Abstract

The radiofrequency-optical double magnetic resonance in cesium atoms filled in a vapor cell is investigated experimentally. One resonant signal involving spin-exchange collisions is observed in the MZ type magnetic resonance spectrum. We solve Liouville equations describing the dynamics of the system and analyze the role of the spin-exchange collisions in the atomic population distributions under resonant conditions. The theoretical calculations agree very well with the experimental results. In contrast with the normal magnetic resonance, the collision induced magnetic resonance exhibits the interesting saturation effect: both the signal amplitude and the signal linewidth are nearly constant when the laser intensity is above a moderate threshold value, which can be useful for precision measurements of the geomagnetic field.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Atomic magnetometers based on the radiofrequency-optical double magnetic resonance have been shown to be useful for practical applications in space physics [1], geomagnetism [2], medical imaging [3] and ocean science [4]. The properties of these resonances have been well studied, which are the basis for high performances in sensitivity and accuracy [5–8]. In a typical radiofrequency-optical double magnetic resonance configuration, the radiofrequency field is applied to excite magnetic dipole transitions and reduce the population imbalance created by the optical field. Obviously, the population transfer between magnetic sublevels is an important process. The spin-exchange collision is also lead to population transfer. But in the literature, it is mainly considered as a relaxation mechanism in the radiofrequency-optical double magnetic resonances with one atomic species [9–11]. However, the contribution of the spin-exchange collisions induced population transfer between the magnetic sublevels in different hyperfine states to the spin orientation was studied [12].

In this paper, we demonstrate the first observation of a new magnetic resonant signal involving the spin-exchange collisions in the MZ type magnetic resonance spectrum. The physical mechanism is similar to transferring spin polarization from optically pumped alkali-metal atoms to noble gas atoms in a spin-exchange optical pumping process [13]. The resonant laser renders atoms in one hyperfine state polarized. The spin polarization is then transferred from the polarized atoms to atoms in other hyperfine states. When a resonant radiofrequency field is applied, the population distribution changes and the new resonant signal occurs. The new signal exhibits two important features: 1. the spectral linewidth is not broadened by the high laser intensity; 2. the amplitude of the signal does not change when the laser intensity is above a threshold value. Therefore, it indicates that when the laser intensity is below the threshold, the ratio of the linewidth and the amplitude of the signal decreases as the laser intensity increases; but when the laser intensity is above the threshold, the ratio is constant. This implies that the sensitivity would only depend on the noise of the magnetic resonance spectrum, if the new magnetic resonant signal is used for the magnetic field measurement in a magnetometer. In a closed-loop atomic magnetometer for geomagnetic field, an invariable ratio of the linewidth and the amplitude of the signal means that the feedback gain is a constant, which is very important for a stable system.

2. Theoretical analysis

When cesium atoms are placed in a weak external magnetic fieldBz along the z direction, the magnetic sublevels split linearly according toΔE|F,mF=μBgFmFBZ0, where μB is Bohr magneton and mF is magnetic quantum number. The hyperfine Landé g-factor is given by [14]:

gF=gJF(F+1)I(I+1)+J(J+1)2F(F+1)+gIF(F+1)+I(I+1)J(J+1)2F(F+1)
SincegI is much smaller thangJ, the nuclear term is usually neglected in most experiments. However, the second term can induce a significant correction in the geomagnetic field measurement, which is important for the precision measurements. Importantly, Eq. (1) implies that there are two different resonant frequencies for magnetic resonance with alkali atoms. The g-factors of the ground states of cesium atoms are g4=(1/8)g1/2+(7/8)g7/2 andg3=(1/8)g1/2+(9/8)g7/2. When BZ0 is in the geomagnetic field range, the difference between the Zeeman shifts of the two ground states is several hundred hertz. If a circular polarized laser field coupled to the transition Fg=4Fe=3 and a radiofrequency field Bt=BX1cosωt are applied to the atoms normal to the static magnetic field, the radiofrequency-optical double magnetic resonance might be excited when the frequency ω equals the Zeeman shifts, as shown in Fig. 1. We define z-direction as the quantization axis and consider the spontaneous decays from the excited states to the two ground states. There are 23 Zeeman sublevels to be considered. We first introduce the Liouville equations for the time evolution of the Zeeman sublevels formulated as following [10,15–17]:
ρ˙=1i[H,ρ]12{R^,ρ}+Λγ+Tr(Fρ)+Lecoρ+Γsec(ρ).
where
H=H0+HE+HB.
Here the Hamiltonian H^0 describes the unperturbed atom:
H0=FmFωFmF|FmFFmF|+F'mF'ωF'mF'|F'm'FF'mF'|.
whereFandmF are the total quantum number and the angular quantum number of the ground states, respectively. F' and mF' are the total quantum number and the angular quantum number of the excited states, respectively. The Hamiltonian HE and HB describe the interactions with laser light and magnetic field:
HE=dE=F,F',mF,mF'F'mF'|d|FmFE|F'mF'FmF|+h.c.
HB=μB=gFμBF,mF,F',m'FFmF|F|FmF'B|FmFFm'F|.
where magnetic field B=BZ0+Bt.

