A study of dark resonance splitting for the D 1 line of 87Rb in strong magnetic fields

The process of electromagnetically induced transparency (EIT) is studied using an extremely thin cell with thickness of a vapor column of rubidium atoms L = 794 nm. Wavelengths of resonant laser beams ?? ?? 794 nm. Results of the study of behavior of the EIT resonance (which is also called the ??dark?? resonance) formed in the ?? system of the D ₁ line of ⁸⁷Rb atoms in strong magnetic fields up to 1700 G (0.17 T) are reported for the first time. Three dark resonances are recorded in magnetic fields with induction B < 300 G, two resonances are recorded at B > 650 G, and only one dark resonance is retained at B > 1200 G. A method of the formation of a dark resonance at a given frequency is demonstrated that will allow, under the corresponding conditions, the formation of a dark resonance also at B > 0.2 T. The experimental results are well described by the known theoretical models. Practical applications of these results are indicated.     

Splitting of the electromagnetically induced transparency resonance on 85Rb atoms in strong magnetic fields up to the Paschen-Back regime

Electromagnetically induced transparency (EIT) resonance in strong magnetic fields of up to 1.7 kG has been investigated with the use of a 30-??m cell filled with an atomic rubidium vapor and neon as a buffer gas. The EIT resonance in the ?? system of the D₁ line of ⁸⁵Rb atoms has been formed with the use of two narrowband (??1 MHz) 795-nm diode lasers. The EIT resonance in a longitudinal magnetic field is split into five components. It has been demonstrated that the frequencies of the five EIT components are either blue- or red-shifted with an increase in the magnetic field, depending on the frequency ??_P of the probe laser. In has been shown that in both cases the ⁸⁵Rb atoms enter the hyperfine Paschen-Back regime in magnetic fields of >1 kG. The hyperfine Paschen-Back regime is manifested by the frequency slopes of all five EIT components asymptotically approaching the same fixed value. The experiment agrees well with the theory.     

Electromagnetically induced transparency in Λ-system involving D 2 line of Rb atoms confined in sub-micron columns

The effect of electromagnetically induced transparency (EIT) in a Λ-system formed by rubidium atoms contained in thin (10–60 μm) and extremely thin (0.3–5 μm) cells was studied experimentally. It was found that parameters of the EIT resonance degrade slowly in the case where the frequency of the coupling laser is in resonance with the D ₂ transition of rubidium, which enabled the registration of the EIT resonance in a record thin cell with a thickness of L = 390 nm. The specific features of EIT in extremely thin cells reveal themselves when the coupling laser has a frequency detuning Δ from the atomic transition. In this case, the width of the EIT resonance rapidly increases upon an increase in Δ at fixed L (an opposite effect takes place in centimeter-scale cells). It is shown that the width of the EIT resonance is inversely proportional to L in the case of fixed large detuning Δ. The nearly tenfold broadening of the EIT resonance for large values of detuning Δ is caused by the influence of atomic collisions with cell windows on dephasing rate of coherence. The expressions that allow the estimation of the EIT-resonance width for various values of detuning Δ and small values of thickness L are found.     

Electromagnetically Induced Transparency and optical pumping processes formed in Cs sub-micron thin cell

The Electromagnetically Induced Transparency (EIT) effect in a Λ-system formed by Cs atoms (6S_1/2 ? 6P_3/2 ? 6S_1/2) confined in an extremely thin cell (ETC) (atomic column thickness L varies in the range of 800 nm –3 µm is studied both experimentally and theoretically. It is demonstrated that when the coupling laser frequency is in exact resonance with the corresponding atomic transition, the EIT resonance parameters weakly depend on L, which allows us to detect the effect at L = λ = 852 nm. EIT process reveals a striking peculiarity in case of the coupling laser detuned by Δ from the atomic transition, namely the width of the EIT resonance rapidly increases upon an increase in Δ (an opposite effect is observed in centimeter-scale cells). The strong broadening of the EIT resonance for large values of detunings Δ is caused by the influence of atom-wall collisions on dephasing rate of coherence. The influence of the coupling laser on the velocity selective optical pumping/saturation resonances formed in ETC has been also studied. The theoretical model well describes the observed results.     

