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

Soviet Journal of Quantum Electronics

Parametric processes in a system of three-level atoms

G. G. Adonts, L. M. Kocharyan, N. V. Shakhnazaryan

Published Jul 31, 1975• 0 citations
Publisher

Abstract

A theoretical investigation is made of four-photon parametric interactions in a medium composed of threelevel atoms. The presence of the third level, associated with the doublet splitting of the excited state, gives rise to new regions of exponential parametric amplification. A study is made of the change in the value of the gain and its spectral range due to variation of the frequency of a strong wave participating in the parametric interaction.

DOI
10.1070/qe1975v005n07abeh011416

Related papers

Four-wave parametric interactions in a strongly driven two-level system

Robert W. Boyd, Michael G. Raymer, Paul Narum +1 more

We present an analysis of four-wave parametric amplification resulting from the nonlinear response of a two-level atomic system. The atomic dipole moment induced by weak optical fields at frequencies ${\ensuremath{\omega}}_{3}$ and ${\ensuremath{\omega}}_{4}$ in the presence of an optical field of arbitrary intensity at frequency ${\ensuremath{\omega}}_{1}$, where ${\ensuremath{\omega}}_{3}+{\ensuremath{\omega}}_{4}=2{\ensuremath{\omega}}_{1}$, is obtained by solving the density-matrix equations of motion with phenomenological damping constants. The resulting nonlinear polarization can induce loss or three-photon gain in either weak wave and can act to parametrically couple these waves. The spatial evolution of the weak-field amplitudes is obtained by finding approximate solutions to the Helmholtz wave equations using the nonlinear polarization for the source terms. These solutions predict large gain for either or both of the weak waves under experimentally attainable conditions. Depending on the circumstance, this gain can be attributed solely to the three-photon gain, solely to the parametric coupling, or to an interplay between these effects. In addition, the solutions show an enhancement in the gain when $|{\ensuremath{\omega}}_{3}\ensuremath{-}{\ensuremath{\omega}}_{1}|=|{\ensuremath{\omega}}_{4}\ensuremath{-}{\ensuremath{\omega}}_{1}|={\ensuremath{\Omega}}^{\ensuremath{'}}$, where ${\ensuremath{\Omega}}^{\ensuremath{'}}$ is the generalized Rabi frequency associated with the driving of the atoms by the wave at frequency ${\ensuremath{\omega}}_{1}$.

Physical Review A•Jul 1, 1981•404 citations

Transient stimulated four-photon parametric scattering in the case of pumping with adiabatic pulses

Б. В. Крыжановский

A theoretical investigation is made of stimulated four-photon parametric scattering in a medium of two-level atoms pumped by high-intensity ultrashort pulses. A simple dependence of the gain on the phase mismatch, pumping duration, and length of the interaction region is obtained. The spectral and angular distributions of the scattered radiation are considered and the features of these distributions associated with the transient nature of the process are discussed.

Soviet Journal of Quantum Electronics•Jul 31, 1987•3 citations

Resonant parametric amplification in four-level systems

U. Hinze, Boris N. Chichkov, B. Wellegehausen

Summary form only given. Resonant four-wave mixing with continuous laser fields has recently gained new interest, because of quantum interference effects that allow to manipulate and control the properties of the nonlinear medium. In this contribution we report on new experimental and theoretical investigations of four-wave mixing and parametric amplification in a resonantly driven double-A scheme as shown. As a nonlinear medium Na/sub 2/-molecules produced in a sodium heat pipe at a typical operation temperature of 720 K are used. In this scheme Raman gain on the 2-3 transition plays an important role and can result in exponential growth of the generated signal intensity at /spl lambda//sub 4/=480 nm in spite of absorption on the 4-1 transition (due to the "gain transfer"). This allows to achieve very high conversion efficiencies into the signal field.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•0 citations

Optical Amplification due to Parametric Interaction of Four Waves with a Four-Level System

Motowo Tsukakoshi

Four-wave parametric interactions in a four-level system are treated using semiclassical theory. Line-shape functions for a weak probe field and three resonant pump fields are presented and are evaluated numerically in a model case of equalized interaction energies and relaxation rates. For sufficiently intense pump fields, the line shape splits into five peaks, and negative absorption, i.e. amplification, occurs in some frequency regions of the probe field.

Japanese Journal of Applied Physics•Jul 1, 1982•1 citation

Strong amplification of sidebands in a four-level atomic system interacting with a strong bichromatic field

Constantine Mavroyannis

We have studied the fluorescent spectra arising from the interaction of a four-level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states \ensuremath{\Vert}3〉 and \ensuremath{\Vert}4〉 and two lower states \ensuremath{\Vert}1〉 and \ensuremath{\Vert}2〉 and the two laser fields, whose frequency modes ${\ensuremath{\omega}}_{a}$ and ${\ensuremath{\omega}}_{b}$ are initially populated, operate between the states \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}4〉 and \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}3〉, respectively. Using the Green-function formalism and a model Hamiltonian, where all the free and interacting fields are quantized, we have studied the transitions \ensuremath{\Vert}4〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 and \ensuremath{\Vert}3〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 of the signal field in the limit of high photon densities of both laser fields. The expression of the spectral function for the \ensuremath{\Vert}1〉\ensuremath{\rightarrow}\ensuremath{\Vert}4〉 transition describes stimulated one-photon and three-photon processes, respectively. The one-photon spectra near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$ of the signal field consist of a central peak and two pairs of sidebands whose intensities take always positive and negative values indicating that attenuation and amplification (stimulated emission) of the signal field takes place at the frequencies in question, respectively. The spectral function for the three-photon process near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$-2${\ensuremath{\omega}}_{a}$ describes two pairs of sidebands whose intensities are always negative implying that strong amplification of the signal field occurs. The computed one-photon and three-photon spectra are presented graphically for different values of Rabi frequencies and detunings of both laser fields, respectively. Then using a classical description of both laser fields, the spectral functions describing one-photon and three-photon processes are calculated and the derived results are compared with the corresponding ones when the fields are quantized. It is found that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical as well as the quantum nature of the photons which is lost in the classical treatment.

