Investigation of Rb <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript> atomic lines in strong magnetic fields by fluorescence from a half-wave-thick cell

It has been experimentally demonstrated that the use of the effect of significant narrowing of the fluorescence spectrum from a nanocell that contains a column of atomic Rb vapor with a thickness of L = 0.5λ (where λ = 794 nm is the wavelength of laser radiation, whose frequency is resonant with the atomic transition of the D ₁ line of Rb) and the application of narrowband diode lasers allow the spectral separation and investigation of changes in probabilities of optical atomic transitions between levels of the hyperfine structure of the D ₁ line of ⁸⁷Rb and ⁸⁵Rb atoms in external magnetic fields of 10–2500 Gs (for example, for one of transitions, the probability increases ∼17 times). Small column thicknesses (∼390 nm) allow the application of permanent magnets, which facilitates significantly the creation of strong magnetic fields. Experimental results are in a good agreement with the theoretical values. The advantages of this method over other existing methods are noted. The results obtained show that a magnetometer with a local spatial resolution of ∼390 nm can be created based on a nanocell with the column thickness L = 0.5λ. This result is important for mapping strongly inhomogeneous magnetic fields.     

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.     

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.     

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.     

Sub-Doppler fluorescence on the atomic <Emphasis Type="Italic">D</Emphasis><Subscript>2</Subscript> line of a submicron rubidium-vapor layer

An extremely thin cell (ETC) with the thickness of a Rb atomic vapor layer in the range of 100–300 nm was fabricated. It is demonstrated that a simple laser-diode technique with a single resonant light beam is sufficient to observe separately all of the atomic hyperfine transitions of the D ₂ line of Rb (780 nm) and also allows us to measure the relative transition probabilities of the hyperfine transitions. The onset of collisional self-broadening of the hyperfine transitions as the number density of atoms increases was studied. The detrimental role of the atoms with slow longitudinal velocity in the sub-Doppler response of the Rb ETC is demonstrated by studies in which the cell is tilted from normal incidence of the laser beam. It is also shown that using an ETC allows us to resolve in a moderate external magnetic field the Zeeman splitting of the hyperfine transitions of the ⁸⁷Rb D ₁ transition F _g=1F _e=1,2. Received: 19 February 2003 / Revised version: 4 April 2003 / Published online: 2 June 2003 RID="*" ID="*"Corresponding author. Fax: +374/32-31172, E-mail: david@ipr.sci.am     

Selective reflection of a laser beam from a dilute rubidium vapor

We study the selective reflection of the laser beam from rubidium atomic vapor at the D₂ line (wavelength λ = 780 nm) at different atomic densities. We use a tunable free-running diode laser. We observed a measurable signal at a low atomic density N when the mean distance between resonance atoms reached two wavelengths. In our experiment, the dimensionless parameter N ^1/3 λ varied from 0.5 to 2.8. The reflectivity increased with density monotonically. It is interesting to perform experiments when the parameter N ^1/3 λ ≪ 1.     

Use of sub-Doppler optical resonances for measurement of weak magnetic fields by means of extremely thin rubidium vapor cell

We study experimentally and theoretically D ₁ lines of ⁸⁵Rb and ⁸⁷Rb atoms and show that using atomic-velocity-selective optical resonances which are formed in the transmission spectrum of an atomic rubidium-filled submicron cell at single pass of linearly polarized laser radiation, it is possible to measure weak magnetic fields beginning with 5 G. Having in mind the results obtained earlier with use of also submicron cell with ⁸⁷Rb (D ₁ line) and circularly polarized laser radiation, the entire range of measurable magnetic fields (both homogeneous and inhomogeneous) becomes 5–5000 G.     

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.     

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.     

Narrow-band N-resonance formed in thin rubidium atomic layers

The narrow-band N-resonance formed in a ?? system of D ₁-line rubidium atoms is studied in the presence of a buffer gas (neon) and the radiations of two continuous narrow-band diode lasers. Special-purpose cells are used to investigate the dependence of the process on vapor column thickness L in millimeter, micrometer, and nanometer ranges. A comparison of the dependences of the N-resonance and the electromagnetically induced transparency (EIT) resonance on L demonstrates that the minimum (record) thickness at which the N-resonance can be detected is L = 50 ??m and that a high-contrast EIT resonance can easily be formed even at L ?? 800 nm. The N-resonance in a magnetic field for ⁸⁵Rb atoms is shown to split into five or six components depending on the magnetic field and laser radiation directions. The results obtained indicate that levels F _g = 2, 3 are initial and final in the N-resonance formation. The dependence of the N-resonance on the angle between the laser beams is analyzed, and practical applications are noted.     

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.     

Saturated absorption spectroscopy: Elimination of crossover resonances with the use of a nanocell

It is demonstrated that the velocity-selective optical pumping/saturation resonances of the reduced absorption in a Rb vapor nanocell with thickness L = λ, 2λ, and 3λ (resonant wavelength λ = 780 nm) allow for the complete elimination of crossover (CO) resonances. We observe well-pronounced resonances corresponding to the F _g = 3 → F _e = 2, 3, and 4 hyperfine transitions of the ⁸⁵Rb D₂ line with line widths close to the natural width. A small CO resonance located midway between F _g = 3 → F _e = 3 and F _g = 3 → F _e = 4 transitions appears only for L ≥ 4λ. The D₂ line (λ = 852 nm) in a Cs nanocell exhibits a similar behavior. From the amplitude ratio of the CO and VSOP resonances, it is possible to determine the thickness of the column of alkali vapor in the range of 1–1000 μm. The absence of the CO resonances for nanocells with L ～ λ is attractive for the frequency reference application and for studying the transitions between the Zeeman sublevels in external magnetic fields.     

