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

Physical Review A

Photon statistics of second-harmonic generation in a gaseous system

N. Nayak, B. K. Mohanty

Published Mar 1, 1977• 15 citations
Publisher

Abstract

Second-harmonic generation in a degenerate two-level gaseous system is considered with atomic motion taken into account. The diagonal elements of the dipole matrix are assumed to be present. We find the photon statistics of the second-harmonic field to be considerably influenced by the detuning in the two-photon absorption. The threshold condition is discussed. We obtain the average second-harmonic photon number and thus calculate the dimensionless intensity parameter. The output variance of the second-harmonic field is discussed.

DOI
10.1103/physreva.15.1173

Related papers

Quantum theory of third-harmonic generation in a gaseous system - Part I

N. Nayak

We present a theoretical treatment for third-harmonic generation in gaseous systems by describing the atomic system as well as the radiation field quantum mechanically. The atomic system is represented by two energy levels. The effects of detuning in the two-photon interactions and the atomic motion on the third-harmonic generation are taken into account. The photon statistics of the third-harmonic field are obtained. The average photon number, second-order coherence, and output variance of the third-harmonic field are discussed. The above results show a nonlinear dependence on the detuning in the two-photon interactions and the Doppler parameter.

IEEE Journal of Quantum Electronics•Aug 1, 1980•6 citations

Quantum Statistics of Stimulated Raman Effect in a Gaseous System

B. K. Mohanty, N. Nayak, Partha Sarathi Gupta

A quantum mechanical treatment of stimulated Raman effect in a gaseous system is presented. The atomic system is described by a two-level system. The radiation fields also obey the laws of quantum mechanics. The effects of atomic motion and the detuning in one-photon absorption and two-photon emission are incorporated in the analysis. The equation of motion describing the photon-statistics of all the fields are obtained. As a special case, the time evolution of the average photon number, second order coherence and output variance of the Stokes field is studied. The results show a non-linear dependence on the parameters representing atomic motion, detuning and atomic relaxation constants.

Optica Acta International Journal of Optics•Aug 1, 1982•6 citations

Quantum theory of third-harmonic generation in a gaseous system - Part II

N. Nayak

In Part I [1], we presented a quantum theory of third-harmonic generation (THG) under two-photon absorption in a two-level atomic medium. We studied the time evolution of the third-harmonic field and its coherence properties by neglecting the depletion of the pump power. In this paper we extend the theory by taking the depletion of pump power into account. The density matrix for the third-harmonic field is derived. The study of the growth rate of the density matrix in time shows the quantum mechanical effects more clearly. The effects of detuning in the two-photon interactions and atomic motion are pointed out. The results are compared with the earlier results and differences are brought out.

IEEE Journal of Quantum Electronics•Feb 1, 1982•2 citations

Nonlinear quantum effects in optics

Daniel F. Walls, C. T. Tindle

Nonlinear optical effects where quantum mechanical predictions are at variance with the results of classical calculations are studied. Certain initial conditions, those of unstable equilibrium or those that lead to unstable equilibrium, classically, give rise to an aperiodicity in the intensity of the emitted radiation. One example of such a system is second-harmonic generation, which is studied in detail because of the potential amenability of the aperiodicity to experimental observation. Numerical and analytic predictions for the evolution of the intensity and photon statistics of the second harmonic light are presented. The photon statistics of the second harmonic light are predicted to undergo a sharp transition following the first maximum of the intensity.

Journal of physics. A, Proceedings of the Physical Society. General•Apr 1, 1972•76 citations

Optical properties of degenerate atomic gases

Janne Ruostekoski

We study interactions of light with a sample of two-level atoms. Quantum statistical effects of degenerate boson and fermion gases are described by using the quantum field theory of atom-photon interactions, fully including the angular momentum degeneracies. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated.^ In the limit of large atom-field detuning, multiple scattering of light and QED linewidths and line shifts may be ignored, and the propagation equations of light and matter fields may be decoupled. A general expression for the spectrum of the scattered light is derived, complete with the dependence on atomic level scheme, on various light polarizations, and on the geometry of the experiment. With these simplifications we are able to find distinct qualitative features in the spectrum of the scattered light in the case of both fermions and bosons that depend on the statistics of atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).^ As the driving light gets closer to the atomic resonance, multiple scattering and vacuum fluctuations of the electromagnetic fields should also be taken into account. We write the equations of motion for the excited state field operators by eliminating the vacuum electromagnetic field. It is always assumed that the driving external laser field is in the coherent state. We find in the limit of low light intensity, a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, two, three, etc., ground state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for the coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of non-cooperative atoms by presenting a mathematical example in which this approach is exact. ^

•Jan 1, 1996•0 citations

Measurements of photon statistics in second-harmonic generation

Yujiang Qu, Surendra Singh

Statistical properties of second-harmonic photons generated by a single-mode laser operating near threshold are investigated by means of photoelectric counting measurements. It is found that second-harmonic photons display superthermal fluctuations below threshold where pump statistics are thermal. Above threshold, as the pump field becomes coherent, second-harmonic photons approach Poisson statistics. These measurements, interpreted as two-photon statistics of the fundamental beam, provide experimental evidence for the dependence of the fluctuation properties of a light beam on the process of detection.

