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Atomic Transitions in Strong Magnetic Fields (>20 Saturated-absorption spectroscopy revisited: atomic transitions in strong magnetic fields (>20 mT) with a micrometer-thin cell A. Sargsyan,1 A. Tonoyan,1 R. Mirzoyan,1 D. Sarkisyan,1 A.M. Wojciechowski,2, ∗ A. Stabrawa,2 and W. Gawlik2 1Institute for Physical Research, NAS of Armenia, Ashtarak, 0203, Armenia 2Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krak´ow, Poland compiled: May 15, 2017 The existence of cross-over resonances makes saturated-absorption spectra very complicated when external magnetic field B is applied. It is demonstrated for the first time that the use of micrometric-thin cells (MTC, L ≈ 40 µm) allows application of SA for quantitative studies of frequency splittings and shifts of the Rb atomic transitions in a wide range of external magnetic fields, from 0.2 up to 6 kG (20-600 mT). We compare the SA spectra obtained with the MTC with those obtained with other techniques, and present applications for optical magnetometry with micrometer spatial resolution and a broadly tunable optical frequency lock. OCIS codes: (300.6460) Spectroscopy, saturation; (140.3425) Laser stabilization; (260.7490) Zeeman effect; (120.6200) Spectrometers and spectroscopic instrumentation http://dx.doi.org/10.1364/XX.99.099999 Saturated absorption (SA) spectroscopy is widely used VSOP resonances have been demonstrated in the trans- in laser spectroscopy of atomic and molecular transitions mission spectrum of one dimensional nanometric-thin [1–3]. In this technique, the laser beam is split into a cell (NTC) filled with alkali metal, with a thickness weak probe and a strong pump fields, which are sent L = λ, where λ is the transition wavelength, yet the to the interaction cell as counter-propagating, overlap- CO lines are absent [6, 7]. ping beams. Opposite Doppler shifts and saturation by In high magnetic fields the atomic optical transitions the pump beam allow the observation of a Doppler-free may dramatically change their frequencies and proba- dip in the probe beam absorption, the so-called velocity bilities, e.g., in the Back-Goudsmit (BG or hyperfine selective optical pumping/saturation (VSOP) resonance Paschen-Back) regime [8, 9]. The related effects were located at the line center [2]. The line width of the recently studied in the fields up to B ∼ 0.6 T with a VSOP resonance may be as narrow as the natural width 1x1x1 mm3 Rb-vapor cell embedded in a permanent of the transition, which finds applications in realization magnet [10]. Even for that large B-field values, the of frequency references. The situation is more complex Doppler-broadened 85Rb and 87Rb lines are strongly when several hyperfine atomic transitions overlap within overlapping. In order to eliminate the Doppler broad- the Doppler profile, which is the case for the majority ening, the SA (and polarization) spectroscopy in the of real atomic lines. Multiple unresolved hyperfine tran- weak/intermediate magnetic fields (up to ∼ 100 G) was sitions result in the formation of the so called crossover implemented to the studies of atomic transitions [11, 12] (CO) resonances. The COs are due to atoms that move or for calibration of the magnetic field [13]. However, the with a particular non-zero velocity relative to the light obtained spectra were rather complicated, primarily due arXiv:1401.6208v2 [physics.atom-ph] 27 Jan 2014 beams and may seriously complicate the applicability of to the presence of strong CO resonances also split into the SA spectral reference technique. In the case of hy- many components [14]. Thus, the SA spectroscopy in perfine levels with a small (10–30 MHz) frequency spac- the typical vapor cells is practical only for B << 200 G. ing, the CO resonances may mask the real atomic VSOP In this paper we demonstrate that for magnetic fields resonances, i.e., those due to the atoms moving with zero B > 200 G, to about 6 kG, the SA spectroscopy can be longitudinal velocity, and hinder or even impede identi- implemented successfully using 20-50 µm-thin cells. fication of the relevant spectral features. The MTC is similar in the design to the extremely thin Several techniques allow for the elimination of cells presented in Ref. [6]. The rectangular 20x30 mm2, crossover resonances in atomic vapors [4, 5]. Similar 2.5 mm-thick sapphire window wafers (chemically resis- tant to hot alkali metal vapors), polished to < 1 nm surface roughness, form a vapor cell, wedged by placing spacers between the windows prior to gluing. MTC is ∗ Corresponding author: [email protected] filled with a natural mixture of rubidium isotopes. The 2 3 2 VSOP-1 8 9 10 7 4 6 5 VSOP-1 3 2 8 5 7 4 6 f requency ref erence Transmission(arb.un.) 