fcx45.
- Optical_equivalence_theorem sameAs Q7098850.
- Optical_equivalence_theorem sameAs Q7098850.
- Optical_equivalence_theorem sameAs Optical_equivalence_theorem.
- Optical_equivalence_theorem wasDerivedFrom Optical_equivalence_theorem?oldid=499123044.
- Optical_equivalence_theorem isPrimaryTopicOf Optical_equivalence_theorem.