Deriving some quantum optical identities using the general ordering theorem

Farid Shähandeh, M. R. Bazrafkan, E. Nahvifard

Using the newly introduced general ordering theorem (GOT) by Shähandeh and Bazrafkan, we derive and generalize some quantum optical identities and give their applications.

Heng-Mei Li, Hong‐Chun Yuan

Nanrun Zhou, Gong Li-Hua, Jia Fang +1 more

On the basis of the new introduced two-mode coherent entangled state representation and the technique of integration within an ordered product of operators, we derived some operator identities of the operator functions about the quadrature of two-mode optical field, such as （X1+X2）/21/2 and （μX1+νX2）/λ, which should be helpful to further studying the high order squeezing properties of optical field and to constructing some generalized-squeezed states.

Mark S. Hillery, Leonard D. Mlodinow

I. A. Aleksandrov, E. V. Perelygin, D. V. Chubukov

We develop a perturbative description of vacuum radiative processes in quantum electrodynamics with a prescribed external electromagnetic background capable of producing electron-positron pairs. Since the initial vacuum is then unstable and the in- and out-vacua are inequivalent, radiative observables require a real-time formulation beyond the ordinary in-out approach of vacuum-stable QED. Using the Keldysh-Schwinger-Fradkin nonequilibrium technique, we derive the mean number density of emitted photons through the second nonvanishing order in the fine-structure constant. The leading term, of order $α$, reproduces the known vertex and tadpole mechanisms, while the complete order-$α^2$ correction contains interference, loop, and induced-current contributions. We also give an independent derivation based on the spectral decomposition of the identity operator in the in-Fock space, where the photon number density is represented as a sum of squared transition amplitudes and vacuum-disconnected terms are canceled by the optical theorem generalized to an unstable vacuum. In addition, we compute the mean electromagnetic field through order $e^3$, including the electromagnetic dressing of the induced vacuum current, and verify it using the corresponding Schwinger-Dyson equations. The final formulas are expressed in terms of exact solutions and propagators of the Dirac equation in the external background and apply to general spacetime-dependent field configurations.

陈锋, 范洪义