 figure: Fig. 1

Fig. 1 Energy structure of the cesium atoms in the external magnetic fieldBZ0. The red solid arrows represent the σ+ polarized laser field that couples the atomic transitions Fg=4,mFFe=3,mF+1(D1 lines at 895 nm). The radiofrequency field RF is scanned and the range of the frequency covers ω1 and ω2 which are the Zeeman shifts of the two hyperfine states. SEC represents the spin-exchange collisions.

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In Eq. (2), R^ describes the relaxation induced by the spontaneous emission and limited interaction time of cesium atom with the laser field:

R^=FmFγ|FmFFmF|+F'mF'(γ+Γ)|F'mF'F'mF'|.
whereγ is the relaxation rate of the transit time effect and Γ is the rate of the spontaneous emission.

The matrixΛγ describes the repopulation of the ground-state levels due to the transit time effect:

Λγ=FmFγ|FmFFmF|ρmFmFeq.
where ρmFmFeqis the equilibrium population of state|FmF.

In the Eq. (2), Tr(Fρ) describes the repopulation of the ground-state levels due to the spontaneous emission, here F^is the spontaneous emission operator [15]. The matrix elements are formulated as:

Tr(Fρ)mn=rsFmnsrρrs.
where

Fmnsr=4ωrm33c3dmrdsn.

The dephasing rate of the excited-state coherences are given by

L^ecoρ^=mF'm'FΓ*D[σmF'mF',σm'Fm'F].
D[σmF'mF',σm'Fm'F]σmF'mF'ρσm'Fm'F12ρσm'Fm'FσmF'mF'12σm'Fm'FσmF'mF'ρ
where σm'Fm'Fis the transition operator, Γ* is the rate of phase-changing collisions [18].

At last, the relaxation induced by the spin-exchange collision is considered in the Eq. (2) [10]:

Γ^sec(ρ)Rsec=34ρ+S^ρS^+S^({S^,ρ}2iS^×ρS^).
In Eq. (13), the third term represents nonlinear effect, which is neglected in our system since it is much weaker than the effect induce by the radiofrequency field.

3. Experimental setup and results discussion

The experimental setup is shown in Fig. 2, which is a conventional configuration of the MZ magnetometer [7]. To detect the MZ signal, we place a 25 mm diameter, 30 mm long paraffin-coated cell filled with cesium atoms in a solenoid coil. In a paraffin-coated cell the depolarization atom-wall collisions are suppressed, which leads to a reduced linewidth of several tens hertz. The static magnetic field BZ0 produced by the coil can be tuned from zero to 5×104 nT (geomagnetic field) with a precision current source (Keysight B2912A). The coils and the cell are magnetically shielded with four layers of μ-metal cylinders and the magnetic field gradient in the middle zone of the coil is below 2 nT/cm even when the magnetic field is5×104 nT. We use an 895 nm DBR laser as the light source which is locked to the transition Fg=4Fe=3with the modulation-free polarization spectroscopy. The power of the laser light sent to the experiment can be tuned with a half wave plate and a polarized beam splitter. The diameter of the light is 3 mm and the polarization is transformed with a quarter wave plate. The radiofrequency field Bt=BX1cosωt is produced with a Helmholtz coil (not drawn in Fig. 2). When the frequency of Bt is on resonance, the magnetic resonance occurs and the laser is strongly absorbed. A photodetector (Newport optical receiver 2031) is used to collect the transmitted laser light and a digital oscilloscope (Tektronix TDS2014C) is used to record the spectrum.

 figure: Fig. 2

Fig. 2 Experimental setup. DBR: distributed Bragg reflector laser; PS: polarization spectroscopy; PID: proportional-integral-derivative controller; HWP: half-wave plate; QWP: quarter-wave plate; PBS: polarization beam splitter; cell: paraffin coated vapor cell filled with cesium atoms; RF: radiofrequency field; Det.: optical receiver; OSC: oscillator.

