Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optica Acta International Journal of Optics

A Canonical Model of Optical Up-conversion with Stochastic Pumping

S. K. Srinivasan

Published Jul 1, 1984• 0 citations
Publisher

Abstract

The frequency up-conversion process with a (classical) stochastic coupling is studied on the basis of canonical equations. Exact results for the number operators and the correlation functions (with zero time-lag) are extracted from the equations by the use of Ito-McShane calculus. The results indicate the absence of antibunching, at least for zero time-delay.

DOI
10.1080/713821569

Related papers

Canonical Extension of a Problem in Parametric Frequency Up-conversion with Stochastic Pumping

S. K. Srinivasan, S. Udayabaskaran

A canonical model for the frequency up-conversion process with stochastic coupling function is proposed. Based on it the first-order coherence functions, the time dependence of the mean photon numbers and the second-order coherence functions are found and compared with the corresponding results already available in the literature. It is shown that the total photon number, as a function of time, has a turning point. The antibunching effect is predicted regardless of the mean photon numbers available in the process.

Optica Acta International Journal of Optics•Dec 1, 1979•9 citations

An Exactly Soluble Model of Optical Up-conversion with Stochastic Pumping

W. J. Mielniczuk

The frequency up-conversion process with the stochastic coupling function is considered. The stochastic coupling function is assumed to be ‘quasi-completely’ random. The mean photon number in both modes and second-order correlation functions for delay time equal to zero are exactly calculated.

Optica Acta International Journal of Optics•Sep 1, 1979•5 citations

Photon statistics of optical frequency up-conversion with stochastic pumping

S Kryszewski, Jacek Chrostowski

The frequency up-conversion process with stochastic coupling function is considered. It is shown that the total photon number increases with time. The antibunching effect (g (2) <1) is predicted regardless of the mean photon numbers available in the process.

Journal of Physics A Mathematical and General•Dec 1, 1977•12 citations

Incoherent effects in the optical up-conversion process

W. J. Mielniczuk, Jacek Chrostowski

The theoretical treatment of the optical frequency up-conversion process with stochastic pumping is presented. This process consists of exchange of photons between two modes of different frequencies. It is assumed that the two modes are coupled by a short memory stochastic function. Statistically averaged occupation numbers of both modes were calculated exactly by means of the theory of multiplicative stochastic processes. The obtained nonperturbative solution sums secular terms and is valid for arbitrary times. The oscillatory-damped nature of the exchange of energy between two modes and the role of partial incoherence of the pump is discussed. It is shown that stochastic coupling causes the equipartition of energy between two modes for sufficiently long times. Analogies between an up-converter and a two-level atom driven by a single mode electromagnetic field are indicated. Optical Bloch equations for an up-conversion process are derived.

Physical Review A•Mar 1, 1981•10 citations

Canonical transformations and multipartite coupled parametric processes

Timur Tlyachev, Alexander Mikhailovich Chebotarev, A. S. Chirkin

A general approach is considered to find wave function and density operator evolution of the systems including the arbitrary number of coupled optical parametric interactions described by the quadratic Hamiltonian. This approach is based on the time-dependent canonical transformations that define the evolution of the system in the Heisenberg picture or in the interaction picture. An application is illustrated with four-frequency entangled light fields, which can be produced at the nonlinear optical interactions in vapors and solid states. The process includes one non-degenerate parametric down-conversion followed by two parametric up-conversions occurring in the field of the same classical pumping wave.

Physica Scripta•Apr 1, 2014•9 citations

Parametric down and up conversion in the Wigner representation of quantum optics

K. Dechoum, Trevor W. Marshall, Emilio Santos

We study spontaneous parametric processes starting from the quantized field equations in the Heisenberg picture using the common approximation of treating the laser pump as classical. After a (standard) linearization procedure we pass to the Wigner representation and the process becomes formally equivalent to the parametric interaction of two incoming zero-point modes with a pumping laser wave coupled by an optically nonlinear medium. Then the treatment of parametric down conversion and parametric up conversion are described by the Maxwell equations and look like a parametric amplification of the vacuum field. The fourth-order correlation function between the signal and idler fields is obtained in a form that makes for easy comparison with experimental results.

Journal of Modern Optics•Jun 1, 2000•25 citations
The frequency up-conversion process with a (classical) stochastic coupling is studied on the basis of canonical equations. Exact results for the number operators and the correlation functions (with zero time-lag) are extracted from the equations by the use of Ito-McShane calculus. The results indicate the absence of antibunching, at least for zero time-delay.
A canonical model for the frequency up-conversion process with stochastic coupling function is proposed. Based on it the first-order coherence functions, the time dependence of the mean photon numbers and the second-order coherence functions are found and compared with the corresponding results already available in the literature. It is shown that the total photon number, as a function of time, has a turning point. The antibunching effect is predicted regardless of the mean photon numbers available in the process.
The theoretical treatment of the optical frequency up-conversion process with stochastic pumping is presented. This process consists of exchange of photons between two modes of different frequencies. It is assumed that the two modes are coupled by a short memory stochastic function. Statistically averaged occupation numbers of both modes were calculated exactly by means of the theory of multiplicative stochastic processes. The obtained nonperturbative solution sums secular terms and is valid for arbitrary times. The oscillatory-damped nature of the exchange of energy between two modes and the role of partial incoherence of the pump is discussed. It is shown that stochastic coupling causes the equipartition of energy between two modes for sufficiently long times. Analogies between an up-converter and a two-level atom driven by a single mode electromagnetic field are indicated. Optical Bloch equations for an up-conversion process are derived.
A general approach is considered to find wave function and density operator evolution of the systems including the arbitrary number of coupled optical parametric interactions described by the quadratic Hamiltonian. This approach is based on the time-dependent canonical transformations that define the evolution of the system in the Heisenberg picture or in the interaction picture. An application is illustrated with four-frequency entangled light fields, which can be produced at the nonlinear optical interactions in vapors and solid states. The process includes one non-degenerate parametric down-conversion followed by two parametric up-conversions occurring in the field of the same classical pumping wave.
We study spontaneous parametric processes starting from the quantized field equations in the Heisenberg picture using the common approximation of treating the laser pump as classical. After a (standard) linearization procedure we pass to the Wigner representation and the process becomes formally equivalent to the parametric interaction of two incoming zero-point modes with a pumping laser wave coupled by an optically nonlinear medium. Then the treatment of parametric down conversion and parametric up conversion are described by the Maxwell equations and look like a parametric amplification of the vacuum field. The fourth-order correlation function between the signal and idler fields is obtained in a form that makes for easy comparison with experimental results.