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

Optical pumping of diatomic molecules in the electronic ground state: Classical and quantum approaches

Marcis P. Auzinsh, R. Ferber

Published Mar 1, 1991• 18 citations
Publisher

Abstract

Optical pumping of the electronic ground state of molecules has been investigated under conditions of plane, elliptically, and circularly polarized light broadband excitation. The analysis has been performed assuming arbitrary angular momentum values, and applying the apparatus of polarization moments, the latter forming the coefficients in the expansion of the density matrix over irreducible tensor operators, including simplifications due to asymptotic limits for large momentum values. In addition to accounting for the external magnetic field, attention has been also given to the dynamical Stark effect arising from the absence of coincidence between the centers of the exciting line and the absorption line. An alternative classical description is also proposed using multiple moments as coefficients of the expansion of a classical quasidensity of states over spherical harmonics. The equivalence of both approaches of description in the limit of infinitely large angular moments is demonstrated, and the meaning of the origin of coherence is clarified, as well as its destruction by the magnetic field in the classical description of the system.

DOI
10.1103/physreva.43.2374

Related papers

The evolution and revival structure of angular momentum quantum wave packets

Marcis P. Auzinsh

In this paper, a coherent superposition of angular-momentum states created by absorption of polarized light by molecules is analyzed. Attention is paid to the time evolution of wave packets representing the spatial orientation of the internuclear axis of a diatomic molecule. Two examples are considered in detail. Molecules absorbing light in a permanent magnetic field experiencing the Zeeman effect and molecules absorbing light in a permanent electric field experiencing the quadratic Stark effect. In a magnetic field, we have a wave packet that evolves in time exactly as a classical dipole oscillator in a permanent magnetic field (classical-physics picture of the Zeeman effect). In the second case, we have a wave packet that goes through periodical changes of shape of the packet with revivals of the initial shape. This is pure quantum behavior. The classical motion of angular momentum in an electric field in the case of a quadratic Stark effect is known to be a periodic. Solutions obtained for wave packet evolution are briefly compared with Rydberg-state coherent wave packets and harmonic-oscillator wave packets. Zeeman and Stark effects in small molecules continuously attract the attention of researchers, theoreticians, as well as experimentalists. These investigations allow us to obtain a deeper understanding of the interaction of molecules with stationary external fields and also can be used as a practical tool to measure different molecular characteristics, such as permanent electric or magnetic dipole moments, intramolecular perturbations, etc. It is worthwhile analyzing these effects as an evolution of wave packets. All this motivates a comparison of the quantum and classical picture of Zeeman and Stark effects in molecules.PACS No.: 33.55.Be

arXiv:physics/9905019•Canadian Journal of Physics•Jan 1, 1999•6 citations

Classical description of angular-momentum motion due to optical pumping

K. A. Nasyrov

The Wigner representation of angular-momentum orientation in the classical limit on $J\ensuremath{\gg}1$ has been used to derive an equation of angular-momentum motion in the case of a closed two-level system interacting with an arbitrary polarized radiation. This equation enables us to carry out a theoretical analysis of angular-momentum motion and consider final states of the quantum system for all types of dipole transitions. We have found that in the case of a zero magnetic field in the final state of the system with $\stackrel{\ensuremath{\rightarrow}}{J}J$ or $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ optical transition, the angular momentum is directed along or opposite to the wave vector of the radiation depending on the sign of the polarization ellipsity, while for a linear polarization the angular momentum is isotropically distributed on the plane orthogonal to the polarization vector. For the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition two directions of angular momentum are possible in the final state. These directions are determined by the ellipsity of polarization. The spatial size of the final distribution of the angular momentum has been defined by the quantum uncertainty, $1/\sqrt{J},$ of the angular-momentum orientation. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ or $\stackrel{\ensuremath{\rightarrow}}{J}J,$ transition particles come into ``dark'' states while for the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition they occupy the ``brightest'' state. In the presence of a nonzero magnetic field, particles with $\stackrel{\ensuremath{\rightarrow}}{J}J$ transition have in the final state only one angular-momentum orientation, i.e., along or opposite to the direction of the magnetic field depending on the polarization ellipsity sign. For the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition both directions are possible, i.e., along and opposite to the magnetic field. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition the directions of the angular momentum form a cone around the magnetic field.