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The static magnetic field BZ0 is about 27806 nT in the experiment. The frequency of the radiofrequency field is scanned from 96.8 kHz to 98 kHz, which covers ω1andω2. The measured spectrum (solid line) is plotted in Fig. 3 and agree very well with the theoretical calculations (dashed line). The left absorption peak is the normal MZ signal corresponding toFg=4, while the right peak, whose resonant frequency equals exactly toω2, represents the collision induced magnetic resonance and has not been observed before. To understand this newly observed peak, we calculate the population distributions of all the Zeeman sublevels in two ground states versus the frequency of the radiofrequency field with and without considering spin-exchange collisions, and the results are shown in Fig. 4.

 figure: Fig. 3

Fig. 3 The magnetic resonance spectrum vs. the frequency of the oscillating magnetic fieldBt. The red solid line represents the experimental data. The blue short dash line is the theoretical calculation.

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 figure: Fig. 4

Fig. 4 Theoretical results of the population distributions of all the Zeeman sublevels in two ground states vs. the frequency of the radiofrequency field with (red lines) and without (blue lines) considering spin-exchange collisions. (a) Fg=4,mF=4; (b) Fg=4,mF=3; (c) Fg=4,mF=2; (d) Fg=4,mF=1; (e) Fg=4,mF=0; (f) Fg=4,mF=+1; (g) Fg=4,mF=+2; (h) Fg=4,mF=+3; (i) Fg=4,mF=+4; (j) Fg=3,mF=3; (k) Fg=3,mF=2; (l) Fg=3,mF=1; (m) Fg=3,mF=0; (n) Fg=3,mF=+1; (o) Fg=3,mF=+2 ;(p) Fg=3,mF=+3.

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The MZ magnetic resonance spectrum shown in Fig. 3 can be understood from the calculated population distribution at different MZ sublevels plotted in Fig. 4. When a σ + polarized laser drives the transitionFg=4Fe=3 of cesium atoms, the laser light is absorbed by the atoms in the statesFg=4,mF=4,,+2. If a far-off-resonance radiofrequency field is applied or the radiofrequency field is turned off, theσ+polarized laser light and the relaxation processes make the atoms reach a dynamic balance under the steady-state condition. The atomic population is mostly concentrated in the Fg=4,mF=+2,+3,+4states due to the optical pumping effect and the spin-exchange collisions. There are only a small amount of atoms in other magnetic sublevels of the Fg=4 states. Therefore, the atoms are polarized in the steady-state.

When the frequency of the radiofrequency field is tuned to match the Zeeman shift of the ground stateFg=4, the populations of the statesFg=4,mF=+3,+4will be transferred to the statesFg=4,mF=4,,+2. In the steady state, the atoms will accumulate in the states Fg=4,mF=4,,+2(the left peaks in Figs. 4 (a)-4(g)). Then theσ+polarized laser light will be absorbed which gives rise to the observed left peak of the magnetic resonance in Fig. 3. At the same time, the population of the statesFg=3,mF=+3 is transferred to the statesFg=4,mF=+3,+4due to the effect of the spin-exchange collision terms |4,m+13,m| and|4,m3,m|, which also contributes to the magnetic resonance signal represented by the left peak in Fig. 3.

Similarly, when the frequency of the radiofrequency field is tuned to match the Zeeman shift of the ground stateFg=3, the populations of the statesFg=3,mF=+2,+3will be transferred to the statesFg=3,mF=3,,+1. In the steady state, the atoms will accumulate in the states Fg=3,mF=3,,+1(the right peaks in Figs. 4 (j)-4(n)). Then the populations in the statesFg=3,mF=3,,+1 are transferred to Fg=4,mF=4,,+2 by the spin-exchange collision, which gives rise to the magnetic resonance represented by the right peak in Fig. 3. Similarly, the populations of the statesFg=4,mF=+4,+3 are transferred to the statesFg=3,mF=+2,+3due to the effect of spin-exchange collision terms |3,m14,m| and|3,m4,m|, which further contributes to the magnetic resonance signal represented by the right peak in Fig. 3 as well.

There are three splittings appearing in the population distribution peaks in Figs. 4(g) and 4(n). Both of the radiofrequency field and the spin-exchange collisions make contribution to the splittings. When the radiofrequency field is far off the resonance, the atoms are mainly in the statesFg=4,mF=+4,+3andFg=3,mF=+2,+3 (Figs. 4(h), 4(i), 4(o) and 4(p)) with the resonant laser and the role of spin-exchange collisions. There are also some atoms in the statesFg=4,mF=+2andFg=3,mF=+1. When the radiofrequency field is near the resonance, the atoms are transferred from the statesFg=4,mF=+4,+3andFg=3,mF=+2,+3to other magnetic sublevels, which leads to the population increase in the statesFg=4,mF=+2andFg=3,mF=+1. When the radiofrequency field is on the resonance, there are still obvious population imbalance between states Fg=4,mF=+2andFg=4,mF=+1 (Fg=3,mF=+1andFg=3,mF=0). Then the radiofrequency field will transfer the atoms from Fg=4,mF=+2toFg=4,mF=+1 (Fg=3,mF=+1toFg=3,mF=0). This is the reason for the splitting of the left peak in Fig. 4(g) and the splitting of the right peak in Fig. 4(n).

