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

IEEE MTT-S International Microwave Symposium digest

Multiple Quantum Frequency Conversion in Extended Interaction Structures

Douglas J. Scalapino, A. Vassiliadis, Robert N. Wilson

Published Jan 1, 1964• 0 citations
Publisher

Abstract

In 1959, E. T. Jaynes suggested that resonant, multiquantum processes could provide an efficient method of frequency conversion at high frequency and high powers. This conversion is mediated by a gas or solid composed of molecules having a strong electric-dipole absorption at a frequency /spl Omega/. Such a system can resonantly absorb energy from an electromagnetic field at all odd subharmonic of /spl Omega/. The /spl omega/ /spl ap/ /spl Omega/ /(2n + 1) subharmonic absorption is said to correspond to a 2n + 1 quantum process. The excited (driven) molecular system has electric dipole moments at all odd harmonics of the drive /spl omega/. The resonant dipole moment at a frequency (2n + 1)/spl omega/ /spl ap/ /spl Omega/ generates an electromagnetic field resulting in the frequency conversion process proposed by Jaynes. Here we report theoretical calculations and experimental observation of this multiquantum frequency conversion in a traveling-wave structure.

DOI
10.1109/ptgmtt.1964.1122433

Related papers

Multiple quantum frequency conversion

Douglas J. Scalapino, A. Vassiliadis, Robert N. Wilson

A molecular system having two energy levels separated by\hbar\Omegaand coupled to an electromagnetic field by a transition dipole moment will resonantly absorb energy at all odd sub-harmonics of the energy level separation\omega =\Omega,\Omega/3,\Omega/5.... These correspond to 1, 3, 5,... quantum absorption processes. Part of this absorbed energy is emitted back into the field at harmonics of\omegaand part is dissipated into the lattice degrees of freedom. It is therefore possible to drive the molecular system with a field of frequency\omega \approx \Omega/m(n odd), and obtain radiation at a frequencym\omega \approx \Omega. Here we present results of a theoretical study of these resonant multi-quantum conversion processes. Two characteristic regions of operation are predicted: one previously discussed by Fontana, Pantell and Smith3in which the molecular efficiency\varepsilon= (power converted ton \omega)/ (power abosrbed at\omega) =\frac{1}{2}under conditions of maximum power converted per unit volume; and another region (not previously reported) in which maximum power conversion per unit volume can occur with molecular efficiencies approaching unity.

IRE International Convention Record•Jan 1, 1964•1 citation

High harmonic generation induced by permanent dipole moments

Óscar G. Calderón, R. Gutiérrez-Castrejón, J.M. Guerra

The interaction between radiation and a two-level molecular system in the presence of permanent dipole moments is analyzed. It is found that the nonzero difference between permanent dipoles induces a polarization that oscillates at frequencies /spl omega/, 2/spl omega/, 3/spl omega/, etc., where /spl omega/ is the frequency of the electromagnetic field resonant with the two-level system. An analysis of the propagation equation of the harmonics shows that even harmonics are amplified while odd harmonics are absorbed.

IEEE Journal of Quantum Electronics•Jan 1, 1999•22 citations

Multiquantum electron paramagnetic resonance transitions excited in a two-level system by tetrachromatic microwave irradiation

Małgorzata Jeleń, Wojciech Froncisz

A method to excite multiquantum transitions in a two-level system by application of continuous irradiation with a four-frequency microwave field is presented. The generated signal is composed of many intermodulation sidebands at different frequencies, which arise from the multiquantum transitions. These processes involve an odd number of photons, that are absorbed from, or emitted to two, three, or four fields. The correspondence between the frequency spectrum of the signal and possible pathways of multiquantum processes is found with recourse to the many mode Floquet theory. The reported experiments demonstrate the multiquantum origin of the detected intermodulation sidebands and their properties.

The Journal of Chemical Physics•Dec 1, 1998•8 citations

Raman frequency mixing under coherent population trapping conditions

Vasily G. Arkhipkin, Д. В. Манушкин, S. A. Myslivets +1 more

An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.

