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

Journal of Physics A Mathematical and General

Exact stationary photon distributions due to competition between one- and two-photon absorption and emission

V. V. Dodonov, Salomon Sylvain Mizrahi

Published Aug 21, 1997• 33 citations
Publisher

Abstract

We consider steady states of the one-mode quantized field interacting with two independent baths, each characterized by the one- and two-photon absorption and emission processes. In the absense of two-photon emission, using an exact analytical solution to the master equation for the diagonal elements of the density matrix in the Fock basis in terms of the confluent hypergeometric function, we obtain simple explicit expressions for the photon distribution function and for the factorial moments in the limiting cases of weak and strong two-photon absorption. If the two-photon absorption is strong enough, the steady state exhibits a sub-Poissonian photon statistics characterizing nonclassical behaviour, but Mandel's -parameter cannot be less . However, the distribution depends essentially on the temperature of the `one-photon bath'. For weak two-photon absorption, the stationary distribution is Gaussian, provided that the temperature of the `one-photon' bath is high enough. For an inversely populated `one-photon' bath, the -parameter is close to . In a generic case of nonzero two-photon emission probability, approximate asymptotic expressions for the factorial moments are found.

DOI
10.1088/0305-4470/30/16/010

Related papers

Competition between one- and two-photon absorption processes

V. V. Dodonov, Salomon Sylvain Mizrahi

We obtain an exact analytical solution to the master equation for the diagonal density matrix elements of the one-mode quantized field, when both one- and two-photon absorption processes are present. Explicit expressions for the time dependences of the factorial moments are found. The special cases of the initial Fock's, binomial, negative binomial, thermal, and coherent states, as well as of their even/odd counterparts are considered in detail. The existence of the universal time-dependent distribution of initially highly excited states is discovered, and simple explicit expressions are given for some specific values of parameters. This distribution holds for times exceeding the transition time of the order of , , being the two-photon absorption coefficient and the initial mean photon number, respectively. The transition time from any initial state to the ground state is shown to be finite even for highly excited states, provided that . Although the final stage of evolution is characterized by the sub-Poissonian statistics for any initial state, Mandel's parameter is shown to be very sensitive to small differences in high-order initial factorial moments at the intermediate stage.

Journal of Physics A Mathematical and General•May 7, 1997•13 citations

Stationary States in Saturated Two-Photon Processes and Generation of Phase-Averaged Mixtures of Even and Odd Quantum States

V. V. Dodonov, Salomon Sylvain Mizrahi

We consider a relaxation of a single mode of the quantized field in a presence of one- and two-photon absorption and emission processes. Exact stationary solutions of the master equation for the diagonal elements of the density matrix in the Fock basis are found in the case of completely saturated two-photon emission. If two-photon processes dominate over single-photon ones, the stationary state is a mixture of phase averaged even and odd coherent states.

arXiv:quant-ph/9811031•Acta Physica Slovaca Reviews and Tutorials•Nov 13, 1998•3 citations

A master equation approach to nonlinear optics

K. J. McNeil, Daniel F. Walls

The nonlinear interaction of light with matter is described from a quantum-statistical point of view. The phenomena of two-photon emission and two-photon absorption including both the single- and two-mode cases and the Raman effect are discussed in detail. A master equation for the density operator of the light fields alone is derived. This operator equation is converted to a c number equation and analytic solutions are obtained for the diagonal matrix elements of the density operator in the Fock representation. No linearizing approximation is introduced. These solutions allow one to compute the moments of the photon distribution for the above nonlinear processes.

Journal of Physics A Mathematical Nuclear and General•Mar 21, 1974•96 citations

Quantum statistics of double-beam two-photon absorption

H D Simaan, R. Loudon

The process of two-photon absorption from two beams of light is treated theoretically. Expressions are derived for the time dependences of the joint photon probability distribution of the beams, their photon-number factorial moments and the photon-number correlation between the beams. These expressions are illustrated by numerical results for special cases and their significance is discussed in physical terms. Simpler approximate expressions are also derived for the case where one beam is much more intense than the other.

Journal of Physics A Mathematical and General•Jul 1, 1975•31 citations

Aspects of the degenerate two-photon laser

S∅ren Bay, M. Elk, P. Lambropoulos

This paper presents new results on aspects of the two-photon laser. A semiclassical investigation of threshold behaviour reveals that the atom-field coupling is already so strong at threshold that a non-perturbative treatment of the dynamics is necessary. A master equation is derived on the basis of an effective Hamiltonian generalized in that it includes the effect of an overall two-photon detuning, the effect of ionization of the upper atomic level and the effect of dynamic Stark shifts. From the diagonal elements of the master equation, a Fokker-Planck equation is obtained and shown to yield a general analytical expression for the photon distribution which is found to simplify considerably in special cases. The agreement with the result obtained through numerical solution of the master equation itself is very good. It is further shown that a detuning from two-photon resonance and a significant Stark shift lead to sub-Poissonian statistics. Finally, time-dependent solutions for the photon distribution under an injected coherent state are presented.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 28, 1995•10 citations