Physical Review A•Mar 7, 2001•8 citations

Resonant effects on the light emitted by a diatomic molecular gas excited by electronic bombardment: theory and possibilities

O. Nédélec, P. Baltayan

Density matrix and irreducible tensor operator formalism have been used to describe optical pumping or similar experiments by electronic excitation in an atomic gas. The authors show that this theory may be extended to diatomic molecules. Experimental possibilities are considered.

Journal of Physics B Atomic and Molecular Physics•Jul 1, 1970•0 citations

Nonlinear magneto-optical resonances for systems with J∼100 observed in K 2 molecules

Marcis P. Auzinsh, R. Ferber, Ilja Fescenko +2 more

We present the results of an experimental as well as a theoretical study of nonlinear magneto-optical resonances in diatomic potassium molecules in the electronic ground state with large values of the angular momentum quantum number $J\ensuremath{\sim}100$. At zero magnetic field, the absorption transitions are suppressed because of population trapping in the ground state due to Zeeman coherences between magnetic sublevels of this state along with depopulation pumping. The destruction of such coherences in an external magnetic field was used to study the resonances in this work. K${}_{2}$ molecules were formed in a glass cell filled with potassium metal at a temperature above 150 ${}^{\ensuremath{\circ}}$C. The cell was placed in an oven and was located in a homogeneous magnetic field B, which was scanned from 0 to 0.7 T. $Q$-type and $R$-type transitions were excited with a tunable, single-mode diode laser with a central wavelength of 660 nm. Well-pronounced nonlinear Hanle effect signals were observed in the intensities of the linearly polarized components of the laser-induced fluorescence (LIF) detected in the direction parallel to the B field with polarization vectors parallel (${I}_{\text{par}}$) and perpendicular (${I}_{\text{per}}$) to the polarization vector of the exciting laser radiation, which was orthogonal to B. The intensities of the LIF components were detected for different experimental parameters, such as laser power density and vapor temperature, in order to compare them with numerical simulations that were based on the optical Bloch equations for the density matrix. We report good agreement of our measurements with numerical simulations. Narrow, subnatural linewidth dark resonances in ${I}_{\text{per}}(B)$ were detected and explained.

arXiv:1110.1255•Physical Review A•Jan 31, 2012•5 citations

Sublevel dynamics

Dieter Suter

After the discussion of ionic solids we shift our attention to atomic vapours. Here, we discuss the dynamics of microscopic order within the angular momentum substates under the influence of light and magnetic fields. For this purpose, we combine optical pumping as outlined in Chapter 5 to prepare the ordered states, and polarisation-selective detection introduced in Chapter 6 for its observation. In contrast to the introductory sections, we no longer discuss these dynamics as mathematical models, but for specific physical systems, using experimental data to illustrate the theoretical description. The systems we use for this illustration are vapours of alkali metal atoms, in particular sodium. These one-electron systems allow the most direct application of the theoretical models developed above. In addition, we concentrate on electronic ground states, whose long lifetimes permit long observation times and correspondingly precise observations. Experimental arrangement General considerations Laser-induced dynamics This chapter surveys the coherent evolution of coherences between angular momentum sublevels. Optical pumping excites this microscopic order, and it evolves under the influence of external magnetic fields and the laser radiation. The primary goal of this section is to show how the mathematical models developed in the preceding sections apply to real physical systems. We discuss how the observed signals arise and by which parameters the experimenter can control the dynamics of these systems.

Cambridge University Press eBooks•Oct 13, 1997•0 citations

Nonlinear Effects in Optical Pumping of Atoms by a High-Intensity Multimode Gas Laser. General Theory

M. Ducloy

The optical pumping of atoms by a multimode gas laser, in the presence of a magnetic field, is studied theoretically. The atoms are described by their density matrix, which is expanded on an irreducible tensorial set. The atomic relaxation is assumed to be isotropic. In order to avoid the usual perturbation theory, we use the so-called "Broad-Line approximation" (BLA). BLA is valid when the width of the "Bennett hole" created by one laser mode in the velocity distribution of the excited atoms is comparable to the spacing between modes; under these conditions, the atomic response does not depend on the velocity and the multimode laser irradiation is equivalent to a broad-line excitation. For the atomic system, BLA leads to a set of coupled equations which is valid at arbitrary intensities of the laser field and which depends on this field through a unique parameter, $\ensuremath{\gamma}$. This parameter can be understood as a laser-induced transition probability. In this article, we analyze the nonlinear effects which can be deduced from this theory, for any value of the angular momenta involved in the laser transition: Hanle-effect broadening, alignment coupling, saturation resonances on the populations are shown. The exact calculations, valid at arbitrary laser intensities for $J=1\ensuremath{\leftrightarrow}J=0$, $J=1\ensuremath{\leftrightarrow}J=1$, and $J=1\ensuremath{\leftrightarrow}J=2$ transitions, and the corresponding experimental results will be presented in forthcoming papers.

