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

arXiv:1501.02259 · The Astrophysical Journal

PHYSICS OF POLARIZED SCATTERING AT MULTI-LEVEL ATOMIC SYSTEMS

Jan Olof Stenflo

Published Mar 4, 2015• 8 citations
arXivHTMLPDF

Abstract

The symmetric peak observed in linear polarization in the core of the solar sodium D 1 line at 5896 Å has remained enigmatic since its discovery nearly two decades ago. One reason is that the theory of polarized scattering has not been experimentally tested for multi-level atomic systems in the relevant parameter domains, although the theory is continually being used for the interpretation of astrophysical observations. A laboratory experiment that was set up a decade ago to find out whether the D 1 enigma is a problem of solar physics or quantum physics revealed that the D 1 system has a rich polarization structure in situations where standard scattering theory predicts zero polarization, even when optical pumping of the m state populations of the hyperfine-split ground state is accounted for. Here we show that the laboratory results can be modeled in great quantitative detail if the theory is extended to include the coherences in both the initial and final states of the scattering process. Radiative couplings between the allowed dipole transitions generate coherences in the initial state. Corresponding coherences in the final state are then demanded by a phase closure selection rule. The experimental results for the well understood D 2 line are used to constrain the two free parameters of the experiment, collision rate and optical depth, to suppress the need for free parameters when fitting the D 1 results.

DOI
10.1088/0004-637x/801/1/70

Related papers

Coherence structure of D1 scattering

Jan Olof Stenflo

Abstract The extensive literature on the physics of polarized scattering may give the impression that we have a solid theoretical foundation for the interpretation of spectro-polarimetric data. This theoretical framework has however not been sufficiently tested by experiments under controlled conditions. While the solar atmosphere may be viewed as a physics laboratory, the observed solar polarization depends on too many environmental factors that are beyond our control. The existence of a symmetric polarization peak at the center of the solar Na D1 line has remained an enigma for two decades, in spite of persistent efforts to explain it with available quantum theory. A decade ago a laboratory experiment was set up to determine whether this was a problem for solar physics or quantum physics. The experiment revealed a rich polarization structure of D1 scattering, although available quantum theory predicted null results. It has now finally been possible to formulate a well-defined and self-consistent extension of the theory of quantum scattering that can reproduce in great quantitative detail the main polarization structures that were found in the laboratory experiment. Here we give a brief overview of the new physical ingredients that were missing before. The extended theory reveals that multi-level atomic systems have a far richer coherence structure than previously believed.

Proceedings of the International Astronomical Union•Dec 1, 2014•0 citations

The D$_1$ enigma and its physical origin

Jan Olof Stenflo

The D$_1$ enigma is an anomaly, which was first observed on the Sun as a symmetric polarization peak centered in the core of the sodium D$_1$ line that is expected to be intrinsically unpolarizable. To resolve this problem the underlying physics was later explored in the laboratory for D$_1$ scattering at potassium vapor. The experiment showed that the scattering phase matrix element $P_{21}$ is positive while $P_{22}$ is negative, although standard quantum scattering theory predicts that both should be zero. This experimental contradiction is currently the main manifestation of the D$_1$ enigma. Subsequent theoretical studies showed that such polarization effects may arise if scattering theory is extended to allow for interference effects due to level splittings of the ground state, in contrast to standard scattering theory, which only allows for interferences from level splittings of the intermediate state. Previous attempts to implement this idea had to rely on heuristic arguments to allow modeling of the experimental data. In the present paper we develop a formulation of the theory that can be self-consistently applied to quantum systems with any combination of electronic and nuclear spins. No statistical equilibrium or optical pumping is needed. The atom is assumed to be unpolarized at the beginning of each scattering event. The theory is capable of explaining both the phase matrix behavior of the laboratory data and the existence of a symmetric polarization peak in the core of the solar D$_1$ line. We also use it to predict the polarization structures that we expect to see in a next-generation laboratory experiment with the rubidium isotopes $^{87}$Rb and $^{85}$Rb.

arXiv:1610.09861•Oct 31, 2016•0 citations

Magnetic Field Dependence of Polarized Scattering on Potassium

C. Thalmann, Jan Olof Stenflo, Alex J. Feller +1 more

The polarization that is generated by scattering of light on atoms depends on the atomic quantum number structure. According to standard scattering theory the sodium D1 (5896 A) and potassium D1 (7699 A) lines should be intrinsically unpolarizable. Since however the existence of D1 scattering polarization in the solar spectrum has been well documented but resisted theoretical explanations, we have carried out a laboratory experiment to find out if this is a problem of solar physics or of quantum physics. We find that the polarization matrix for scattering of the Stokes vector in the potassium D1 line exhibits a rich structure that changes dramatically when the field strength is varied in the sub-gauss regime. In contrast, standard scattering theory predicts zero polarization, even when optical pumping of the magnetic sub-levels of the hyperfine structure multiplet is accounted for.