As mentioned above, there is strong coupling between the statesFg=4,mF=+2and Fg=3,mF=+2 by the spin-exchange collisions. When the frequency of the radiofrequency field equals the Zeeman shift of the ground stateFg=3, the population of the stateFg=3,mF=+2is transferred toFg=3,mF=+1by the radiofrequency field (Fig. 4(o)). Then, the population of the stateFg=4,mF=+2is transferred toFg=3,mF=+2by the spin-exchange collisions, which leads to the reduction of the population in the stateFg=4,mF=+2 (Fig. 4(g)). This is the reason for the splitting of the right peak in Fig. 4(g).

For further verification, we change the scanning time of the RF field and see if it reduces the amplitude of collisional induced magnetic resonance signal. For reference, we define the amplitudes of two signal peaks as 1 when the scanning time is 10s. The experimental results are shown in Fig. 5. The right peak amplitude of the collisional induced resonance is limited by the collision time and decreases rapidly as the scanning time is decreased. The signal disappears when the scanning time is 0.1s or less. By contrast, the signal amplitude of the left peak form the normal resonance decreases slowly and is still observed when the scanning time is 0.1 s or less.

 figure: Fig. 5

Fig. 5 The amplitudes of the two magnetic resonances vs. scanning time: 0.1s, 0.5s, 1s, 5s and 10s. The upper blue line is for the left peak (normal resonance) and the lower red one is for the right peak, the collision induced resonance.

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With the discussion above, we conclude that the observed right peak represents the magnetic resonance induced by the spin-exchange collisions. It has been shown that that the collisional induced resonance peak will be immune to the power broadening of the light [12]. This is indeed the case for the observed right peak in Fig. 3. We measured the linewidth for the left peak and right peak in Fig. 3 versus the laser input power and the results are plotted in Fig. 6. It clearly shows that the linewidth of the left peak from the normal resonance is power broadened while the linewidth of the right peak due to the collision induced resonance exhibits no power broadening and the light narrowing effect is observed in the high intensity regime which was also observed and studied in Refs [12,19,20]. There are three processes that make contribution to the linewidth of the magnetic resonances: collision with walls, spin-exchange relaxation and power broadening effect [12]. The laser light field drives the transitionFg=4Fe=3, so the left normal magnetic resonance exhibits obvious laser power broadening effect while the right collision induced magnetic resonance is not affected. In our experiment, the linewidth of the right collision induced magnetic resonance is dominated by the spin-exchange relaxation which scales linearly with atomic density and depends on the state composition of the atoms [12]. Magnetic sublevels with different populations will have different spin-exchange relaxation rates, which makes the linewidths of the different magnetic resonance transition signals different. When the experiment is operated in the low intensity regime, the atoms distribute in the statesFg=3,mFand have different populations, so the right collision induced magnetic resonance signal consists of multiple magnetic resonance transitions. Therefore, the linewidth of the collision induced magnetic resonance is the superposition of different values. When the experiment is operated in the high intensity regime, the atoms are mostly in the statesFg=3,mF=+2,+3, so the right collision induced magnetic resonance signal is mainly from the magnetic resonance transitionFg=3,mF=2mF=1. Then the linewidth is dominated by one value, which leads to the narrowing effect.

 figure: Fig. 6

Fig. 6 Line widths of the two magnetic resonance signals vs. light power. (a) left normal resonance; (b) right collision induced resonance.

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Furthermore, we also measured the signal amplitude of the right peak (from the collision induced resonance) and left peak (the normal magnetic resonance) versus the laser power and the results are plotted in Fig. 7. It shows that as the laser intensity increases, the signal amplitude of the normal magnetic resonance increases monotonically, but the amplitude of the collision induced resonance signal increases first and then is nearly constant when the laser power is increased to be above a threshold value. The phenomenon can be explained as following: First, the atoms will be mostly optically pumped to theFg=3states in the high laser power regime and the number of atoms in theFg=4states decreases when the laser power increases, which is the reason why the amplitude of the normal magnetic resonance is very small. Second, the amplitude of the collision induced resonance depends on both the spin-exchange collision rate and the optical pumping rate. When the laser power is low, the optical pumping rate is smaller than the spin-exchange collision rate. Then the amplitude is largely determined by the optical pumping rate and increases when the laser power increases. When the laser power is high, the optical pumping rate is much larger than the spin-exchange collision rate. Then the amplitude is largely determined by the spin-exchange collision rate and shows saturation effect.

 figure: Fig. 7

Fig. 7 Amplitudes of the two magnetic resonance signals vs. light power. (a) left normal resonance; (b) right collision induced resonance.