Physical Review A•Mar 1, 1995•17 citations
Second-harmonic generation in a degenerate two-level gaseous system is considered with atomic motion taken into account. The diagonal elements of the dipole matrix are assumed to be present. We find the photon statistics of the second-harmonic field to be considerably influenced by the detuning in the two-photon absorption. The threshold condition is discussed. We obtain the average second-harmonic photon number and thus calculate the dimensionless intensity parameter. The output variance of the second-harmonic field is discussed.
We present a theoretical treatment for third-harmonic generation in gaseous systems by describing the atomic system as well as the radiation field quantum mechanically. The atomic system is represented by two energy levels. The effects of detuning in the two-photon interactions and the atomic motion on the third-harmonic generation are taken into account. The photon statistics of the third-harmonic field are obtained. The average photon number, second-order coherence, and output variance of the third-harmonic field are discussed. The above results show a nonlinear dependence on the detuning in the two-photon interactions and the Doppler parameter.
A quantum mechanical treatment of stimulated Raman effect in a gaseous system is presented. The atomic system is described by a two-level system. The radiation fields also obey the laws of quantum mechanics. The effects of atomic motion and the detuning in one-photon absorption and two-photon emission are incorporated in the analysis. The equation of motion describing the photon-statistics of all the fields are obtained. As a special case, the time evolution of the average photon number, second order coherence and output variance of the Stokes field is studied. The results show a non-linear dependence on the parameters representing atomic motion, detuning and atomic relaxation constants.
In Part I [1], we presented a quantum theory of third-harmonic generation (THG) under two-photon absorption in a two-level atomic medium. We studied the time evolution of the third-harmonic field and its coherence properties by neglecting the depletion of the pump power. In this paper we extend the theory by taking the depletion of pump power into account. The density matrix for the third-harmonic field is derived. The study of the growth rate of the density matrix in time shows the quantum mechanical effects more clearly. The effects of detuning in the two-photon interactions and atomic motion are pointed out. The results are compared with the earlier results and differences are brought out.
Nonlinear optical effects where quantum mechanical predictions are at variance with the results of classical calculations are studied. Certain initial conditions, those of unstable equilibrium or those that lead to unstable equilibrium, classically, give rise to an aperiodicity in the intensity of the emitted radiation. One example of such a system is second-harmonic generation, which is studied in detail because of the potential amenability of the aperiodicity to experimental observation. Numerical and analytic predictions for the evolution of the intensity and photon statistics of the second harmonic light are presented. The photon statistics of the second harmonic light are predicted to undergo a sharp transition following the first maximum of the intensity.
We study interactions of light with a sample of two-level atoms. Quantum statistical effects of degenerate boson and fermion gases are described by using the quantum field theory of atom-photon interactions, fully including the angular momentum degeneracies. Coupled propagation equations are given for light and matter fields, and plausible general simplifications are enumerated.^ In the limit of large atom-field detuning, multiple scattering of light and QED linewidths and line shifts may be ignored, and the propagation equations of light and matter fields may be decoupled. A general expression for the spectrum of the scattered light is derived, complete with the dependence on atomic level scheme, on various light polarizations, and on the geometry of the experiment. With these simplifications we are able to find distinct qualitative features in the spectrum of the scattered light in the case of both fermions and bosons that depend on the statistics of atoms. This is because for bosons (fermions), those scattering events in which an atom recoils to an already occupied state are enhanced (inhibited).^ As the driving light gets closer to the atomic resonance, multiple scattering and vacuum fluctuations of the electromagnetic fields should also be taken into account. We write the equations of motion for the excited state field operators by eliminating the vacuum electromagnetic field. It is always assumed that the driving external laser field is in the coherent state. We find in the limit of low light intensity, a hierarchy of equations of motion for correlation functions that contain one excited-atom field and one, two, three, etc., ground state atom fields. It is conjectured that the entire linear hierarchy may be solved by solving numerically the classical equations for the coupled system of electromagnetic fields and charged harmonic oscillators. We discuss the emergence of resonant dipole-dipole interactions and collective linewidths, and delineate the limits of validity of the column density approach in terms of non-cooperative atoms by presenting a mathematical example in which this approach is exact. ^
Statistical properties of second-harmonic photons generated by a single-mode laser operating near threshold are investigated by means of photoelectric counting measurements. It is found that second-harmonic photons display superthermal fluctuations below threshold where pump statistics are thermal. Above threshold, as the pump field becomes coherent, second-harmonic photons approach Poisson statistics. These measurements, interpreted as two-photon statistics of the fundamental beam, provide experimental evidence for the dependence of the fluctuation properties of a light beam on the process of detection.