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Journal of Experimental and Theoretical Physics

“Unmoved” Atomic Transitions of Alkali Metals in External Magnetic Fields

David G. Sarkisyan, G. Hakhumyan, Armen D. Sargsyan

Published Nov 1, 2020• 2 citations
Publisher

Abstract

Abstract The “mixing” of magnetic sublevels of the ground and excited levels of an atomic transition with magnetic sublevels of a nearby transition (in the hyperfine structure of atoms of alkali metals) is responsible for a strong modification of its probability. A dramatic manifestation of this mixing effect is a huge increase in the probability of the atomic transition in magnetic fields that is forbidden by selection rules in zero magnetic field B = 0; the latter is called a magnetically induced (MI) transition. Two MI transitions with different dependences on B have been studied. Another dramatic manifestation of the mixing effect is that there are atomic transitions whose frequency is practically fixed in a wide range of magnetic fields, i.e., the slope S [MHz/G] of the frequency shifts as a function of B is practically zero, with the transition probability being significant. We call these transitions “unmoved” transitions (UTs). We have studied the UTs of 87Rb atoms, the D2 line, |1, +1〉 → |1', +1'〉 and Cs atoms, the D2 line, |3, –3〉 → |5', –4'〉, where the quantum numbers F and mF of the excited and ground levels are marked with and without primes, respectively. We show that in the range B = 180–705 G for 87Rb, the D2 line, |S| ≤ 0.03 MHz/G; for comparison, S ≈ 3.6 MHz/G for 87Rb in the same B range for the MI transition |1, +1〉 → |3', +2'〉 is greater by a factor of 120. A second laser was used to control the UT amplitude. Our theoretical model describes well the experiment.

DOI
10.1134/s1063776120100143

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Abstract Two types of magnetically induced (MI) transitions in cesium atoms were studied experimentally and theoretically. The MI transitions are forbidden in the absence of magnetic field. Probabilities of MI transitions rapidly grow with increase in magnetic field and can exceed those of transitions allowed in the absence of magnetic field. Asymptotic behavior of probabilities of MI transitions in strong magnetic fields is different. In the case of magnetically induced transitions of the first type (MI1), transition probabilities experience giant increase with increase in the applied magnetic field, and with a further increase of the magnetic field, the probabilities of these transitions tend to asymptotic large value. Probabilities of magnetically induced transitions of the second type (MI2) also experience giant increase with increase in the applied magnetic field. However, probabilities of such transitions tend to zero again with further increase in the magnetic field. It is demonstrated that measurement of the second derivative (SD) of absorption spectra of Cs vapor contained in a nanocell with thickness L = 426 nm corresponding to half the wavelength of the D2 line of cesium (λ = 852 nm) enables conducting Doppler-free spectroscopy. Narrow width of atomic lines and linear relation between the SD signal amplitudes and transition probabilities allows studying individual atomic transitions in an external transverse magnetic field with induction varying from 0.5 to 5.3 kG. In particular, four MI transitions were studied: two MI1 and two MI2 ones. Theoretical calculations agree well with the experimental results.

