About integration within ordered products in quantum optics

Time evolution of Wigner functions governed by bipartite Hamiltonian system with kinetic coupling

“…(11) and |00 00| = : exp(−a † 1 a 1 − a † 2 a 2 ) : and perfoming the integration in Eq. (10) by virtue of the IWOP technique [7,8], we obtain the normally ordered form of the Wigner operator ∆ (σ, γ)…”

“…Using the technique of integration within an ordered product of operators (IWOP) [7,8] and the vacuum projector |0 0| = : exp −a † a : ( : : denotes normal ordering), we have obtained the explicitly normal ordering form of ∆ (x, p) …”

Time Evolution of Density Operator for Field Damping in Squeezed Bath Calculated by Squeezing Transformation and Entangled State Representation

“…Using the technique of integration within an ordered product (IWOP) of operators [6][7][8][9], we can prove the completeness relation of |η ,…”

Explicit state vector for Torres-Vega–Frederick phase space representation and its statistical behavior

“…Using the normally ordered form of vacuum projector |0 0| = : exp[−a † a] : , where : : denotes normal ordering, and the technique of integration within an ordered product (IWOP) of operators [5,6], the integration in Eq. (2) can be performed, leading to the explicit operator ∆(q, p) = 1 π : e −(q−Q) 2 −(p−P )…”