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Journal of Modern Optics

Faraday rotation in cesium nano-layers in strong magnetic fields

A. Amiryan, Armen D. Sargsyan, Y. Pashayan-Leroy, Claude Leroy, David G. Sarkisyan

Published Oct 8, 2018• 3 citations
Publisher

Abstract

We show that the Faraday rotation (FR) in strong longitudinal magnetic fields is a convenient tool to study atomic transitions by using the D1 line in a Cs vapour confined in a nanocell of thickness L≈450 nm. We use strong magnetic fields ranging from 0.1 to 6 kG, in which Cs atomic transitions are split into a large number of components, and FR signals of spectral width of ∼ 50 MHz are frequency-resolved allowing the investigation of individual transitions. For magnetic fields of several kG, the hyperfine Paschen–Back regime is reached that is manifested by the presence in the spectrum of the eight FR components having the amplitudes of the same height and located with almost equidistant frequencies. A remarkable feature of FR spectrum is the proportionality of its amplitude to the probability of an atomic transition in a strong magnetic field. A theoretical model which agrees well with the experiment is developed.

DOI
10.1080/09500340.2018.1526343

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arXiv:1610.09807•Journal of the Optical Society of America B•Mar 6, 2017•50 citations
We show that the Faraday rotation (FR) in strong longitudinal magnetic fields is a convenient tool to study atomic transitions by using the D1 line in a Cs vapour confined in a nanocell of thickness L≈450 nm. We use strong magnetic fields ranging from 0.1 to 6 kG, in which Cs atomic transitions are split into a large number of components, and FR signals of spectral width of ∼ 50 MHz are frequency-resolved allowing the investigation of individual transitions. For magnetic fields of several kG, the hyperfine Paschen–Back regime is reached that is manifested by the presence in the spectrum of the eight FR components having the amplitudes of the same height and located with almost equidistant frequencies. A remarkable feature of FR spectrum is the proportionality of its amplitude to the probability of an atomic transition in a strong magnetic field. A theoretical model which agrees well with the experiment is developed.
The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D 1 line in atomic Rb vapor has been studied with the use of a nanocell with the thickness L varying in the range of 100–900 nm. It has been shown that an important parameter is the ratio L/λ, where λ = 795 nm is the wavelength of laser radiation resonant with the D 1 line. The best parameters of the signal of rotation of the radiation polarization plane have been obtained at the thickness L = λ/2 = 397.5 nm. The fabricated nanocell had a large region with such a thickness. The spectral width of the signal reached at the thickness L = 397.5 nm is approximately 30 MHz, which is much smaller than the spectral width (≈ 500 MHz) reached with ordinary cells with a thickness in the range of 1–100 mm. The parameters of the Faraday rotation signal have been studied as functions of the temperature of the nanocell, the laser power, and the magnetic field strength. The signal has been reliably detected at the laser power P L ≥ 1 μW, magnetic field strength B ≥ 0.5 G, and the temperature of the nanocell T ≥ 100°C. It has been shown that the maximum rotation angle of the polarization plane in the longitudinal magnetic field is reached on the F g = 3 → F e = 2 transition of the 85Rb atom. The spectral profile of the Faraday rotation signal has a specific shape with a sharp peak, which promotes its applications. In particular, Rb atomic transitions in high magnetic fields about 1000 G are split into a large number of components, which are completely spectrally resolved and allow the study of the behavior of an individual transition.
Theoretical studies of the Faraday rotation (FR) effect in alkali vapors contained in extremely thin cells are presented. It is shown that the spectra of the FR signal are well frequency resolved despite the huge number of atomic transitions. This allows one to study the evolution of the Cs D 1 (λ = 895 nm) line hyperfine structure of F g = 4 → F e = 3, 4 atomic transitions in magnetic fields. The presented theoretical model predicts the coherent Dicke narrowing effect and its revival with a periodicity Δ L = λ. The practical applications of the FR are noted.
Abstract The interaction of rubidium atoms with sapphire cell windows at an interwindow distance L = 40–100 nm is studied. For studies, we used the Faraday rotation (FR) effect (rotation of the plane of radiation polarization in a magnetic field) in a thin rubidium atom vapor column for D1, 2 lines. When L decreases from 100 to 40 nm, a red shift of the FR signal frequency is detected: it increases from 10 to 250 MHz, and the broadening of the low-frequency wing increases to ~1 GHz. The atomic transition Fg = 3 → Fe = 2 for the D1 line of 85Rb is shown to be convenient for such investigations, since it can be spectrally separated from other strongly broadened atomic transitions. Coefficients C3, which characterize the atom–surface interaction for the D1 and D2 lines of Rb, are determined. An additional red frequency shift takes place at a nanocell thickness L < 100 nm when the Rb atom density increases, and this shift is absent at large L. A practical application of an FR signal for measuring strong magnetic fields of several kilogausses is described.
A modified Faraday rotation method is developed using a nanocell filled with cesium vapor. Formed atomic lines have a spectral width 1.5–2 times narrower than those obtained by the Faraday rotation method. In magnetic fields of B = 5000–7000 G, all the atomic transitions of the Cs D 2 lines, formed in the spectra, are spectrally resolved and identified. In particular, transitions that are forbidden at B = 0 G have been investigated, however, at certain values of the magnetic field, there is a gigantic increase in their probabilities. It is shown that the modified Faraday rotation method is convenient and efficient for high-resolution spectroscopy for Cs atoms. There is а good agreement between the experimental results and calculated values. The practical applications are also noted.
Features of the effect of Faraday rotation (the rotation of the radiation polarization plane) in a magnetic field of the D 1 line in Cs atomic vapor in a nanocell with the thickness L varying in the range of 80–900 nm have been analyzed. The key parameter is the ratio L/λ, where λ = 895 nm is the wavelength of laser radiation resonant with the D 1 line. The comparison of the parameters for two selected thicknesses L = λ and λ/2 has revealed an unusual behavior of the Faraday rotation signal: the spectrum of the Faraday rotation signal at L = λ/2 = 448 nm is several times narrower than the spectrum of the signal at L = λ, whereas its amplitude is larger by a factor of about 3. These differences become more dramatic with an increase in the power of the laser: the amplitude of the Faraday rotation signal at L = λ/2 increases, whereas the amplitude of the signal at L = λ almost vanishes. Such dependences on L are absent in centimeter-length cells. They are inherent only in nanocells. In spite of a small thickness, L = 448 nm, the Faraday rotation signal is certainly detected at magnetic fields ≥0.4 G, which ensures its application. At thicknesses L < 150 nm, the Faraday rotation signal exhibits “redshift,” which is manifestation of the van der Waals effect. The developed theoretical model describes the experiment well.
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.