Physical Review A•Oct 1, 1973•83 citations
Optical pumping of the electronic ground state of molecules has been investigated under conditions of plane, elliptically, and circularly polarized light broadband excitation. The analysis has been performed assuming arbitrary angular momentum values, and applying the apparatus of polarization moments, the latter forming the coefficients in the expansion of the density matrix over irreducible tensor operators, including simplifications due to asymptotic limits for large momentum values. In addition to accounting for the external magnetic field, attention has been also given to the dynamical Stark effect arising from the absence of coincidence between the centers of the exciting line and the absorption line. An alternative classical description is also proposed using multiple moments as coefficients of the expansion of a classical quasidensity of states over spherical harmonics. The equivalence of both approaches of description in the limit of infinitely large angular moments is demonstrated, and the meaning of the origin of coherence is clarified, as well as its destruction by the magnetic field in the classical description of the system.
In this paper, a coherent superposition of angular-momentum states created by absorption of polarized light by molecules is analyzed. Attention is paid to the time evolution of wave packets representing the spatial orientation of the internuclear axis of a diatomic molecule. Two examples are considered in detail. Molecules absorbing light in a permanent magnetic field experiencing the Zeeman effect and molecules absorbing light in a permanent electric field experiencing the quadratic Stark effect. In a magnetic field, we have a wave packet that evolves in time exactly as a classical dipole oscillator in a permanent magnetic field (classical-physics picture of the Zeeman effect). In the second case, we have a wave packet that goes through periodical changes of shape of the packet with revivals of the initial shape. This is pure quantum behavior. The classical motion of angular momentum in an electric field in the case of a quadratic Stark effect is known to be a periodic. Solutions obtained for wave packet evolution are briefly compared with Rydberg-state coherent wave packets and harmonic-oscillator wave packets. Zeeman and Stark effects in small molecules continuously attract the attention of researchers, theoreticians, as well as experimentalists. These investigations allow us to obtain a deeper understanding of the interaction of molecules with stationary external fields and also can be used as a practical tool to measure different molecular characteristics, such as permanent electric or magnetic dipole moments, intramolecular perturbations, etc. It is worthwhile analyzing these effects as an evolution of wave packets. All this motivates a comparison of the quantum and classical picture of Zeeman and Stark effects in molecules.PACS No.: 33.55.Be
The Wigner representation of angular-momentum orientation in the classical limit on $J\ensuremath{\gg}1$ has been used to derive an equation of angular-momentum motion in the case of a closed two-level system interacting with an arbitrary polarized radiation. This equation enables us to carry out a theoretical analysis of angular-momentum motion and consider final states of the quantum system for all types of dipole transitions. We have found that in the case of a zero magnetic field in the final state of the system with $\stackrel{\ensuremath{\rightarrow}}{J}J$ or $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ optical transition, the angular momentum is directed along or opposite to the wave vector of the radiation depending on the sign of the polarization ellipsity, while for a linear polarization the angular momentum is isotropically distributed on the plane orthogonal to the polarization vector. For the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition two directions of angular momentum are possible in the final state. These directions are determined by the ellipsity of polarization. The spatial size of the final distribution of the angular momentum has been defined by the quantum uncertainty, 1/J,1/\sqrt{J},1/J​, of the angular-momentum orientation. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ or $\stackrel{\ensuremath{\rightarrow}}{J}J,$ transition particles come into ``dark'' states while for the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition they occupy the ``brightest'' state. In the presence of a nonzero magnetic field, particles with $\stackrel{\ensuremath{\rightarrow}}{J}J$ transition have in the final state only one angular-momentum orientation, i.e., along or opposite to the direction of the magnetic field depending on the polarization ellipsity sign. For the $\stackrel{\ensuremath{\rightarrow}}{J}J+1$ transition both directions are possible, i.e., along and opposite to the magnetic field. In the case of the $\stackrel{\ensuremath{\rightarrow}}{J}J\ensuremath{-}1$ transition the directions of the angular momentum form a cone around the magnetic field.