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Combination of Fig. 6 and Fig. 7 indicates that at high laser intensities, the ratio of the signal amplitude to the linewidth is nearly constant. Since the sensitivity of a magnetometer is given byδB=(ΔB/S)noise: With a constant ratio of the line widthΔBand the signal amplitude S, the sensitivity only depends on the noise, which would be the characteristic feature of the magnetometer based on the collision induced magnetic resonance observed here and provides the advantage for precision measurements of the geomagnetic field.

4. Summary

We experimentally and theoretically investigate the collision induced magnetic resonance in Cs atoms. We show that the population transfer among magnetic sublevels induced by the spin-exchange collisions can lead to a new type of the magnetic resonance. Specifically in the collisional process, the polarization in state Fg=4 created by the optical pumping is transferred to the stateFg=3. With the radiofrequency field and the spin-exchange collisions, the imbalanced population in the stateFg=3 can be transferred to the magnetic sublevels in the stateFg=4, which are coupled to the resonant laser field. It is a kind of radiofrequency-optical double magnetic resonance involving collisions. We observed that the collision induced magnetic resonance exhibits saturation effect for the signal amplitude with the increase of laser power, but the resonance linewidth is immune to the power broadening. This phenomenon will be useful for precision measurement of the geomagnetic field.

Funding

National Natural Science Foundation of China (Grant No. 11774118) and Fundamental Research Funds for the Central Universities (Grant No. CCNU18CXTD01).

References

1. H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016). [CrossRef]   [PubMed]  

2. M. Mandea and M. Korte, Geomagnetic Observations and Models (Springer, 2011).

3. A. Weis, “Optically pumped alkali magnetometers for biomedical applications,” Europhys. News 43(3), 20–23 (2012). [CrossRef]  

4. C. Deans, L. Marmugi, and F. Renzoni, “Active underwater detection with an array of atomic magnetometers,” Appl. Opt. 57(10), 2346–2351 (2018). [CrossRef]   [PubMed]  

5. E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

6. A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74(3), 033401 (2006). [CrossRef]  

7. D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University, 2013).

8. E. Pulz, K.-H. Jäckel, and H.-J. Linthe, “A new optically pumped tandem magnetometer: principles and experiences,” Meas. Sci. Technol. 10(11), 1025–1031 (1999). [CrossRef]  

9. W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972). [CrossRef]  

10. T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016). [CrossRef]  

11. Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018). [CrossRef]  

12. W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012). [CrossRef]  

13. T. G. Walker and W. Happer, “Spin-exchange optical pumping of noble-gas nuclei,” Rev. Mod. Phys. 69(2), 629–642 (1997). [CrossRef]  

14. H. Kleinpoppen, “Atoms,” in L. Bergmann and C. Schaefer, Constituents of Matter: Atoms, Molecules, Nuclei, and Particles, W. Raith, Ed. (Walter de Gruyter, 1997).

15. M. Auzinsh, D. Budker, and S. M. Rocherster, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

16. D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002). [CrossRef]  

17. S. M. Rocherster, “Modeling Nonlinear Magneto-optical Effects in Atomic Vapors”, Ph.D thesis, (Universtiy of California, Berkeley, 2010).

18. L. Margalit, M. Rosenbluh, and A. D. Wilson-Gordon, “Degenerate two-level system in the presense of a transverse magnetic field,” Phys. Rev. A 87(3), 033808 (2013). [CrossRef]  

19. S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999). [CrossRef]  

20. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011). [CrossRef]  

