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.     

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.     

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.     

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.     

Implementation of a double-scanning technique for studies of the Hanle effect in rubidium vapor

We have studied the resonance fluorescence of a room-temperature rubidium vapor exited to the atomic ⁵P_3/2 state (D₂ line) by powerful single-frequency cw laser radiation (1.25 W/cm²) in the presence of a magnetic field. In these studies, the slow, linear scanning of the laser frequency across the hyperfine transitions of the D₂ line is combined with a fast linear scanning of the applied magnetic field, which allows us to record frequency-dependent Hanle resonances from all the groups of hyperfine transitions including V- and Λ-type systems. Rate equations were used to simulate fluorescence signals for ⁸⁵Rb due to circularly polarized exciting laser radiation with different mean frequency values and laser intensity values. The simulation show a dependence of the fluorescence on the magnetic field. The Doppler effect was taken into account by averaging the calculated signals over different velocity groups. Theoretical calculations give a width of the signal peak in good agreement with experiment.     

Resonant interaction of femtosecond radiation with a cloud of cold <Superscript>87</Superscript>Rb atoms

The resonant interaction of ⁸⁷Rb atoms in a magneto-optical trap with femtosecond laser radiation in the spectral range 760–820 nm has been investigated experimentally. It has been demonstrated that femtosecond laser radiation with a spectral width of 10 nm interacts with an atomic ensemble as a set of spectrally narrow modes and as an ionizing laser field simultaneously. The dynamics of trap loading in the presence of ionization by femtosecond radiation has been studied, and the 5D _5/2 level population produced by an additional weak laser field has been measured.     

87Rb D1线法拉第反常色散光学滤波

为了得到在高背景噪音下对弱信号光的提取,实验研究了基于⁸⁷Rb D₁线5S_1/2F=2→5P_1/2 F'=1跃迁的795 nm法拉第反常色散光学滤波器.充铷的样品池所含⁸⁷Rb的比例高于自然铷,样品池处在均匀的磁场中并且夹在两个相互正交的偏振片之间.入射的探测光通过样品池,与原子相互作用,由于法拉第旋转效应实现滤波功能.改变实验条件,透射结果随之明显变化.当温度从340 K升高到360 K,透射谱的变化情况被细致记录,并且分析了导致透射情况变化的原因.在适当的工作温度以及磁场条件下,得到线宽为约220 MHz的超窄带透射谱线,谱线透过率约为48%.⁸⁷Rb D₁线的实验结果优于⁸⁵Rb的吸收线.     

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.     

Frequency-modulation spectroscopy of coherent dark resonances in <Superscript>87</Superscript>Rb atoms

The results of frequency-modulation (FM) spectroscopy of coherent dark resonances from the Zeeman sublevels of the transition F=2↔ F=1 of D ₁ line in absorption of ⁸⁷Rb atoms are presented and discussed in detail. By contrast with the conventional spectroscopy of coherent dark resonances employing two laser beams, relative frequency of which can be varied, these data has been obtained with the help of a single frequency-modulated laser field. Variation of the modulation frequency plays then a similar role as the variation of the relative frequency in conventional spectroscopy. Experimental data are fit to the theoretical calculations, which are based on the theory of FM spectroscopy of coherent dark resonances recently developed by us. Feasibility of using such experimental technique for accurate measurements of magnetic fields is also discussed.     

Laser frequency stabilization using a balanced bi-polarimeter

We report on a Doppler-free polarization spectroscopy based technique of laser frequency stabilization using a balanced bi-polarimeter set-up. Two linearly polarized weak laser beams are used to probe birefringence induced by two oppositely circularly polarized strong pump beams in a vapour cell. Subtraction of balanced polarimeter signals obtained from the two probe beams results in a background-free dispersion-like reference signal without frequency modulation. The dispersion-like signal corresponding to the closed transition 5 ² S _1/2 (F=2) →5 ² P _3/2 (F^′=3) of ⁸⁷Rb was used for frequency locking of a diode laser. The frequency fluctuations and the drift were measured to be less than 0.25 MHz and 0.02 MHz, respectively, for an observation period of more than 10 hours. PACS 42.62.Fi; 42.55.Px; 32.30.-r     