Quantum statistics of light after two-photon absorption and emission processest

Salvatore Carusotto

Two-photon absorption and emission for a collection of two level atoms from a single mode beam of light are considered and the statistical proper- ties of the field after the interaction are investigated without placing any restriction of the population of the atomic levels . The dynamical behaviour of the field is described by assuming the atomic levels maintained with a nearly fixed popula- tion distribution . By applying iteration methods the time development for the density operator of the field is written and an expression for the coherent component is obtained . This component appears to be present only when there is a coherent component in the field before the interaction . The statistical properties of the field after the interaction, when the mean photon number is large initially, are then discussed and explicit calculations are carried out for some special cases of initial fields . Finally, it is shown that two-photon spontaneous emission field can be expressed as a superposition of chaotic fields .

•Jan 1, 1980•1 citation
We consider steady states of the one-mode quantized field interacting with two independent baths, each characterized by the one- and two-photon absorption and emission processes. In the absense of two-photon emission, using an exact analytical solution to the master equation for the diagonal elements of the density matrix in the Fock basis in terms of the confluent hypergeometric function, we obtain simple explicit expressions for the photon distribution function and for the factorial moments in the limiting cases of weak and strong two-photon absorption. If the two-photon absorption is strong enough, the steady state exhibits a sub-Poissonian photon statistics characterizing nonclassical behaviour, but Mandel's -parameter cannot be less . However, the distribution depends essentially on the temperature of the one-photon bath'. For weak two-photon absorption, the stationary distribution is Gaussian, provided that the temperature of the one-photon' bath is high enough. For an inversely populated `one-photon' bath, the -parameter is close to . In a generic case of nonzero two-photon emission probability, approximate asymptotic expressions for the factorial moments are found.
We obtain an exact analytical solution to the master equation for the diagonal density matrix elements of the one-mode quantized field, when both one- and two-photon absorption processes are present. Explicit expressions for the time dependences of the factorial moments are found. The special cases of the initial Fock's, binomial, negative binomial, thermal, and coherent states, as well as of their even/odd counterparts are considered in detail. The existence of the universal time-dependent distribution of initially highly excited states is discovered, and simple explicit expressions are given for some specific values of parameters. This distribution holds for times exceeding the transition time of the order of , , being the two-photon absorption coefficient and the initial mean photon number, respectively. The transition time from any initial state to the ground state is shown to be finite even for highly excited states, provided that . Although the final stage of evolution is characterized by the sub-Poissonian statistics for any initial state, Mandel's parameter is shown to be very sensitive to small differences in high-order initial factorial moments at the intermediate stage.
The nonlinear interaction of light with matter is described from a quantum-statistical point of view. The phenomena of two-photon emission and two-photon absorption including both the single- and two-mode cases and the Raman effect are discussed in detail. A master equation for the density operator of the light fields alone is derived. This operator equation is converted to a c number equation and analytic solutions are obtained for the diagonal matrix elements of the density operator in the Fock representation. No linearizing approximation is introduced. These solutions allow one to compute the moments of the photon distribution for the above nonlinear processes.
The process of two-photon absorption from two beams of light is treated theoretically. Expressions are derived for the time dependences of the joint photon probability distribution of the beams, their photon-number factorial moments and the photon-number correlation between the beams. These expressions are illustrated by numerical results for special cases and their significance is discussed in physical terms. Simpler approximate expressions are also derived for the case where one beam is much more intense than the other.
This paper presents new results on aspects of the two-photon laser. A semiclassical investigation of threshold behaviour reveals that the atom-field coupling is already so strong at threshold that a non-perturbative treatment of the dynamics is necessary. A master equation is derived on the basis of an effective Hamiltonian generalized in that it includes the effect of an overall two-photon detuning, the effect of ionization of the upper atomic level and the effect of dynamic Stark shifts. From the diagonal elements of the master equation, a Fokker-Planck equation is obtained and shown to yield a general analytical expression for the photon distribution which is found to simplify considerably in special cases. The agreement with the result obtained through numerical solution of the master equation itself is very good. It is further shown that a detuning from two-photon resonance and a significant Stark shift lead to sub-Poissonian statistics. Finally, time-dependent solutions for the photon distribution under an injected coherent state are presented.
Two-photon absorption and emission for a collection of two level atoms from a single mode beam of light are considered and the statistical proper- ties of the field after the interaction are investigated without placing any restriction of the population of the atomic levels . The dynamical behaviour of the field is described by assuming the atomic levels maintained with a nearly fixed popula- tion distribution . By applying iteration methods the time development for the density operator of the field is written and an expression for the coherent component is obtained . This component appears to be present only when there is a coherent component in the field before the interaction . The statistical properties of the field after the interaction, when the mean photon number is large initially, are then discussed and explicit calculations are carried out for some special cases of initial fields . Finally, it is shown that two-photon spontaneous emission field can be expressed as a superposition of chaotic fields .