References

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  1. H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
    [Crossref] [PubMed]
  2. M. Mandea and M. Korte, Geomagnetic Observations and Models (Springer, 2011).
  3. A. Weis, “Optically pumped alkali magnetometers for biomedical applications,” Europhys. News 43(3), 20–23 (2012).
    [Crossref]
  4. C. Deans, L. Marmugi, and F. Renzoni, “Active underwater detection with an array of atomic magnetometers,” Appl. Opt. 57(10), 2346–2351 (2018).
    [Crossref] [PubMed]
  5. E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).
  6. A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74(3), 033401 (2006).
    [Crossref]
  7. D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University, 2013).
  8. E. Pulz, K.-H. Jäckel, and H.-J. Linthe, “A new optically pumped tandem magnetometer: principles and experiences,” Meas. Sci. Technol. 10(11), 1025–1031 (1999).
    [Crossref]
  9. W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972).
    [Crossref]
  10. T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
    [Crossref]
  11. Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
    [Crossref]
  12. W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
    [Crossref]
  13. T. G. Walker and W. Happer, “Spin-exchange optical pumping of noble-gas nuclei,” Rev. Mod. Phys. 69(2), 629–642 (1997).
    [Crossref]
  14. H. Kleinpoppen, “Atoms,” in L. Bergmann and C. Schaefer, Constituents of Matter: Atoms, Molecules, Nuclei, and Particles, W. Raith, Ed. (Walter de Gruyter, 1997).
  15. M. Auzinsh, D. Budker, and S. M. Rocherster, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).
  16. D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
    [Crossref]
  17. S. M. Rocherster, “Modeling Nonlinear Magneto-optical Effects in Atomic Vapors”, Ph.D thesis, (Universtiy of California, Berkeley, 2010).
  18. L. Margalit, M. Rosenbluh, and A. D. Wilson-Gordon, “Degenerate two-level system in the presense of a transverse magnetic field,” Phys. Rev. A 87(3), 033808 (2013).
    [Crossref]
  19. S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999).
    [Crossref]
  20. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
    [Crossref]

2018 (2)

C. Deans, L. Marmugi, and F. Renzoni, “Active underwater detection with an array of atomic magnetometers,” Appl. Opt. 57(10), 2346–2351 (2018).
[Crossref] [PubMed]

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

2016 (2)

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

2013 (1)

L. Margalit, M. Rosenbluh, and A. D. Wilson-Gordon, “Degenerate two-level system in the presense of a transverse magnetic field,” Phys. Rev. A 87(3), 033808 (2013).
[Crossref]

2012 (2)

A. Weis, “Optically pumped alkali magnetometers for biomedical applications,” Europhys. News 43(3), 20–23 (2012).
[Crossref]

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

2011 (1)

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
[Crossref]

2006 (1)

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74(3), 033401 (2006).
[Crossref]

2002 (1)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

1999 (2)

S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999).
[Crossref]

E. Pulz, K.-H. Jäckel, and H.-J. Linthe, “A new optically pumped tandem magnetometer: principles and experiences,” Meas. Sci. Technol. 10(11), 1025–1031 (1999).
[Crossref]

1997 (1)

T. G. Walker and W. Happer, “Spin-exchange optical pumping of noble-gas nuclei,” Rev. Mod. Phys. 69(2), 629–642 (1997).
[Crossref]

1996 (1)

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

1972 (1)

W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972).
[Crossref]

Alexandrov, E.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

Andreou, A. G.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Anielski, P.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

Appelt, S.

S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999).
[Crossref]

Balabas, M.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

Ben-Amar Baranga, A.

S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999).
[Crossref]

Bison, G.

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74(3), 033401 (2006).
[Crossref]

Budker, D.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Chalupczak, W.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

Deans, C.

Dolgovskiy, V.

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

Fritzsche, S.

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

Gawlik, W.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Godun, R. M.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

Grujic, Z.

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

Happer, W.

S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999).
[Crossref]

T. G. Walker and W. Happer, “Spin-exchange optical pumping of noble-gas nuclei,” Rev. Mod. Phys. 69(2), 629–642 (1997).
[Crossref]

W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972).
[Crossref]

IJsselsteijn, R.

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
[Crossref]

Jäckel, K.-H.

E. Pulz, K.-H. Jäckel, and H.-J. Linthe, “A new optically pumped tandem magnetometer: principles and experiences,” Meas. Sci. Technol. 10(11), 1025–1031 (1999).
[Crossref]

Kafel, M.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Kimball, D. F.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Kitching, J.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Knappe, S.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Korth, H.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Lebedev, V.

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

Lehtonen, S. J.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Linthe, H.-J.

E. Pulz, K.-H. Jäckel, and H.-J. Linthe, “A new optically pumped tandem magnetometer: principles and experiences,” Meas. Sci. Technol. 10(11), 1025–1031 (1999).
[Crossref]

London, S. M.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Margalit, L.

L. Margalit, M. Rosenbluh, and A. D. Wilson-Gordon, “Degenerate two-level system in the presense of a transverse magnetic field,” Phys. Rev. A 87(3), 033808 (2013).
[Crossref]

Marmugi, L.

Meyer, H.-G.

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
[Crossref]

Pasgalev, A.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

Pazgalev, A. S.

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74(3), 033401 (2006).
[Crossref]

Pulz, E.