We present the results of an experimental as well as a theoretical study of nonlinear magneto-optical resonances in diatomic potassium molecules in the electronic ground state with large values of the angular momentum quantum number $J\ensuremath{\sim}100$. At zero magnetic field, the absorption transitions are suppressed because of population trapping in the ground state due to Zeeman coherences between magnetic sublevels of this state along with depopulation pumping. The destruction of such coherences in an external magnetic field was used to study the resonances in this work. K2{}_{2}2​ molecules were formed in a glass cell filled with potassium metal at a temperature above 150 ${}^{\ensuremath{\circ}}$C. The cell was placed in an oven and was located in a homogeneous magnetic field B, which was scanned from 0 to 0.7 T. QQQ-type and RRR-type transitions were excited with a tunable, single-mode diode laser with a central wavelength of 660 nm. Well-pronounced nonlinear Hanle effect signals were observed in the intensities of the linearly polarized components of the laser-induced fluorescence (LIF) detected in the direction parallel to the B field with polarization vectors parallel (Ipar{I}_{\text{par}}Ipar​) and perpendicular (Iper{I}_{\text{per}}Iper​) to the polarization vector of the exciting laser radiation, which was orthogonal to B. The intensities of the LIF components were detected for different experimental parameters, such as laser power density and vapor temperature, in order to compare them with numerical simulations that were based on the optical Bloch equations for the density matrix. We report good agreement of our measurements with numerical simulations. Narrow, subnatural linewidth dark resonances in Iper(B){I}_{\text{per}}(B)Iper​(B) were detected and explained.
After the discussion of ionic solids we shift our attention to atomic vapours. Here, we discuss the dynamics of microscopic order within the angular momentum substates under the influence of light and magnetic fields. For this purpose, we combine optical pumping as outlined in Chapter 5 to prepare the ordered states, and polarisation-selective detection introduced in Chapter 6 for its observation. In contrast to the introductory sections, we no longer discuss these dynamics as mathematical models, but for specific physical systems, using experimental data to illustrate the theoretical description. The systems we use for this illustration are vapours of alkali metal atoms, in particular sodium. These one-electron systems allow the most direct application of the theoretical models developed above. In addition, we concentrate on electronic ground states, whose long lifetimes permit long observation times and correspondingly precise observations. Experimental arrangement General considerations Laser-induced dynamics This chapter surveys the coherent evolution of coherences between angular momentum sublevels. Optical pumping excites this microscopic order, and it evolves under the influence of external magnetic fields and the laser radiation. The primary goal of this section is to show how the mathematical models developed in the preceding sections apply to real physical systems. We discuss how the observed signals arise and by which parameters the experimenter can control the dynamics of these systems.
The optical pumping of atoms by a multimode gas laser, in the presence of a magnetic field, is studied theoretically. The atoms are described by their density matrix, which is expanded on an irreducible tensorial set. The atomic relaxation is assumed to be isotropic. In order to avoid the usual perturbation theory, we use the so-called "Broad-Line approximation" (BLA). BLA is valid when the width of the "Bennett hole" created by one laser mode in the velocity distribution of the excited atoms is comparable to the spacing between modes; under these conditions, the atomic response does not depend on the velocity and the multimode laser irradiation is equivalent to a broad-line excitation. For the atomic system, BLA leads to a set of coupled equations which is valid at arbitrary intensities of the laser field and which depends on this field through a unique parameter, $\ensuremath{\gamma}$. This parameter can be understood as a laser-induced transition probability. In this article, we analyze the nonlinear effects which can be deduced from this theory, for any value of the angular momenta involved in the laser transition: Hanle-effect broadening, alignment coupling, saturation resonances on the populations are shown. The exact calculations, valid at arbitrary laser intensities for $J=1\ensuremath{\leftrightarrow}J=0$, $J=1\ensuremath{\leftrightarrow}J=1$, and $J=1\ensuremath{\leftrightarrow}J=2$ transitions, and the corresponding experimental results will be presented in forthcoming papers.