Physical Review A•Mar 1, 1985•5 citations

Resonant four-wave mixing and parametric amplification in a double-Λ level scheme

U. Hinze, Boris N. Chichkov, E. Tiemann +1 more

Summary form only given. Double-/spl Lambda/ level schemes offer rich possibilities to study the non-linear interaction of continuous resonant radiation fields with multi-level systems. Efficient four-wave mixing with up- and down-conversion has been demonstrated previously. We report on theoretical and experimental investigations related to four-wave difference-frequency mixing and parametric amplification. As a nonlinear medium Na/sub 2/ molecules produced in a sodium heatpipe are used.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Nov 11, 2002•0 citations
A theoretical investigation is made of four-photon parametric interactions in a medium composed of threelevel atoms. The presence of the third level, associated with the doublet splitting of the excited state, gives rise to new regions of exponential parametric amplification. A study is made of the change in the value of the gain and its spectral range due to variation of the frequency of a strong wave participating in the parametric interaction.
We present an analysis of four-wave parametric amplification resulting from the nonlinear response of a two-level atomic system. The atomic dipole moment induced by weak optical fields at frequencies ${\ensuremath{\omega}}_{3}$ and ${\ensuremath{\omega}}_{4}$ in the presence of an optical field of arbitrary intensity at frequency ${\ensuremath{\omega}}_{1}$, where ${\ensuremath{\omega}}_{3}+{\ensuremath{\omega}}_{4}=2{\ensuremath{\omega}}_{1}$, is obtained by solving the density-matrix equations of motion with phenomenological damping constants. The resulting nonlinear polarization can induce loss or three-photon gain in either weak wave and can act to parametrically couple these waves. The spatial evolution of the weak-field amplitudes is obtained by finding approximate solutions to the Helmholtz wave equations using the nonlinear polarization for the source terms. These solutions predict large gain for either or both of the weak waves under experimentally attainable conditions. Depending on the circumstance, this gain can be attributed solely to the three-photon gain, solely to the parametric coupling, or to an interplay between these effects. In addition, the solutions show an enhancement in the gain when $|{\ensuremath{\omega}}_{3}\ensuremath{-}{\ensuremath{\omega}}_{1}|=|{\ensuremath{\omega}}_{4}\ensuremath{-}{\ensuremath{\omega}}_{1}|={\ensuremath{\Omega}}^{\ensuremath{'}}$, where ${\ensuremath{\Omega}}^{\ensuremath{'}}$ is the generalized Rabi frequency associated with the driving of the atoms by the wave at frequency ${\ensuremath{\omega}}_{1}$.
Summary form only given. Resonant four-wave mixing with continuous laser fields has recently gained new interest, because of quantum interference effects that allow to manipulate and control the properties of the nonlinear medium. In this contribution we report on new experimental and theoretical investigations of four-wave mixing and parametric amplification in a resonantly driven double-A scheme as shown. As a nonlinear medium Na/sub 2/-molecules produced in a sodium heat pipe at a typical operation temperature of 720 K are used. In this scheme Raman gain on the 2-3 transition plays an important role and can result in exponential growth of the generated signal intensity at /spl lambda//sub 4/=480 nm in spite of absorption on the 4-1 transition (due to the "gain transfer"). This allows to achieve very high conversion efficiencies into the signal field.
We have studied the fluorescent spectra arising from the interaction of a four-level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states \ensuremath{\Vert}3〉 and \ensuremath{\Vert}4〉 and two lower states \ensuremath{\Vert}1〉 and \ensuremath{\Vert}2〉 and the two laser fields, whose frequency modes ${\ensuremath{\omega}}_{a}$ and ${\ensuremath{\omega}}_{b}$ are initially populated, operate between the states \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}4〉 and \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}3〉, respectively. Using the Green-function formalism and a model Hamiltonian, where all the free and interacting fields are quantized, we have studied the transitions \ensuremath{\Vert}4〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 and \ensuremath{\Vert}3〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 of the signal field in the limit of high photon densities of both laser fields. The expression of the spectral function for the \ensuremath{\Vert}1〉\ensuremath{\rightarrow}\ensuremath{\Vert}4〉 transition describes stimulated one-photon and three-photon processes, respectively. The one-photon spectra near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$ of the signal field consist of a central peak and two pairs of sidebands whose intensities take always positive and negative values indicating that attenuation and amplification (stimulated emission) of the signal field takes place at the frequencies in question, respectively. The spectral function for the three-photon process near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$-2${\ensuremath{\omega}}_{a}$ describes two pairs of sidebands whose intensities are always negative implying that strong amplification of the signal field occurs. The computed one-photon and three-photon spectra are presented graphically for different values of Rabi frequencies and detunings of both laser fields, respectively. Then using a classical description of both laser fields, the spectral functions describing one-photon and three-photon processes are calculated and the derived results are compared with the corresponding ones when the fields are quantized. It is found that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical as well as the quantum nature of the photons which is lost in the classical treatment.