E. Pulz, K.-H. Jäckel, and H.-J. Linthe, “A new optically pumped tandem magnetometer: principles and experiences,” Meas. Sci. Technol. 10(11), 1025–1031 (1999).
[Crossref]

Pustelny, S.

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

Renzoni, F.

Rocherster, S. M.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Rosenbluh, M.

L. Margalit, M. Rosenbluh, and A. D. Wilson-Gordon, “Degenerate two-level system in the presense of a transverse magnetic field,” Phys. Rev. A 87(3), 033808 (2013).
[Crossref]

Scholtes, T.

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
[Crossref]

Schultze, V.

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
[Crossref]

Shi, Y.

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

Stolz, R.

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

Strohbehn, K.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Tejada, F.

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Vershovskii, A.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

Walker, T. G.

T. G. Walker and W. Happer, “Spin-exchange optical pumping of noble-gas nuclei,” Rev. Mod. Phys. 69(2), 629–642 (1997).
[Crossref]

Weis, A.

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

A. Weis, “Optically pumped alkali magnetometers for biomedical applications,” Europhys. News 43(3), 20–23 (2012).
[Crossref]

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74(3), 033401 (2006).
[Crossref]

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Wilson-Gordon, A. D.

L. Margalit, M. Rosenbluh, and A. D. Wilson-Gordon, “Degenerate two-level system in the presense of a transverse magnetic field,” Phys. Rev. A 87(3), 033808 (2013).
[Crossref]

Woetzel, S.

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
[Crossref]

Wojciechowski, A.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

Yakobson, N.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

Yashchuk, V. V.

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Young, A. R.

S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999).
[Crossref]

Appl. Opt. (1)

Europhys. News (1)

A. Weis, “Optically pumped alkali magnetometers for biomedical applications,” Europhys. News 43(3), 20–23 (2012).
[Crossref]

J. Geophys. Res. Space Phys. (1)

H. Korth, K. Strohbehn, F. Tejada, A. G. Andreou, J. Kitching, S. Knappe, S. J. Lehtonen, S. M. London, and M. Kafel, “Miniature atomic scalar magnetometer for space based on the rubidium isotope 87Rb,” J. Geophys. Res. Space Phys. 121(8), 7870–7880 (2016).
[Crossref] [PubMed]

Laser Phys. (1)

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6(2), 244–251 (1996).

Meas. Sci. Technol. (1)

E. Pulz, K.-H. Jäckel, and H.-J. Linthe, “A new optically pumped tandem magnetometer: principles and experiences,” Meas. Sci. Technol. 10(11), 1025–1031 (1999).
[Crossref]

Phys. Rev. A (5)

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74(3), 033401 (2006).
[Crossref]

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85(4), 043402 (2012).
[Crossref]

L. Margalit, M. Rosenbluh, and A. D. Wilson-Gordon, “Degenerate two-level system in the presense of a transverse magnetic field,” Phys. Rev. A 87(3), 033808 (2013).
[Crossref]

S. Appelt, A. Ben-Amar Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59(3), 2078–2084 (1999).
[Crossref]

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84(4), 043416 (2011).
[Crossref]

Phys. Rev. A (Coll. Park) (2)

T. Scholtes, S. Pustelny, S. Fritzsche, V. Schultze, R. Stolz, and H.-G. Meyer, “Suppression of spin-exchange relaxation in tilted magnetic fields within the geophysical range,” Phys. Rev. A (Coll. Park) 94 (1), 013403 (2016).
[Crossref]

Y. Shi, T. Scholtes, Z. Grujic, V. Lebedev, V. Dolgovskiy, and A. Weis, “Quantitative study of optical pumping in the presence of spin-exchange relaxation,” Phys. Rev. A (Coll. Park) 97(1), 013419 (2018).
[Crossref]

Rev. Mod. Phys. (3)

D. Budker, W. Gawlik, D. F. Kimball, S. M. Rocherster, V. V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

T. G. Walker and W. Happer, “Spin-exchange optical pumping of noble-gas nuclei,” Rev. Mod. Phys. 69(2), 629–642 (1997).
[Crossref]

W. Happer, “Optical Pumping,” Rev. Mod. Phys. 44(2), 169–249 (1972).
[Crossref]

Other (5)

M. Mandea and M. Korte, Geomagnetic Observations and Models (Springer, 2011).

D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University, 2013).

H. Kleinpoppen, “Atoms,” in L. Bergmann and C. Schaefer, Constituents of Matter: Atoms, Molecules, Nuclei, and Particles, W. Raith, Ed. (Walter de Gruyter, 1997).