87 85 2733 MHz Rb,Fg=1 Fe=2 Rb,Fg=2 Fe=3 Laser frequency detuning, MHz Fig. 2. Rb D1 line SA spectrum in the intermediate fields of 1075 G (upper curve) and 500 G (middle curve). Laser power is 1 mW. The lower curve is the reference. Fig. 1. (a) Sketch of the experimental setup. ECDL is the diode laser, FI - Faraday isolator, PM - permanent magnet, λ/4 - quarter waveplate, PBS - polarization beam splitter, spectrum, while there are twelve (twenty) Zeeman tran- PD - photodetectors, F - filter, M - mirror; (b) Energy level 87 85 sitions allowed at low fields. This strong reduction of the diagram of the D1 line of the Rb (left) and Rb (right) + numbers of atomic transitions for large magnetic field is in a magnetic field with the σ transitions of non-vanishing probability in the BG regime. caused by the effect of decoupling of the total electronic momentum J and the nuclear spin momentum I (the BG effect) in the magnetic field B>B0 ≡ Ahfs/µB, where Ahfs is the ground-state hyperfine coupling coefficient wedged gap allows one to study the SA spectra with and µB is the Bohr magneton. Thus, with increasing B a variable column thickness by probing various cell re- majority of Zeeman transitions vanish. The calculated gions. probabilities of all transitions allowed in the BG regime The small thickness of MTC is advantageous for the (1-10) as a function of B-field can be found in [15]. They application of very strong magnetic fields with the use all smoothly increase with B and reach their maximum of permanent ring magnets, otherwise not practical for values for B of several kG. spectroscopy because of strong magnetic field gradients. The SA spectra recorded with MTC in the moderate In MTC, however, the B-field inhomogeneity over the magnetic fields are shown in Fig. 2. Atomic transi- narrow atomic vapor column is lower by a few orders of tions labeled 1–3 and 10 for 87Rb and 4–9 for 85Rb [see magnitude than the applied B values. The magnets were Fig. 1(b)] are clearly resolved and no COs are present, mounted onto two nonmagnetic stages with the possibil- thanks to the small thickness of the MTC. Our experi- ity of adjusting their distance. ment shows that the presented method is applicable for The laser beam from an extended cavity diode laser B ≥ 200 G, which allows the study of the atomic spectra resonant with the Rb D1 line (λ = 795 nm, beam diam- in the intermediate and high fields, i.e., the nonlinear eter of ∼ 1 mm) was directed through MTC with the va- Zeeman and BG regimes. Examples of high magnetic por column thickness L = 40 µm [Fig. 1(a)]. To achieve field SA spectra are shown in Fig. 3 and Fig. 4 together + σ circular polarization of the laser radiation, we used a with the spectra obtained in the NTC with the thickness polarizing beam splitter followed by a λ/4 plate. After λ/2 and λ, respectively. Both techniques allow for ob- passing the MTC, the beam was retroreflected and the servation of the high resolution spectra, and we shortly transmission signal was detected by a photodiode and summarize their advantages. recorded by a digital scope. The MTC was heated to Spectroscopy with the NTC [16, 17] exploits the ◦ ∼70 C by a hot air to yield atomic number density of strong narrowing in absorption spectrum at L = λ/2 11 −3 the order of N = 5·10 cm . The magnetic field was as compared with the case of an ordinary cm-size vapor oriented along the beam propagation direction. A frac- cell. Particularly, the absorption linewidth for the Rb tion of the laser power was sent to the reference arm with D1 line reduces to ∼120 MHz (FWHM), as opposed to the Rb-filled NTC of a thickness L = λ or λ/2 and the ∼500 MHz Doppler width. Moreover, the relative tran- transmission spectrum was used as a B = 0 frequency sition probabilities can be directly extracted from the reference. resonance amplitudes, since the spectrum is essentially For high magnetic fields B ≫ 200 G, the only allowed background-free. On the other hand, for the NTC with transitions between magnetic sublevels of the hf states L = λ, the achieved lines are much narrower (∼20 MHz), 87 85 + for Rb and Rb D1 lines in case of σ polarized ex- which is beneficial for investigation of closely-spaced res- citation are shown in Fig. 1(b). Only four (six) atomic onances. The peak amplitudes are again proportional to transitions for 87Rb (85Rb) remain in the transmission the transition probability as it was demonstrated in [8], 3 VSOP-1 method 10000 5 4 6 7 8 3 2 L= 2 9 2 1 10 8000 3 Absorption 6000 Fg=1 Fe=2(B=0) 4000 SA,L=40 m 85 Rb,F =2 F =3 2000 g e Frequency shift,MHz 87 Transmission Rb,F =1 F =2 g e 0 2732 MHz 0 2000 4000 6000 Laser frequency detuning, MHz Magnetic field, G Fig.
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