Quantum Electronics•Jul 31, 1998•7 citations

Quantum Optics. III. Two-Frequency Interactions

I. R. Senitzky

A large number of "molecules," which are taken to be angular momentum oscillators of frequency $\ensuremath{\nu}$, are considered to interact through their dipole moment with two electromagnetic cavity modes of frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$, respectively, where $\ensuremath{\nu}={\ensuremath{\omega}}_{1}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}_{2}$. The behavior of the combined system is analyzed up to fourth order in perturbation theory. Phenomena known as two-photon emission or absorption, parametric amplification, various types of Raman emission, and frequency conversion are exhibited. The analytical method used is applicable to both a quantum-mechanical and a classical description of the modes and molecules; it displays explicitly the resulting differences. Expressions for the rate of energy change of the modes and molecules indicate resonance in second and fourth order. The second-order results are the same for the classical and quantum-mechanical treatments, while the fourth-order results show certain differences, which are examined in detail. The conditions under which each of the above phenomena occurs are discussed in a self-consistent manner, both classically and quantum-mechanically. It is shown that the second-order expression and the most significant part of the fourth-order expression can be derived very simply from a resonance interaction Hamiltonian that consists of a sum of products of three variables---two referring to the two modes, and the third to the molecules. The relationship between this resonance Hamiltonian and the fundamental dipole-moment Hamiltonian is examined, and the approximations by which the resonance Hamiltonian may be derived are considered. Arguments concerning the applicability of perturbation theory to steady-state situations are presented; it is pointed out that the second-order expressions for the energy transfer between molecules and field may be applicable to such a situation, in which case the classical and quantum-mechanical treatments are equivalent.