M. Auzinsh, D. Budker, and S. M. Rocherster, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

S. M. Rocherster, “Modeling Nonlinear Magneto-optical Effects in Atomic Vapors”, Ph.D thesis, (Universtiy of California, Berkeley, 2010).

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Figures (7)

Fig. 1
Fig. 1 Energy structure of the cesium atoms in the external magnetic field B Z 0 . The red solid arrows represent the σ + polarized laser field that couples the atomic transitions F g = 4 , m F F e = 3 , m F + 1 (D1 lines at 895 nm). The radiofrequency field RF is scanned and the range of the frequency covers ω 1 and ω 2 which are the Zeeman shifts of the two hyperfine states. SEC represents the spin-exchange collisions.
Fig. 2
Fig. 2 Experimental setup. DBR: distributed Bragg reflector laser; PS: polarization spectroscopy; PID: proportional-integral-derivative controller; HWP: half-wave plate; QWP: quarter-wave plate; PBS: polarization beam splitter; cell: paraffin coated vapor cell filled with cesium atoms; RF: radiofrequency field; Det.: optical receiver; OSC: oscillator.
Fig. 3
Fig. 3 The magnetic resonance spectrum vs. the frequency of the oscillating magnetic field B t . The red solid line represents the experimental data. The blue short dash line is the theoretical calculation.
Fig. 4
Fig. 4 Theoretical results of the population distributions of all the Zeeman sublevels in two ground states vs. the frequency of the radiofrequency field with (red lines) and without (blue lines) considering spin-exchange collisions. (a) F g = 4 , m F = 4 ; (b) F g = 4 , m F = 3 ; (c) F g = 4 , m F = 2 ; (d) F g = 4 , m F = 1 ; (e) F g = 4 , m F = 0 ; (f) F g = 4 , m F = + 1 ; (g) F g = 4 , m F = + 2 ; (h) F g = 4 , m F = + 3 ; (i) F g = 4 , m F = + 4 ; (j) F g = 3 , m F = 3 ; (k) F g = 3 , m F = 2 ; (l) F g = 3 , m F = 1 ; (m) F g = 3 , m F = 0 ; (n) F g = 3 , m F = + 1 ; (o) F g = 3 , m F = + 2 ;(p) F g = 3 , m F = + 3 .
Fig. 5
Fig. 5 The amplitudes of the two magnetic resonances vs. scanning time: 0.1s, 0.5s, 1s, 5s and 10s. The upper blue line is for the left peak (normal resonance) and the lower red one is for the right peak, the collision induced resonance.
Fig. 6
Fig. 6 Line widths of the two magnetic resonance signals vs. light power. (a) left normal resonance; (b) right collision induced resonance.
Fig. 7
Fig. 7 Amplitudes of the two magnetic resonance signals vs. light power. (a) left normal resonance; (b) right collision induced resonance.

Equations (13)

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g F = g J F ( F + 1 ) I ( I + 1 ) + J ( J + 1 ) 2 F ( F + 1 ) + g I F ( F + 1 ) + I ( I + 1 ) J ( J + 1 ) 2 F ( F + 1 )
ρ ˙ = 1 i [ H , ρ ] 1 2 { R ^ , ρ } + Λ γ + T r ( F ρ ) + L e c o ρ + Γ sec ( ρ ) .
H = H 0 + H E + H B .
H 0 = F m F ω F m F | F m F F m F | + F ' m F ' ω F ' m F ' | F ' m ' F F ' m F ' | .
H E = d E = F , F ' , m F , m F ' F ' m F ' | d | F m F E | F ' m F ' F m F | + h . c .
H B = μ B = g F μ B F , m F , F ' , m ' F F m F | F | F m F ' B | F m F F m ' F | .
R ^ = F m F γ | F m F F m F | + F ' m F ' ( γ + Γ ) | F ' m F ' F ' m F ' | .
Λ γ = F m F γ | F m F F m F | ρ m F m F e q .
T r ( F ρ ) m n = r s F m n s r ρ r s .
F m n s r = 4 ω r m 3 3 c 3 d m r d s n .
L ^ e c o ρ ^ = m F ' m ' F Γ * D [ σ m F ' m F ' , σ m ' F m ' F ] .
D [ σ m F ' m F ' , σ m ' F m ' F ] σ m F ' m F ' ρ σ m ' F m ' F 1 2 ρ σ m ' F m ' F σ m F ' m F ' 1 2 σ m ' F m ' F σ m F ' m F ' ρ
Γ ^ sec ( ρ ) R sec = 3 4 ρ + S ^ ρ S ^ + S ^ ( { S ^ , ρ } 2 i S ^ × ρ S ^ ) .

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