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Register a new userHyperfine Paschen-Back regime in alkali metal atoms: consistency of two theoretical considerations and experiment
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Yevgenya Pashayan-Leroy T
Publication date
2013
fields
Physics
and research's language is
English
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Simple and efficient lambda-method and lambda/2-method (lambda 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 85Rb and 87Rb D_1 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 85Rb (87Rb) spectra in the case of sigma+ 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, m_J ; I, m_I) describe very well the experimental results for 85Rb 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, m_F) basis, which adequately describe the system for low magnetic field, also predict reduction of number of transition components from 20 to 6 for 85Rb, and from 12 to 4 for 87Rb 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.
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We demonstrate a technique to lock simultaneously two laser frequencies to each step of a two-photon transition in the presence of a magnetic field sufficiently large to gain access to the hyperfine Paschen-Back regime. A ladder configuration with the 5S$_{1/2}$, 5P$_{3/2}$ and 5D$_{5/2}$ terms in a thermal vapour of $^{87}$Rb atoms is used. The two lasers remain locked for more than 24 hours. For the sum of the laser frequencies, which represents the stability of the two-photon lock, we measure a frequency instability of less than the Rb D$_2$ natural linewidth of 6 MHz for nearly all measured time scales
An efficient $lambda/2$-method ($lambda$ is the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium is implemented to study the splitting of hyperfine transitions of $^{85}$Rb and $^{87}$Rb $D_2$ lines in an external magnetic field in the range of $B =3$~kG -- 7~kG. It is experimentally demonstrated that at $B > 3$~kG from 38 (22) Zeeman transitions allowed at low $B$-field in $^{85}$Rb ($^{87}$Rb) spectra in the case of $sigma^+$ polarized laser radiation there remain only 12 (8) which is caused by decoupling of the total electronic momentum $textbf{J}$ and the nuclear spin momentum $textbf{I}$ (hyperfine Paschen-Back regime). Note that at $B > 4.5$~kG in the absorption spectrum these $20$ atomic transitions are regrouped in two completely separate groups of $10$ atomic transitions each. Their frequency positions and fixed (within each group) frequency slopes, as well as the probability characteristics are determined. A unique behavior of the atomic transitions of $^{85}$Rb and $^{87}$Rb labeled $19$ and $20$ (for low magnetic field they could be presented as transitions $F_g=3, m_F=+3 rightarrow F_e=4, m_F=+4$ and $F_g=2, m_F=+2 rightarrow F_e=3, m_F=+3$, correspondingly) is stressed. The experiment agrees well with the theory. Comparison of the behavior of atomic transitions for $D_2$ line compared with that of $D_1$ line is presented. Possible applications are described.
Selective reflection of a laser radiation from an interface formed by a dielectric window and a potassium atomic vapour confined in a nano-cell with $350~$nm gap thickness is implemented for the first time to study the atomic transitions of K D$_2$ line in external magnetic fields. In moderate $B$-fields, there are 44 individual Zeeman transitions which reduce to two groups (one formed by $sigma^+$ the other one by $sigma^-$ circularly-polarised light), each containing eight atomic transitions, as the magnetic field increases. Each of these groups contains one so-called guiding transition whose particularities are to have a probability (intensity) as well as a frequency shift slope (in MHz/G) that are constant in the whole range of $0 - 10~$kG magnetic fields. In the case of $pi$-polarised laser radiation, among eight transitions two are forbidden at $B = 0$, yet their probabilities undergo a giant modification under the influence of a magnetic field. We demonstrate that for $B$-fields $> 165~$G a complete hyperfine Paschen-Back regime is observed. Other peculiarities of K D$_2$ line behaviour in magnetic field are also presented. We show a very good agreement between theoretical calculations and experiments. The recording of the hyperfine Paschen-Back regime of K D$_2$ line with high spectral resolution is demonstrated for the first time.
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 $lambda/2$- and $lambda$-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 $lambda/2$ and to $lambda$(with $lambda = 770un{nm}$ being the resonant laser radiation wavelength). In particular, for a $pi$-polarized radiation excitation the $lambda$-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 versus 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 $B$ = 0) with the probabilities undergoing strong modification under the influence of magnetic fields. Practically the complete hyperfine Paschen-Back regime is observed at relatively low ($sim 1un{kG}$) magnetic fields. Note that for K $D_2$ line GT are absent. Theoretical models describe the experiment very well.
We have shown that it is possible to model accurately optical phenomena in intense laser fields by taking into account the intensity distribution over the laser beam. We developed a theoretical model that divided an intense laser beam into concentric regions, each with a Rabi frequency that corresponds to the intensity in that region, and solved a set of coupled optical Bloch equations for the density matrix in each region. Experimentally obtained magneto-optical resonance curves for the $F_g=2longrightarrow F_e=1$ transition of the $D_1$ line of $^{87}$Rb agreed very well with the theoretical model up to a laser intensity of around 200 mW/cm$^2$ for a transition whose saturation intensity is around 4.5 mW/cm$^2$. We have studied the spatial dependence of the fluorescence intensity in an intense laser beam experimentally and theoretically. An experiment was conducted whereby a broad, intense pump laser excited the $F_g=4longrightarrow F_e=3$ transition of the $D_2$ line of cesium while a weak, narrow probe beam scanned the atoms within the pump beam and excited the $D_1$ line of cesium, whose fluorescence was recorded as a function of probe beam position. Experimentally obtained spatial profiles of the fluorescence intensity agreed qualitatively with the predictions of the model.
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