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Proceedings of the International Astronomical Union

Coherence structure of D1 scattering

Jan Olof Stenflo

Published Dec 1, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.1017/s1743921315004664

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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 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.
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.
Under the light of recent developments of the theory of matter-radiation interaction in the presence of magnetic field applied to non-LTE spectropolarimetry in astrophysics, we have revisited the theory of anisotropic resonance line scattering in moving media by means of the density-matrix formulation. This has led us to present a theoretical method of determination of the matter velocity field vector in the solar wind acceleration region. The example of the O Vi 103.2 nm line has been chosen for putting this theory into operation. It has been observed by the ultraviolet spectrograph \textsc{Sumer} of \textsc{Soho} in different regions of the solar wind acceleration region; it is partially formed by resonance scattering of the incident underlying transition region radiation which competes (and can predominate) with electron collisional excitation at the low densities which prevail at these high altitudes. The theory which is developed hereafter not only shows that this line is shifted and its intensity dimmed by the Doppler effect, due to the matter velocity field of the solar wind, but also predicts that it is linearly polarized, owing to the anisotropy of the incident radiation field; its two linear polarization parameters, degree and direction of polarization, are sensitive to the matter velocity field vector. Our results show that the interpretation of polarimetric data, associated to the shift and the Doppler-dimming effect, may offer a method of diagnostic of the complete velocity field vector, provided that the partial anisotropy of the incident radiation field be taken into account. In fact such a diagnostic is currently missing. Yet its interest is crucial to understand various problems in astrophysics, such as stellar winds, and especially the acceleration mechanisms of the solar wind. It is also essential for a dynamical modelling of solar structures.
We present a laboratory-constrained phenomenological framework linking controlled quantum coherence experiments to large-scale cosmological observables. Using experimental results from superconducting qubits subjected to structured low-frequency toroidal magnetic fields, we define a dimensionless coherence proxy, κ_lab = 0.728 ± 0.020, which captures both temporal decoherence suppression and spatial field uniformity. This observable is derived directly from measured enhancements in qubit relaxation time (T1), without modification to materials or circuit design. We then introduce a calibrated laboratory-to-cosmology bridge, mapping κ_lab into an effective coupling parameter within a coherence-driven cosmological framework. This mapping enables a quantitative pre-data prediction for an environmental modulation of the Hubble expansion rate:ΔH0/H0 = 0.73^{+0.21}_{-0.18}%,for the benchmark regime m_φ ~ H0 and α = 1. The key contribution of this work is not the assumption of a confirmed cross-scale mechanism, but the construction of a transparent and falsifiable bridge between a laboratory-measured coherence observable and a cosmological testable quantity. The prediction lies within the sensitivity range of DESI Year 3, enabling a clear binary test: • Detection of a ~0.5–1.0% environmental step supports the viability of scale-bridging coherence dynamics.• A null result constrains the phenomenological bridge while preserving the laboratory result as an independent demonstration of environmental coherence engineering. This approach establishes a new paradigm in which controlled quantum systems can serve as quantitative anchors for testing phenomenological extensions of large-scale physics, connecting laboratory coherence and cosmological expansion in a falsifiable framework.