Measurement of electric field strengths in a waveguide by means of the dynamic Stark effect in hydrogen and neutral helium spectral lines

The dynamic Stark effect of the spectral lines H_β and of the neutral helium lines λ=402.6 nm (2³ P ⁰−5³ D) and λ=438.8 nm (2¹ P ⁰−5¹ D) emitted from a discharge tube was used for probing rf electric fields in a transverse waveguide. Calculations accounting for the pertubation of the atomic states by strong unidirectional fields prove to be suitable in order to interprete the main experimental results. If the waveguide is terminated with a metallic reflector and the plasma in the discharge tube becomes overdense—then representing a slightly permeable mirror—a resonant enhancement of the electric field strength may be achieved by tuning. This enhancement is well recognizable in the spectral line contours.     

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.     

Zeeman effect on the hyperfine structure of the D 1 line of a submicron layer of 87Rb vapor

An extremely thin cell with a wedge gap was developed that makes it possible to form a column of Rb atom vapor with thickness in the range from 100 to 600 nm. It is experimentally shown that the use of this cell, along with commercially available diode lasers, allows one to spectrally resolve individual transitions between the Zeeman sublevels of the hyperfine structure of the ⁸⁷Rb D ₁ line (transitions F _g =1, 2→F _e =1, 2) in the resonance fluorescence spectrum in the presence of an external magnetic field (B≈200 G). This makes it possible to realize systems consisting of nondegenerate atomic levels. For comparison, it is shown that transitions between the Zeeman sublevels in the fluorescence spectrum obtained with the aid of a conventional cell (1–10 cm long) in an external magnetic field with B～200 G remain completely masked by the Doppler-broadened profile. The results obtained can be used for the creation of a simple magnetometer based on an extremely thin cell with Rb vapor for the measurement of magnetic fields with a submicron local spatial resolution.     

Visible superfluorescence from optically pumped europium atoms

We have observed superfluorescence (SF) on five atomic transitions at visible wavelengths 633.58, 635.00, 640.09, 640.61 and 736.22 nm in Doppler broadened gas of europium (Eu) atom. The nanosecond SF pulses were observed by longitudinally pumping Eu vapor column with a pulsed dye laser to upper states 4f⁶5d6s², ⁸D_7/2at 346.79 nm and 4f⁷5d6p, ¹⁰F_5/2at 348.73 nm from the ground state 4f⁷6s², ⁸S_7/2. High optical conversion efficiency ≈10% was measured for these SF transitions. Our experiment deals with the large sample multilevel SF in the regime where the length of the excited column L is greater than the maximum value of the Arecchi-Courtens length (L_c). The observed variation of SF peak intensity (I_fl) and time delay for SF evolution (τ_D) with number of atoms in the excited state (N) resemble theoretically predicted SF scaling laws for transverse excitation, namely I_fl∝N and t_D μ 1/?N\tau_D \propto 1/{\sqrt N} although the experimental condition is similar to the swept excitation. This could be due to the Rabi frequency associated with the pump transition which is comparable to the SF delay time precluding the initiation of SF at different times along the sample and results in transverse (instantaneous) excitation. The experimental τ_D values were found to be in agreement with the quantum mechanical calculations describing SF.     

Amplification of radiation in atomic vapor induced by a linearly polarized laser radiation

We present the results of spectroscopic and polarization studies of dilute rubidium vapor exposed to a single-frequency linearly polarized diode laser radiation in a spectral range of atomic D₂ line. We report the origin of a circularly polarized radiation on V-type transitions of ⁸⁷Rb F _g = 2 → F _e = 3 and ⁸⁵Rb F _g = 3 → F _e = 4, and amplification of this radiation in backward direction caused by a partial population inversion among magnetic sublevels of the ground and excited levels. This is confirmed experimentally by high directivity of backward radiation, absence in its spectrum of ⁸⁵Rb F _g = 2 → F _e = 1 (Λ-type) radiation, as well as by different nature of intensity dependences of backward and fluorescence radiations.     

Laser-noise-induced correlations and anti-correlations in electromagnetically induced transparency

High degrees of intensity correlation between two independent lasers were observed after propagation through a rubidium vapor cell in which they generate Electromagnetically Induced Transparency (EIT). As the optical field intensities are increased, the correlation changes sign (becoming anti-correlation). The experiment was performed in a room temperature rubidium cell, using two diode lasers tuned to the ⁸⁵Rb D₂ line (λ= 780 nm). The cross-correlation spectral function for the pump and probe fields is numerically obtained by modeling the temporal dynamics of both field phases as diffusing processes. We explored the dependence of the atomic response on the atom-field Rabi frequencies, optical detuning and Doppler width. The results show that resonant phase-noise to amplitude-noise conversion is at the origin of the observed signal and the change in sign for the correlation coefficient can be explained as a consequence of the competition between EIT and Raman resonance processes.     

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.     

High-spatial-resolution monitoring of strong magnetic field using Rb vapor nanometric-thin cell

We have implemented the so-called λ-Zeeman technique (LZT) to investigate individual hyperfine transitions between Zeeman sublevels of the Rb atoms in a strong external magnetic field B in the range of 2500 ? 5000 G (recently it was established that LZT is very convenient for the range of 10 ? 2500 G). Atoms are confined in a nanometric thin cell (NTC) with the thickness L = λ, where λ is the resonant wavelength 794 nm for Rb D₁ line. Narrow velocity selective optical pumping (VSOP) resonances in the transmission spectrum of the NTC are split into several components in a magnetic field with the frequency positions and transition probabilities depending on the B-field. Possible applications are described, such as magnetometers with nanometric local spatial resolution and tunable atomic frequency references.