Two strongly contrasting Λ-systems in the <Emphasis Type="Italic">D</Emphasis> <Subscript>1</Subscript> line of <Superscript>87</Superscript>Rb in a transverse magnetic field

Four different types of spectroscopic cells that cover all possible existing versions of sealed-off cells (containing alkali atomic vapor) characterized by drastically different relaxation rates γ_rel are used to study the electromagnetically induced transparency spectra of two Λ-systems in the D₁ line of ⁸⁷Rb in the presence of transverse magnetic field. Two cw narrowband diode-lasers are used to form the coupling laser radiation (with a fixed frequency) and the probe radiation with a tunable frequency. Two strongly contrasting Λ-systems are found: the first shows resonances that are transformed from dark resonances to bright resonances in all cases apart from nanocells, whereas the second shows four dark resonances in all four different types of cell. The theoretical simulations are in good agreement with the experimental results.     

Structure of magnetic resonance in <Superscript>87</Superscript>Rb atoms

Magnetic resonance at the F_g = 1 \( \rightleftarrows \)F_e = 1 transition of the D₁ line in ⁸⁷Rb has been studied with pumping and detection by linearly polarized radiation and detection at the double frequency of the radiofrequency field. The intervals of allowed values of the static and alternating magnetic fields in which magnetic resonance has a single maximum have been found. The structure appearing beyond these intervals has been explained. It has been shown that the quadratic Zeeman shift is responsible for the three-peak structure of resonance; the radiofrequency shift results in the appearance of additional extrema in resonance, which can be used to determine the relaxation constant Γ₂. The possibility of application in magnetometry has been discussed.     

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     

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.     

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.     

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.     

STUDY OF FARADAY ANOMALOUS DISPERSION SPECTRA OF THE HYPERFINE STRUCTURE OF Rb D2 LINES

Natural rubidium is a mixture of the two isotopes, ⁸⁵Rb and ⁸⁷Rb, the natural abundances of which are 72.2 and 27.8 percent, respectively. Taking into account their hyperfine structure, we have cal-culated the Faraday anomalous dispersion spectra (FADS)of Rb D₂ lines in different magnetic fields and observed them experimentally. The theoretical calculations are in good agreement with the experi-mental results. In this paper, we also discuss the results.     

Coherent spectroscopy of the 87RbFg=1→ Fe=0 closed transition

This paper has observed linewidth narrowing of dark states in rubidium cell by using the Hanle configuration. The reduction of the coherent resonance width under the transition of ^87Rb Fg = 1 → Fe = 0 is observed and the qualitative explanation about its mechanism is presented. Multiple subnatural width dips are obtained with a linearly polarized laser beam for the transitions of ^87Rb Fg = 1→Fe = 0, 1, 2. The feature of negative and positive slope, namely dispersionlike feature, is observed in the transmitted light.     

<Superscript>87</Superscript>Rb NMR study of the magnetic structure of the quasi-two-dimensional antiferromagnet RbFe(MoO<Subscript>4</Subscript>)<Subscript>2</Subscript> on a triangular lattice

⁸⁷Rb nuclear magnetic resonance was experimentally studied in a quasi-two-dimensional Heisenberg antiferromagnet RbFe(MoO₄)₂. Dipole fields at the ⁸⁷Rb nuclei were found over a wide range of temperatures and static magnetic fields. Magnetic structures in the ordered phase were determined at various magnetic fields.     

Frequency stabilization of a laser diode to hyperfine structure of the 4D5/2 state of Rb atoms

We observed hyperfine structures of the 4D_5/2 state of ⁸⁵Rb atoms and applied them to the frequency stabilization of a laser diode by using the double resonance optical pumping (DROP). The hyperfine structures of the 4D_5/2 states of ⁸⁵Rb atoms were highly resolved in the Rb vapor cell. We compared the DROP with the optical-optical double resonance (OODR) in the 5S_1/2-5P_3/2-4D_5/2 ladder-type system of ⁸⁵Rb atoms. When we stabilized the frequency of a laser diode to the hyperfine structure of the 5P_3/2(F″ = 4)-4D_5/2(F″ = 3) transition by using the DROP spectrum, the frequency stability was approximately 2.3 × 10^− 12 after 100 s.