•Jun 1, 2009•0 citations

Optical pumping of the Na D2 transition with elliptically polarized light

Benjamin T. H. Varcoe, Robert T. Sang, W. R. Macgillivary +2 more

The quantum electrodynamic description of circularly and linearly polarized, single mode radiation exciting atomic transitions in a hyperfine manifold is extended to the more general case of elliptic polarization. Calculations for the sodium D2 line are tested by observing the line polarization of the resonance flourescence scattered perpendicular to the plane containing laser and atomic beams as a function of the laser polarization. Very good agreement between the calculations and the measurements is achieved. It is demonstrated that predetermined populations and substate coherences can be engineered by optically pumping the transition with the appropriately polarized radiation.

Journal of Modern Optics•Apr 1, 1999•13 citations

P-state-to-P-state transitions in optically prepared atomic collisions: I. Theory of measurement in terms of Stokes parameters

Emil Y. Sidky, Sonia Grego, D. Dowek +1 more

We present a parametrization in terms of Stokes parameters for the scattering from a P state to a P state for atomic collisions in a beam experiment. The classic approach to a `complete scattering experiment', well known for S-state-to-P-state transitions, is generalized by a systematic combination of optical preparation of specific initial P states with Stokes parameter analysis of the radiation pattern from the final P state. The anisotropy of the initial and final state provides the possibility of extraction of a complete set of nine parameters describing the reaction at the level of five independent scattering amplitudes. We discuss the minimum number of experiments required to obtain a complete set of parameters in the cases of scattering angle-integrated and scattering angle-differential measurements. Relations to collision parameters for the reverse process are derived. Finally, effects due to fine and hyperfine depolarization, as well as inclusion of electron spin polarization, are treated.

Journal of Physics B Atomic Molecular and Optical Physics•Apr 24, 2002•6 citations

Frequency-dependent polarization of light scattered near the Na D2 resonance line

Robert E. Walkup, Alan L. Migdall, David E. Pritchard

We report measurements of the degree of linear polarization of scattered light as a function of excitation frequency near the Doppler-broadened $\mathrm{Na} D2$ resonance line. For resonant excitation of the $D2$ line, the hyperfine interaction strongly depolarizes the emitted light due to precession of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ prior to spontaneous emission. However, as the laser frequency is tuned away from resonance, the polarization degree sharply rises to the level predicted using a simple $J{M}_{J}$ basis, i.e., neglecting any coupling of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ with the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$. Roughly speaking, there is a transition from $F$ selection rules ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$) for resonant excitation to $J$ selection rules for off-resonant excitation. We present a rigorous calculation of the polarization degree with the use of multipole moments of the density matrix which agrees quantitatively with our data and also predicts complicated interference structure when Doppler broadening is negligible. We show that this structure may shift peaks observed in precision laser-spectroscopy experiments. For Doppler-broadened transitions we discuss a simplified approach (based on an approximation to the Voigt profile) which treats separately the contributions of resonant and off-resonant scattering.

