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arXiv:1707.04468

Theoretical Investigation of $^{41}$K States Behavior under Strong Magnetic Field and $π$ Polarized Laser Field

A. Tonoyan

Published Jul 14, 2017• 0 citations
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Abstract

Theoretically research of the behavior of $^{41}$K $D_1$ and $D_2$ lines for $π$ polarized resonant light is conducted in the presence of strong magnetic field when the total electronic angular momentum $J$ and nuclear spin $I$ are decoupled. We show that in the case of linear polarization and for D1 line there are two transitions, so called guiding transitions (GT) that maintain their probabilities and frequency slopes. In Hyperfine Paschen-Back (HPB) regime other transitions are coming together to those GTs, making 2 groups (4 in each). Each transition in the group has the same frequency slope and probability as the GT in their group. It is demonstrated that from 12 ($D_1$) and 20 ($D_2$) initially allowed Zeeman transitions (taking into account the selection rules) at low B-field, only 8 transitions in each $D$ line remain in absorption spectra at $B > 200$ G. A complete HPB regime for relatively low magnetic fields $B \sim 200$ G has been observed. This value is the smallest for all alkali metals.

DOI
10.48550/arxiv.1707.04468

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Theoretical Investigation of 41^{41}41K States Behavior under Strong Magnetic Field and πππ Polarized Laser Field
Theoretically research of the behavior of 41^{41}41K D1D_1D1​ and D2D_2D2​ lines for πππ polarized resonant light is conducted in the presence of strong magnetic field when the total electronic angular momentum JJJ and nuclear spin III are decoupled. We show that in the case of linear polarization and for D1 line there are two transitions, so called guiding transitions (GT) that maintain their probabilities and frequency slopes. In Hyperfine Paschen-Back (HPB) regime other transitions are coming together to those GTs, making 2 groups (4 in each). Each transition in the group has the same frequency slope and probability as the GT in their group. It is demonstrated that from 12 (D1D_1D1​) and 20 (D2D_2D2​) initially allowed Zeeman transitions (taking into account the selection rules) at low B-field, only 8 transitions in each DDD line remain in absorption spectra at B>200B > 200B>200 G. A complete HPB regime for relatively low magnetic fields B∼200B \sim 200B∼200 G has been observed. This value is the smallest for all alkali metals.
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Atomic transitions of the 39 K potassium isotope in strong (up to 1 kG) longitudinal and transverse magnetic fields have been studied with a high spectral resolution. It has been shown that crossover resonances are almost absent in the saturated absorption spectrum of potassium vapors in a 30-μm-thick microcell. This, together with the small spectral width of atomic transitions (~30 MHz), allows one to use the saturated absorption spectrum for determining frequencies and probabilities of individual transitions. Among the alkali metals, potassium atoms have the smallest magnitude of the hyperfine splitting of the lower level. This allows one to observe the break of the coupling between the electronic and nuclear angular momentums at comparatively low magnetic fields B > 500 G, i.e., to implement the hyperfine Paschen–Back regime (HPB). In the HPB regime, four equidistantly positioned transitions with the same amplitude are detected in circularly polarized light (σ + ). In linearly polarized light (π) at the transverse orientation of the magnetic field, the spectrum consists of eight lines which are grouped in two groups each of which consists of four lines. Each group has a special distinguished G-transition and the transition that is forbidden in the zero magnetic field. In the HPB regime, the probabilities of transitions in a group and derivatives of their frequency shifts with respect to the magnetic field asymptotically tend to magnitudes that are typical for the aforesaid distinguished G-transition. Some practical applications for the used microcell are mentioned.
Simple and efficient λ-method and λ/2-method (λ is the resonant wavelength of laser radiation) based on a nanometric-thickness cell filled with rubidium (Rb) are implemented to study the splitting of hyperfine transitions of an Rb85 and Rb87D1 line in an external magnetic field in the range of B=0.5–0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in Rb85 (Rb87) spectra in the case of σ+ polarized laser radiation, only 6 (4) remain at B>0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen–Back regime). The expressions derived in the frame of completely uncoupled basis (J,mJ;I,mI) describe the experimental results extremely well for Rb85 transitions at B>0.6 T (that is a manifestation of hyperfine Paschen–Back regime). A remarkable result is that the calculations based on the eigenstates of the coupled (F,mF) basis, which adequately describe the system for a low magnetic field, also predict reduction of the number of transition components from 20 to 6 for Rb85 and from 12 to 4 for Rb87 spectrum at B>0.5 T. Also, the Zeeman transition frequency shifts, frequency intervals between the components and their slope versus B, are in agreement with the experiment.
A one-dimensional nano-metric-thin cell (NC) filled with potassium metal has been built and used to study optical atomic transitions in external magnetic fields. These studies benefit from the remarkable features of the NC allowing one to use and λ methods for effective investigations of individual transitions of the K D 1 line. The methods are based on strong narrowing of the absorption spectrum of the atomic column of thickness L equal to and to λ (with being the resonant laser radiation wavelength). In particular, for a π -polarized radiation excitation the λ -method allows us to resolve eight atomic transitions (in two groups of four atomic transitions) and to reveal two remarkable transitions that we call guiding transitions (GT). The probabilities of all other transitions inside the group (as well as the frequency slope vs . magnetic field) tend to the probability and to the slope of GT. Note that for circular polarization there is one group of four transitions and GT do not exist. Among eight transitions there are also two transitions (forbidden for ) with the probabilities undergoing strong modification under the influence of magnetic fields. Practically the complete hyperfine Paschen-Back regime is observed at relatively low magnetic fields. Note that for the K D 2 line GT are absent. Theoretical models describe the experiment very well.
It has been shown that the D 1 line of atomic vapors of alkali metals excited by π-polarized radiation in a strong transverse magnetic field includes specific “guiding” (indicating) atomic transitions between the magnetic sublevels of the hyperfine structure. The dependence of the frequency shift of the guiding transitions on the magnetic field, as well as on their dipole moments, is asymptotic for all other transitions. An experiment with a nanocell with Rb vapor with a thickness of half the wavelength (λ/2 method) for ensuring a sub-Doppler spectral resolution has completely confirmed the presence of guiding transitions. Two groups of six transitions for 85 Rb and two groups of four transitions for 87 Rb have been detected in the absorption spectra in magnetic fields above 4 kG. A guiding transition has been identified in each of four groups. Four transitions forbidden at B = 0 have been also detected; with an increase in the magnetic field, their probabilities also approach the probabilities of the guiding transitions.
Decoupling of total electronic and nuclear spin moments of Cs atoms in an external magnetic field for the case of atomic D1 line, leading to onset of the hyperfine Paschen–Back (HPB) regime, is studied theoretically and experimentally. Selective reflection (SR) of laser radiation from an interface of dielectric window and atomic vapor confined in a nanocell with 300 nm gap thickness is implemented for the experimental studies. The real-time derivative of SR signal with a frequency position coinciding with atomic transitions is used in the measurements, providing ∼40 MHz spectral resolution and linearity of the signal response with respect to the transition probability. The behavior of 28 individual Zeeman transitions in a wide range of longitudinal magnetic field (0–6 kG) is tracked under the excitation of Cs vapor by a low-intensity σ+-polarized cw laser radiation. For B≥6 kG, only eight transitions with nearly equal probabilities and the same frequency slope remain in the spectrum, which is a manifestation of the HPB regime. The obtained experimental results are in very good agreement with the numerical modeling. A small divergence of the SR signal as well as subwavelength thickness and sub-Doppler spectral linewidth inherent to nanocell make it possible for the employed technique to be used for distant remote sensing of a magnetic field with high spatial and B-field resolution.