High-contrast atomic dark resonances formed in a ladder system of rubidium atoms in submicron structures

It is shown that high-contrast resonance of electromagnetically induced transparency (EIT) in a ladder Ξ-system of 5S _1/2-5P _3/2-5D _5/2 levels can be formed in optical cells containing a column of rubidium vapor with thickness L in an interval of 100 nm ≤ L ≤ 780 nm. Using bichromatic laser radiation with certain parameters, an 83% contrast of the EIT resonance (or dark resonance, DR) has been achieved for a vapor column thickness of L = 780 nm. An important condition for the formation of high-contrast DR is that the frequency of the coupling laser radiation must be resonant with the frequency of the corresponding 5P _3/2-5D _5/2 transition (for the probe radiation frequency scanned over the 5S _1/2-5P _3/2 transition). It is also shown that a DR can be formed at a record small vapor column thickness of L ≈ 100 nm. Expressions that can be used to estimate the expected DR width at small L values are presented.     

Electromagnetically induced transparency resonances inverted in magnetic field

The phenomenon of electromagnetically induced transparency (EIT) is investigated in a Λ-system of the ⁸⁷Rb D ₁ line in an external transverse magnetic field. Two spectroscopic cells having strongly different values of the relaxation rates γ_rel are used: an Rb cell with antirelaxation coating (L ~ 1 cm) and an Rb nanometric- thin cell (nanocell) with a thickness of the atomic vapor column L = 795 nm. For the EIT in the nanocell, we have the usual EIT resonances characterized by a reduction in the absorption (dark resonance (DR)), whereas for the EIT in the Rb cell with an antirelaxation coating, the resonances demonstrate an increase in the absorption (bright resonances (BR)). We suppose that such an unusual behavior of the EIT resonances (i.e., the reversal of the sign from DR to BR) is caused by the influence of an alignment process. The influence of alignment strongly depends on the configuration of the coupling and probe frequencies as well as on the configuration of the magnetic field.     

High contrast <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript> line electromagnetically induced transparency in nanometric-thin rubidium vapor cell

The electromagnetically induced transparency (EIT) on the atomic D ₁ line of rubidium is studied using a nanometric-thin cell with atomic vapor column length in the range of L=400–800 nm. It is shown that the reduction of the cell thickness by four orders as compared with an ordinary cm-size cell still allows to form an EIT resonance for L=λ=794 nm with the contrast of up to 40%. Further reduction of thickness to L=λ/2 leads to significant reduction of EIT contrast, verifying that the key parameter for EIT in wavelength-scale-thickness cells is not the value of L itself but L/λ ratio. Remarkable distinctions of EIT formation in nanometric-thin and ordinary cells are demonstrated. Well-resolved splitting of the EIT resonance in a magnetic field for L=λ can be used for magnetometry with nanometric spatial resolution. The presented theoretical model well describes the observed results.     

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

Electromagnetically induced transparency (EIT) resonances are investigated with the ⁸⁵Rb D₁ line (795 nm) in strong magnetic fields (up to 2 kG) with three different types of spectroscopic vapor cells: the nano-cell with a thickness along the direction of laser light L ≈ 795 nm, the micro-cell with L = 30 μm with the addition of a neon buffer gas, and the centimeter-long glass cell. These cells allowed us to observe systematic changes of the EIT spectra when the increasing magnetic field systematically decoupled the total atomic electron and nuclear angular moments (the Paschen-Back/Back-Goudsmit effects). The observations agree well with a theoretical model. The advantages and disadvantages of a particular type of cell are discussed along with the possible practical applications.     

Study of optical narrow-band N-resonance formed in the vapor of isotope 87Rb atoms in an external magnetic field

Narrow-band cascade N-resonance formed in a Λ-system of rubidium atoms was investigated. Radiation of two continuous narrow-band lasers was used, one of which had a fixed frequency, while the second one was a probe laser. N-resonance may have a sub-natural width and exhibits enhancement of absorption. The behavior of N-resonance in an external magnetic field was examined with use of ⁸⁷Rb atomic vapors.     

Determination of copper content in soils and ores by laser-induced breakdown spectrometry

Features of electromagnetically induced transparency (EIT) in potassium vapors at the D₁ line of the ³⁹K isotope are studied. EIT resonances with a subnatural width of 3.5 MHz have been recorded upon excitation by two independent narrow-band diode lasers in a 1-cm-long cell filled with a natural mixture of potassium isotopes and buffer gas. The splitting of EIT resonances in potassium vapors in longitudinal and transverse magnetic fields has been studied for the first time. The splitted components also have a subnatural width. The smallness of the coupling factor of the hyperfine structure in ³⁹K atoms leads to a transition to the Paschen—Back regime at relatively weaker magnetic fields than in the case of Cs, Rb, and Na atoms. Practical applications of the phenomena under study are noted. The theoretical model well explains the experiment.     

