Hyperfine Paschen–Back regime in alkali metal atoms: consistency of two theoretical considerations and experiment

Abstract

Simple and efficient "λ-method" and "λ/2-method" (λ is the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium are implemented to study the splitting of hyperfine transitions of 85 Rb and 87 Rb D1 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 85 Rb ( 87 Rb) 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 very well the experimental results for 85 Rb 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 coupled (F, mF ) basis, which adequately describe the system for low magnetic field, also predict reduction of number of transition components from 20 to 6 for 85 Rb, and from 12 to 4 for 87 Rb spectrum at B > 0.5 T. Also, the Zeeman transitions frequency shift, frequency interval between the components and their slope versus B are in agreement with the experiment.

EIT resonance features in strong magnetic fields in rubidium atomic columns with length varying by 4 orders

“…Despite the fact that the amplitudes of the EIT components decrease with an increase of the magnetic field, the components are well resolved up to 1 kG. The magnetic-field dependent decrease of the amplitudes of the EIT components has two reasons: an increase in the magnetic field leads to an increase in the detuning Δ of the frequency ν C from the respective atomic transition, and (more importantly [16]) a decrease of the atomic transition probabilities at frequencies ν C and ν P [17][18][19].…”

“…The energies of the Zeeman sublevels can easily be calculated as, e.g. in [17,19]. Figure 5 shows the calculated curves (solid lines) for the EIT-components with the numbers 1-5 corresponding to the configuration of the ν P and ν C frequencies, such as shown in the inset in Fig.…”

Micron-thick spectroscopic cells for studying the Paschen-Back regime on the hyperfine structure of cesium atoms

“…5, which shows some lower (F g = 3, 4) and upper (F e = 3, 4, 5) energy levels and their mag netic sublevels m F . A perturbation induced by the external magnetic field (under σ + excitation) only couples the magnetic sublevels with Δm F = 0 (indi cated by circular arrows), which must also obey the selection rules ΔL = 0, ΔJ = 0, and ΔF = ±1 [20,21]. To modify the probability of atomic transitions between magnetic sublevels, it is necessary that at least one magnetic sublevel m F be "mixed" with another sublevel.…”

“…4b) are described by the following expression [17]: (1) Here, A HFS and B HFS are the hyperfine structure cou pling coefficients for levels 6S 1/2 and 6P 3/2 , respec tively; g J and g I are the Lande factors for the total angular momentum J of electron and nuclear spin I, respectively [17]. As was shown in [21], a theoretical model that exactly describes the frequencies of transi tions in the magnetic field and formula (1) give close values for B ≥ 10B 0 (with discrepancies below 2%), which implies B ≥ 16 kG for Cs. Figure 7 shows the frequency corrections that must be added to the values It should be noted that excitation with σ -(right handed) polarized light in the hyperfine Paschen-Back regime also yields 16 transitions in two groups, each with eight transitions, but these are situated in the low frequency wing of transition F g = 4 F e = 3.…”

Saturated-absorption spectroscopy revisited: atomic transitions in strong magnetic fields (>20 mT) with a micrometer-thin cell

“…Thus, with increasing B, the majority of Zeeman transitions vanish. The calculated probabilities of all transitions allowed in the BG regime (1-10) as a function of B-field can be found in [16]. They all smoothly increase with B and reach their maximum values for B of several kilogauss.…”