Optics and Spectroscopy•Dec 1, 2020•3 citations
Abstract The “mixing” of magnetic sublevels of the ground and excited levels of an atomic transition with magnetic sublevels of a nearby transition (in the hyperfine structure of atoms of alkali metals) is responsible for a strong modification of its probability. A dramatic manifestation of this mixing effect is a huge increase in the probability of the atomic transition in magnetic fields that is forbidden by selection rules in zero magnetic field B = 0; the latter is called a magnetically induced (MI) transition. Two MI transitions with different dependences on B have been studied. Another dramatic manifestation of the mixing effect is that there are atomic transitions whose frequency is practically fixed in a wide range of magnetic fields, i.e., the slope S [MHz/G] of the frequency shifts as a function of B is practically zero, with the transition probability being significant. We call these transitions “unmoved” transitions (UTs). We have studied the UTs of 87Rb atoms, the D2 line, |1, +1〉 → |1', +1'〉 and Cs atoms, the D2 line, |3, –3〉 → |5', –4'〉, where the quantum numbers F and mF of the excited and ground levels are marked with and without primes, respectively. We show that in the range B = 180–705 G for 87Rb, the D2 line, |S| ≤ 0.03 MHz/G; for comparison, S ≈ 3.6 MHz/G for 87Rb in the same B range for the MI transition |1, +1〉 → |3', +2'〉 is greater by a factor of 120. A second laser was used to control the UT amplitude. Our theoretical model describes well the experiment.
Atomic transitions in alkali metals that have zero probability in the absence of a magnetic field but have large probabilities in the presence of a magnetic field are called magnetically induced (MI). They are of interest because of their large probabilities, which exceed the probabilities of usual transitions in a wide magnetic field range. Magnetically induced transitions are classified as type-1 (MI1) and type-2 (MI2) and their total number is about 100. In this work, MI2 transitions are examined between ground Fg and excited levels Fe of the hyperfine structure satisfying the condition Fe−Fg=ΔF=±2{{F}_{{\text{e}}}} - {{F}_{{\text{g}}}} = \Delta F = \pm 2Fe​−Fg​=ΔF=±2 , which are forbidden in zero magnetic field but have large probabilities in the presence of a magnetic field. The probabilities of the MI2 transitions with ΔF=+2\Delta F = + 2ΔF=+2 and the MI transitions with ΔF=−2\Delta F = - 2ΔF=−2 are maximal in the case of optical radiation with the σ+ and σ– polarizations, respectively. This difference is called type-1 magnetically induced circular dichroism (MICD1). It has been shown for the first time that the probability of the strongest MI2 transition in the 85Rb atom corresponding to the D2 line in magnetic fields >100 G in the case of σ+{{\sigma }^{ + }}σ+ radiation is larger than the probability of the strongest MI2 transition in the case of σ– radiation by a factor of 2.5. This difference is called type-2 magnetically induced circular dichroism (MICD2). It has been shown how to determine the strongest MI transition for any alkali metal atom, which is important for its application in magneto-optical processes. Theoretical curves reproduce well experimental results.
The probabilities of atomic transitions F e − F g = ± 2 between a ground F g and an excited F e level of the D 2 line of any alkali metal atom are zero when no external magnetic field is applied. In an external magnetic field in the range of 0.1–3 kG, the probabilities of these transitions called magnetically induced (MI) are highly modified. For MI transitions, we previously exhibited the following rule: the probabilities of MI transitions with Δ F = + 2 are maximal when using σ + -polarized laser radiation, while the probabilities of MI transitions with Δ F = − 2 are maximal when using σ − -polarized laser radiation. This difference has been termed type 1 MI circular dichroism. It is demonstrated for the first time, to our knowledge, that for alkali atoms with a nuclear spin I = 3 / 2 ( 87 R b , 39 K , 23 N a , 7 L i ) in magnetic fields > 100 G , the probability of the strongest σ + MI transition of the group F g = 1 → F e = 3 ′ (transition | 1 , − 1 ⟩ → | 3 ′ , 0 ′ ⟩ ) is about four times higher than the probabilities of the strongest MI σ − -transitions | 1 , − 1 ⟩ → | 3 ′ , − 2 ′ ⟩ and | 2 , + 1 ⟩ → | 0 ′ , 0 ′ ⟩ . These properties make the σ + MI transition | 1 , − 1 ⟩ → <m
Abstract Magnetically induced (MI) transitions of the D2 line of 39K atom in an external magnetic field of 10–600 G have been experimentally and theoretically investigated for the first time using circularly polarized σ+ and σ− radiations. According to the selection rules, the transitions between the sublevels of the ground and excited levels of a hyperfine structure with Fe – Fg = ΔF = ±2 are forbidden in the zero magnetic field, whereas their probabilities increase radically in a magnetic field. For the Fg = 1 → Fe = 3 (ΔF = +2) and Fg = 2 → Fe = 0 MI transitions, the highest probabilities are achieved using the σ+ and σ– radiations, respectively. The atomic transitions have been spectrally resolved using selective reflection of laser radiation from a nanocell filled with potassium atomic vapor, which makes it possible to investigate the behavior of the MI transitions. The experimental and theoretical data are shown to be in good agreement.
The magnetic field-induced giant modification of probabilities for seven components of 6S 1/2 , F g = 3 → 6P 3/2 , F e = 5 transition of the Cs D 2 line, forbidden by selection rules, is observed experimentally for the first time. For the case of excitation with circularly polarized laser radiation, the probability of a F g = 3, m F = −3 → F e = 5, m F = −2 transition becomes the largest of 25 transitions of the F g = 3 → F e = 2,3,4,5 group in a wide-range magnetic field of 200–3200 G. Moreover, the modification is the largest among D 2 lines of alkali metals. A half-wave-thick cell (the length along the beam propagation axis L = 426 nm) filled with Cs has been used in order to achieve sub-Doppler resolution, which allows the large number of atomic transitions that appear in the absorption spectrum to be separated when an external magnetic field is applied. For B > 3000 G the group of seven transitions F g = 3 → F e = 5 is completely resolved and is located at the high frequency level of F g = 3 → F e = 2,3,4 transitions. The applied theoretical model describes very well the experimental curves.
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.
Abstract Two types of magnetically induced (MI) transitions in cesium atoms were studied experimentally and theoretically. The MI transitions are forbidden in the absence of magnetic field. Probabilities of MI transitions rapidly grow with increase in magnetic field and can exceed those of transitions allowed in the absence of magnetic field. Asymptotic behavior of probabilities of MI transitions in strong magnetic fields is different. In the case of magnetically induced transitions of the first type (MI1), transition probabilities experience giant increase with increase in the applied magnetic field, and with a further increase of the magnetic field, the probabilities of these transitions tend to asymptotic large value. Probabilities of magnetically induced transitions of the second type (MI2) also experience giant increase with increase in the applied magnetic field. However, probabilities of such transitions tend to zero again with further increase in the magnetic field. It is demonstrated that measurement of the second derivative (SD) of absorption spectra of Cs vapor contained in a nanocell with thickness L = 426 nm corresponding to half the wavelength of the D2 line of cesium (λ = 852 nm) enables conducting Doppler-free spectroscopy. Narrow width of atomic lines and linear relation between the SD signal amplitudes and transition probabilities allows studying individual atomic transitions in an external transverse magnetic field with induction varying from 0.5 to 5.3 kG. In particular, four MI transitions were studied: two MI1 and two MI2 ones. Theoretical calculations agree well with the experimental results.