V.L. Ginzburg’s elliptic screw polarization modes in an optical medium with linear birefringence and twist: Determination of their parameters by the method of Jones matrices

The effect of electromagnetically induced transparency (EIT) has been experimentally implemented for the first time for the (4S _1/2–4P _1/2–4S _1/2) Λ-system of potassium atom levels in a nanocell with a 770-nm-thick column of atomic vapor. It is shown that, at such a small thickness of the vapor column, the EIT resonance can be observed only when the coupling-laser frequency is in exact resonance with the frequency of the corresponding atomic transition. The EIT resonance disappears even if the coupling-laser frequency differs slightly (by ~50 MHz) from that of the corresponding atomic transition, which is due to the high thermal velocity of K atoms. The EIT resonance and related velocity selective optical pumping resonances caused by optical pumping (formed by the coupling) can be simultaneously recorded because of the small (~462 MHz) hyperfine splitting of the lower 4S _1/2 level.     

Dependence of the cesium absorption D1 linewidth on the thickness of atomic vapor column

A new nanocell has been elaborated, where the thickness of the atomic vapor column varies smoothly in the range L = 350–5100 nm. The cell allows studying the behavior of the resonance absorption at the D₁ line of cesium atoms by varying the thickness from L = λ / 2 to L = 5 λ with the step λ / 2 (λ being the resonant wavelength of the laser, 894 nm) and the laser intensity. It is shown that at low laser intensities a narrowing of the resonance absorption spectrum is observed for L = (2n + 1)λ/2 (with an integer n) up to L = (7/2)λ, whereas for L = nλ the spectrum broadens. The developed theoretical model well describes the experiment.     

Nanocell with a pressure-controlled Rb atomic vapor column thickness: Critical influence of the thickness on optical processes

A new device is designed: it consists of a nanocell (NC) filled with Rb atom vapors and placed in a vacuum chamber. When the pressure in the chamber changes in the range 0–1 atm, the NC thickness is smoothly varied in the range L = 140–1700 nm, which is caused by the pressure-induced deformation of thin garnet windows in the chamber. The pressure dependence has excellent reproducibility even after many hundreds of cycles of letting in of air and its complete pumping out from the chamber. The accuracy of setting required thickness L is much better than in the wedge-gap NCs to be moved mechanically that were used earlier. The processes of Faraday rotation (FR) of a polarization plane, resonance absorption, and fluorescence are studied using the D ₁-line narrow-band continuous laser radiation when the thickness changes from L = λ/2 (398 nm) to L = 2λ (1590 nm) at a step λ/2. The FR signal is shown to be maximal at L = λ/2 and 3λ/2 and to have the minimum spectral width (≈60 MHz). At L = λ and 2λ, the FR signal is minimal and has the maximum spectral width (≈200 MHz). The resonance absorption demonstrates the same oscillating behavior; however, the effect in the case of FR is much more pronounced. The oscillating effect is absent for resonance fluorescence: its spectral width and amplitude increase monotonically with L. The detected effects are explained and possible applications are noted.     

Splitting of N-type optical resonance formed in Λ-system of 85Rb atoms in a strong transverse magnetic field

We study narrow-band N-type resonance formed in a Λ-system of ⁸⁵Rb atoms. Even when thin (micrometer) optical cells are employed, N-type resonance has a high contrast. We used radiation of two cw diode lasers. Peculiarities of splitting of N-type resonance into six components in a strong transverse magnetic field are studied experimentally and theoretically and the conversion to the Paschen-Back regime on the hyperfine structure of ⁸⁵Rb atoms is recorded.     

Optical magnetometer with submicron spatial resolution based on Rb vapors

It is shown experimentally that use of fluorescence and transmission spectra obtained from nanocells with the thickness of column of rubidium atomic vapor L = λ/2 and L = λ, respectively (λ = 794 nm is the wavelength of laser radiation close to resonance with D ₁-line transition of Rb atoms), by means of a narrowband diode laser allows spectral separation and study of variations of probabilities of atomic transitions between ground and excited states of hfs of D ₁ lines of ⁸⁵Rb and ⁸⁷Rb atoms in the range of magnetic fields from 10 to 5000 G. Small thickness of atomic vapor column (∼390 nm and ∼794 nm) allows applying permanent magnets simplifying essentially creation of strong magnetic fields. Advantages of this technique are discussed as compared with the technique of saturated absorption. The obtained results show that a nanocell with submicrom thickness of vapor column may serve as a basis for designing a magnetometer with submicron local spatial resolution which is important in case of measuring strongly inhomogeneous magnetic fields. Experimental data are in good agreement with the theoretical results.     