Physical Review•Jul 25, 1969•6 citations

Level splitting effects in CW resonant four-wave mixing

Sergei A Babin, S.I. Kalukov, U. Hinze +2 more

Summary form only given. Various schemes of resonant frequency conversion using four-wave mixing (FWM) have been investigated recently. For example, sum-frequency FWM in Hg atoms has been used for generation of CW radiation at 121.56 nm, corresponding to the Lyman-/spl alpha/ line of hydrogen and efficient difference frequency mixing has been demonstrated in double-/spl Lambda/ level configurations of Na/sub 2/ molecules. We present novel investigations on the resonance structure of the FWM-spectra in the case of up-conversion in a double-/spl Lambda/ scheme realized in Na/sub 2/.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Nov 11, 2002•0 citations
In 1959, E. T. Jaynes suggested that resonant, multiquantum processes could provide an efficient method of frequency conversion at high frequency and high powers. This conversion is mediated by a gas or solid composed of molecules having a strong electric-dipole absorption at a frequency /spl Omega/. Such a system can resonantly absorb energy from an electromagnetic field at all odd subharmonic of /spl Omega/. The /spl omega/ /spl ap/ /spl Omega/ /(2n + 1) subharmonic absorption is said to correspond to a 2n + 1 quantum process. The excited (driven) molecular system has electric dipole moments at all odd harmonics of the drive /spl omega/. The resonant dipole moment at a frequency (2n + 1)/spl omega/ /spl ap/ /spl Omega/ generates an electromagnetic field resulting in the frequency conversion process proposed by Jaynes. Here we report theoretical calculations and experimental observation of this multiquantum frequency conversion in a traveling-wave structure.
A molecular system having two energy levels separated by\hbar\Omegaand coupled to an electromagnetic field by a transition dipole moment will resonantly absorb energy at all odd sub-harmonics of the energy level separation\omega =\Omega,\Omega/3,\Omega/5.... These correspond to 1, 3, 5,... quantum absorption processes. Part of this absorbed energy is emitted back into the field at harmonics of\omegaand part is dissipated into the lattice degrees of freedom. It is therefore possible to drive the molecular system with a field of frequency\omega \approx \Omega/m(n odd), and obtain radiation at a frequencym\omega \approx \Omega. Here we present results of a theoretical study of these resonant multi-quantum conversion processes. Two characteristic regions of operation are predicted: one previously discussed by Fontana, Pantell and Smith3in which the molecular efficiency\varepsilon= (power converted ton \omega)/ (power abosrbed at\omega) =\frac{1}{2}under conditions of maximum power converted per unit volume; and another region (not previously reported) in which maximum power conversion per unit volume can occur with molecular efficiencies approaching unity.
The interaction between radiation and a two-level molecular system in the presence of permanent dipole moments is analyzed. It is found that the nonzero difference between permanent dipoles induces a polarization that oscillates at frequencies /spl omega/, 2/spl omega/, 3/spl omega/, etc., where /spl omega/ is the frequency of the electromagnetic field resonant with the two-level system. An analysis of the propagation equation of the harmonics shows that even harmonics are amplified while odd harmonics are absorbed.
A method to excite multiquantum transitions in a two-level system by application of continuous irradiation with a four-frequency microwave field is presented. The generated signal is composed of many intermodulation sidebands at different frequencies, which arise from the multiquantum transitions. These processes involve an odd number of photons, that are absorbed from, or emitted to two, three, or four fields. The correspondence between the frequency spectrum of the signal and possible pathways of multiquantum processes is found with recourse to the many mode Floquet theory. The reported experiments demonstrate the multiquantum origin of the detected intermodulation sidebands and their properties.
An investigation is reported of resonant four-wave frequency mixing of the type ω 4 =ω 1 —ω 2 +ω 3 under coherent population trapping conditions. Such mixing may appear when radiations of frequencies ω 1,2 are strong and when ω 1 —ω 2 =ω 20 (ω 20 is the frequency of a dipole-forbidden transition). The density matrix method is used to calculate (taking quantum interference into account) the absorption coefficients, the refractive indices, and the nonlinear susceptibilities exactly for the strong fields and in the first order of perturbation theory for the weak fields. A study is made of the dependence of the power of nonlinear optical generation on various characteristics of the transitions and of the radiation, subject to the propagation effects. The cases of homogeneous and Doppler broadening of the resonant transitions are considered. The characteristics of transitions in the barium atom are used in numerical illustrations. It is shown that the efficiency of resonant nonlinear-optical conversion of radiation can be enhanced by utilising interference processes in quantum transitions, which represent coherent population trapping.
A large number of "molecules," which are taken to be angular momentum oscillators of frequency $\ensuremath{\nu}$, are considered to interact through their dipole moment with two electromagnetic cavity modes of frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$, respectively, where $\ensuremath{\nu}={\ensuremath{\omega}}_{1}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\omega}}_{2}$. The behavior of the combined system is analyzed up to fourth order in perturbation theory. Phenomena known as two-photon emission or absorption, parametric amplification, various types of Raman emission, and frequency conversion are exhibited. The analytical method used is applicable to both a quantum-mechanical and a classical description of the modes and molecules; it displays explicitly the resulting differences. Expressions for the rate of energy change of the modes and molecules indicate resonance in second and fourth order. The second-order results are the same for the classical and quantum-mechanical treatments, while the fourth-order results show certain differences, which are examined in detail. The conditions under which each of the above phenomena occurs are discussed in a self-consistent manner, both classically and quantum-mechanically. It is shown that the second-order expression and the most significant part of the fourth-order expression can be derived very simply from a resonance interaction Hamiltonian that consists of a sum of products of three variables---two referring to the two modes, and the third to the molecules. The relationship between this resonance Hamiltonian and the fundamental dipole-moment Hamiltonian is examined, and the approximations by which the resonance Hamiltonian may be derived are considered. Arguments concerning the applicability of perturbation theory to steady-state situations are presented; it is pointed out that the second-order expressions for the energy transfer between molecules and field may be applicable to such a situation, in which case the classical and quantum-mechanical treatments are equivalent.
Summary form only given. Various schemes of resonant frequency conversion using four-wave mixing (FWM) have been investigated recently. For example, sum-frequency FWM in Hg atoms has been used for generation of CW radiation at 121.56 nm, corresponding to the Lyman-/spl alpha/ line of hydrogen and efficient difference frequency mixing has been demonstrated in double-/spl Lambda/ level configurations of Na/sub 2/ molecules. We present novel investigations on the resonance structure of the FWM-spectra in the case of up-conversion in a double-/spl Lambda/ scheme realized in Na/sub 2/.