Physical Review A•Jun 1, 1982•21 citations
The symmetric peak observed in linear polarization in the core of the solar sodium D 1 line at 5896 Å has remained enigmatic since its discovery nearly two decades ago. One reason is that the theory of polarized scattering has not been experimentally tested for multi-level atomic systems in the relevant parameter domains, although the theory is continually being used for the interpretation of astrophysical observations. A laboratory experiment that was set up a decade ago to find out whether the D 1 enigma is a problem of solar physics or quantum physics revealed that the D 1 system has a rich polarization structure in situations where standard scattering theory predicts zero polarization, even when optical pumping of the m state populations of the hyperfine-split ground state is accounted for. Here we show that the laboratory results can be modeled in great quantitative detail if the theory is extended to include the coherences in both the initial and final states of the scattering process. Radiative couplings between the allowed dipole transitions generate coherences in the initial state. Corresponding coherences in the final state are then demanded by a phase closure selection rule. The experimental results for the well understood D 2 line are used to constrain the two free parameters of the experiment, collision rate and optical depth, to suppress the need for free parameters when fitting the D 1 results.
Abstract The extensive literature on the physics of polarized scattering may give the impression that we have a solid theoretical foundation for the interpretation of spectro-polarimetric data. This theoretical framework has however not been sufficiently tested by experiments under controlled conditions. While the solar atmosphere may be viewed as a physics laboratory, the observed solar polarization depends on too many environmental factors that are beyond our control. The existence of a symmetric polarization peak at the center of the solar Na D1 line has remained an enigma for two decades, in spite of persistent efforts to explain it with available quantum theory. A decade ago a laboratory experiment was set up to determine whether this was a problem for solar physics or quantum physics. The experiment revealed a rich polarization structure of D1 scattering, although available quantum theory predicted null results. It has now finally been possible to formulate a well-defined and self-consistent extension of the theory of quantum scattering that can reproduce in great quantitative detail the main polarization structures that were found in the laboratory experiment. Here we give a brief overview of the new physical ingredients that were missing before. The extended theory reveals that multi-level atomic systems have a far richer coherence structure than previously believed.
The D1_11​ enigma and its physical origin
The D1_11​ enigma is an anomaly, which was first observed on the Sun as a symmetric polarization peak centered in the core of the sodium D1_11​ line that is expected to be intrinsically unpolarizable. To resolve this problem the underlying physics was later explored in the laboratory for D1_11​ scattering at potassium vapor. The experiment showed that the scattering phase matrix element P21P_{21}P21​ is positive while P22P_{22}P22​ is negative, although standard quantum scattering theory predicts that both should be zero. This experimental contradiction is currently the main manifestation of the D1_11​ enigma. Subsequent theoretical studies showed that such polarization effects may arise if scattering theory is extended to allow for interference effects due to level splittings of the ground state, in contrast to standard scattering theory, which only allows for interferences from level splittings of the intermediate state. Previous attempts to implement this idea had to rely on heuristic arguments to allow modeling of the experimental data. In the present paper we develop a formulation of the theory that can be self-consistently applied to quantum systems with any combination of electronic and nuclear spins. No statistical equilibrium or optical pumping is needed. The atom is assumed to be unpolarized at the beginning of each scattering event. The theory is capable of explaining both the phase matrix behavior of the laboratory data and the existence of a symmetric polarization peak in the core of the solar D1_11​ line. We also use it to predict the polarization structures that we expect to see in a next-generation laboratory experiment with the rubidium isotopes 87^{87}87Rb and 85^{85}85Rb.
The polarization that is generated by scattering of light on atoms depends on the atomic quantum number structure. According to standard scattering theory the sodium D1 (5896 A) and potassium D1 (7699 A) lines should be intrinsically unpolarizable. Since however the existence of D1 scattering polarization in the solar spectrum has been well documented but resisted theoretical explanations, we have carried out a laboratory experiment to find out if this is a problem of solar physics or of quantum physics. We find that the polarization matrix for scattering of the Stokes vector in the potassium D1 line exhibits a rich structure that changes dramatically when the field strength is varied in the sub-gauss regime. In contrast, standard scattering theory predicts zero polarization, even when optical pumping of the magnetic sub-levels of the hyperfine structure multiplet is accounted for.
The quantum electrodynamic description of circularly and linearly polarized, single mode radiation exciting atomic transitions in a hyperfine manifold is extended to the more general case of elliptic polarization. Calculations for the sodium D2 line are tested by observing the line polarization of the resonance flourescence scattered perpendicular to the plane containing laser and atomic beams as a function of the laser polarization. Very good agreement between the calculations and the measurements is achieved. It is demonstrated that predetermined populations and substate coherences can be engineered by optically pumping the transition with the appropriately polarized radiation.
We present a parametrization in terms of Stokes parameters for the scattering from a P state to a P state for atomic collisions in a beam experiment. The classic approach to a `complete scattering experiment', well known for S-state-to-P-state transitions, is generalized by a systematic combination of optical preparation of specific initial P states with Stokes parameter analysis of the radiation pattern from the final P state. The anisotropy of the initial and final state provides the possibility of extraction of a complete set of nine parameters describing the reaction at the level of five independent scattering amplitudes. We discuss the minimum number of experiments required to obtain a complete set of parameters in the cases of scattering angle-integrated and scattering angle-differential measurements. Relations to collision parameters for the reverse process are derived. Finally, effects due to fine and hyperfine depolarization, as well as inclusion of electron spin polarization, are treated.
We report measurements of the degree of linear polarization of scattered light as a function of excitation frequency near the Doppler-broadened NaD2\mathrm{Na} D2NaD2 resonance line. For resonant excitation of the D2D2D2 line, the hyperfine interaction strongly depolarizes the emitted light due to precession of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ prior to spontaneous emission. However, as the laser frequency is tuned away from resonance, the polarization degree sharply rises to the level predicted using a simple JMJJ{M}_{J}JMJ​ basis, i.e., neglecting any coupling of the electronic angular momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$ with the nuclear spin $\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}$. Roughly speaking, there is a transition from FFF selection rules ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{F}}=\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$) for resonant excitation to JJJ selection rules for off-resonant excitation. We present a rigorous calculation of the polarization degree with the use of multipole moments of the density matrix which agrees quantitatively with our data and also predicts complicated interference structure when Doppler broadening is negligible. We show that this structure may shift peaks observed in precision laser-spectroscopy experiments. For Doppler-broadened transitions we discuss a simplified approach (based on an approximation to the Voigt profile) which treats separately the contributions of resonant and off-resonant scattering.