Multilayer transition in a spin 3/2 Blume-Capel model with RKKY interaction

Using Monte Carlo simulation and mean-field theory, we have studied the effect of RKKY interaction on the multi-layer transition and magnetic properties of a spin-3/2 Blume-Capel model of a system formed by two magnetic multi-layer materials, of different thicknesses, separated by a non-magnetic spacer of thickness M. It is found that the multi-layer magnetic order-disorder transition temperature depends strongly on the thicknesses of the magnetic layer and the non-magnetic layer. The transition temperature increases with increasing thickness of the magnetic multi-layers and decreases with increasing thickness of the non-magnetic one. Furthermore, there exists a critical thickness M_L of the non-magnetic spacer beyond which the effect of the RKKY interaction becomes negligible and separate transitions occur in the two magnetic layers. The critical thickness M_L decreases on increasing the magnetic crystal field and/or the Fermi level k_f. Moreover, the multi-layer transition temperature undergoes oscillations as a function of the Fermi level. The susceptibility critical exponents are computed within Monte Carlo simulations.     

Study of atomic spectral lines in a magnetic field with use of a nanocell with the thickness <Emphasis Type="Italic">L</Emphasis> = λ

We propose a technique which we call “L = λ Zeeman technique” (LZT) for investigation of the transitions between the Zeeman sublevels of the hfs structure of alkali metal atoms in external magnetic fields. The technique is based on the employment of a nanocell with the thickness of the Rb atom vapor column equal to the wavelength of the laser radiation, 780 nm, resonant with the atomic rubidium D₂ transition. At the laser intensities of about 1 mW/cm² in the transmission spectrum of the nanocell narrow (～ 30 MHz) resonant peaks of reduced absorption appear localized exactly on the atomic transitions. In magnetic fields these peaks are split and their amplitudes and frequency positions depend on the magnetic field strength. The theoretical model well describes the experimental results.     

Faraday effect on the Rb <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line in a cell with a thickness of half the wavelength of light

The rotation of the radiation polarization plane in a longitudinal magnetic field (Faraday effect) on the D₁ 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 D₁ 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.     

The magnetic field dependence of the PEM effect in melt-grown InSb thin layers

The room temperature dependence of the PEM effect on magnetic field has been measured in intrinsic, melt-regrown layers of InSb of thickness from 1 to 10 μm. When illuminated on the surface of higher recombination velocity (the back surface of the InSb layer) the samples showed an anomalous magnetic field dependence of the PEM effect. This was manifested in most of the samples as a sign reversal in the PEM voltage, from a negative voltage in weak magnetic fields to a positive voltage in strong fields. Since, theoretically, such a PEM voltage dependence might result from a strong dependence of the bipolar diffusion length L on the magnetic field H, several scattering mechanisms have been investigated to find the strongest dependence of L = L(H) in InSb layers. It has been found that the dependence L = L(H) could in no case be responsible for the experimental magnetic field dependence of the PEM effect. Good agreement between theory and experiment is reached if a magnetic field-dependent surface recombination velocity at the InSb-substrate interface is postulated. The shape of the dependence which gave the best fitting of theoretical to experimental results is given.     

Faraday effect in alkali-metal vapors in a strong bichromatic field of laser light

Results of a numerical study of the Faraday effect arising upon propagation of the light beams with the frequencies ω _L1 (resonant to the nS _1/2-nP _{1/2, 3/2} transitions) and ω _L2 (resonant to the nP _{1/2, 3/2}-(n+2)S _1/2 transitions) through alkali-metal vapors are presented. Characteristics of the magneto-optical rotation spectra at each of the frequencies are strongly affected by the second intense radiation field resonant to the adjacent transition. When the atoms interact with two strong light waves, resonant to adjacent transitions, and with a magnetic field, the shape of the Faraday rotation spectra depends on the energy shifts of the atomic states that arise due to the dynamic Stark effect and the Zeeman effect (the Paschen-Back or an intermediate-type effect), as well as due to the difference of populations of these states caused by the interaction of the atoms with the fields. The results obtained show that in the frequency selection method, based on the resonance Faraday effect, the frequency of the generated narrow-band beam can be tuned by the intensity of the strong wave, resonant to the transition between the excited states.