We compare the performance of two methods for the synchronization of the atomic spins in optically pumped magnetometers: intensity modulation of the pump light and the classical Mx method using B1 field modulation. Both techniques use the same set-up and measure the resulting features of the light after passing a micro-fabricated Cs cell. The intensity-modulated pumping shows several advantages: better noise-limited magnetic field sensitivity, misalignment between pumping and spin synchronization is excluded, and magnetometer arrays without any cross-talk can be easily set up.
© 2012 OSA
CorrectionsVolkmar Schultze, Rob Ijsselsteijn, Theo Scholtes, Stefan Woetzel, and Hans-Georg Meyer, "Characteristics and performance of an intensity-modulated optically pumped magnetometer in comparison to the classical Mx magnetometer: Erratum," Opt. Express 20, 28056-28056 (2012)
Optical magnetometers rely on the measurement of light transmitted through a sample of atoms, whose optical properties are modified by its interaction with the magnetic field [1–4]. The details of both the light-atom and atom-field interactions can vary significantly between magnetometer types and operating modes. For magnetometers using alkali atoms, all methods rely on incident resonant light driving an optical pumping process in the atomic sample to create a polarization of the atoms in the magnetic sublevels of the hyperfine ground states. The resulting atomic polarization moment then couples to the magnetic field B0 to be measured. The temporal evolution of the ensemble polarization in the magnetic field hence is driven away from the value created by the incident light, and thus modifies the light absorption, transmission or polarization properties of the sample in a dynamic way. Detection of the field-induced perturbation of the transmitted light then yields information on the field B0 itself.
In the Mx method, the coupling of magnetic moment of the alkali atoms and magnetic field B0 manifests itself in a precession of the atomic spins about the magnetic field direction at the Larmor frequency fL = γ⋅B0 (with γ being the gyromagnetic factor of the used alkali atom) [5–7]. The maximal modulation of the transmitted light is obtained if all spins precess with the same phase. This phase synchronization is provided by a small magnetic field B1 modulated at the Larmor frequency.
An alternative technique for phase synchronization was presented early on in the pioneering work of Bell and Bloom  (what gave the Bell-Bloom (BB) method its name). The authors modulated the intensity of the pumping lamp and measured the transmission through metastable helium (with one single electron in the outer energy level similar to alkali atoms). However, in this original BB arrangement only the dc change of the transmission was evaluated for equal modulation and Larmor frequency. This resulted in a very poor magnetic field resolution compared to the Mx method with its phase-sensitive measurement. The equivalence of Mx method and intensity modulation (IM) of the pump light with regard to phase coherence was later on shown both theoretically and experimentally by Novikov et al. . Thereafter the IM method was used as a tool to prepare and investigate the atomic sublevel coherence itself [10–12]. One prominent example for this method is its application in the search for a permanent electric dipole of 199Hg .
In optical magnetometers, intensity or frequency modulation of the pumping beam is common to both nonlinear magneto-optical rotation (NMOR) [14,15] and the BB method. In NMOR, the change in polarization direction of a linearly polarized light beam due to the interaction of magnetic field B0 and the atomic spin system is evaluated. Concerning the BB method, very recent adaption was presented by Jiménez-Martínez et al. . They introduced the phase-sensitive evaluation of the measurement signal to the original BB arrangement. However, this phase-synchronization was not performed by intensity but frequency modulation (FM) of the pumping beam. So, none of these optical magnetometer concepts uses the combination of intensity-modulated pumping and phase-selective measurement. To our knowledge, only once has a measurement been performed in such a configuration . However, this did not result in a working magnetometer. Instead, additionally to the intensity-modulated pumping light beam, a second, unmodulated probe beam was introduced .
Here, we present an optical magnetometer with intensity-modulated pumping of a Cs magnetometer cell and phase-selective measurement of the resulting intensity modulation of the transmitted light. This arrangement is then applied for magnetic field measurement. These investigations were performed with an array of identical micro-fabricated cells . Various array configurations can be formed, which allow for the formation of gradiometers, cancellation of heading errors with conversely circularly pumped cells , or noise reduction with reference cells . In this context, we expected various advantages of the IM method compared to the Mx method. Firstly, there is no alignment problem between pumping and spin synchronization and no associated errors of the magnetic field measurement  arise, because the role of the B1-field is replaced by intensity modulation of the pump beam. Secondly, any cross-talk between magnetometer cells in an array due to the B1-fields is avoided. Thirdly, the same laser source can be used for all magnetometer cells. In this way, the noise caused by the laser can be eliminated later on.
2. Experimental setup
The experimental setup is displayed in Fig. 1 . For all experiments (with B1-field as well as with intensity modulation IM) the setup remained fixed and the same magnetometer cell M out of an integrated 2x2 array was used. The manufacturing of the cells  followed the general principles developed at the National Institute of Standards and Technology (NIST) [21,22]. Our cells, of 50 mm3 volume, each consist of holes with 4 mm diameter in a 4 mm thick silicon wafer, connected via canals to a central reservoir for the Cs metal. The cell assembly is closed by anodically bonded glass plates on both sides. In addition to the Cs as the active medium the cells are filled with nitrogen as buffer gas. The nitrogen pressure is 21 mbar, determined by the shift of the Cs D1 lines in the absorption spectrum . The array is enclosed by two printed circuit boards PCB, containing the B1-field coils. These rectangular coils with 7 mm side-lengths and 6 mm distance produce a field oriented in laser beam direction, thus keeping the system’s axial symmetry [2,5]. The cell is heated by off-resonant heating laser radiation (λ = 808 nm), fiber-coupled on the cell’s Si side walls. All measurements were carried out at 76°C, corresponding to a saturated alkali vapor density of n = 3.2⋅1012 cm−3 .
This magnetometer cell setup is fixed in the middle of a three-fold concentric µ-metal shielding barrel, suppressing outside magnetic fields and disturbances by a factor of about 103 for dc fields, increasing up to 104 to 105 for frequencies of several 10 Hz for axial and transverse direction, respectively. The measurement field B0 is generated by a three-axis Helmholtz coil system with additional correction coils. In this way, a central cube of 10 cm side length with distortion less than 2x10−3 from magnetic field homogeneity is created . The magnetic field was varied in direction, while its magnitude was kept at B0 = 5 µT. Due to the limited shielding factor of the barrel, diurnal earth’s magnetic field variations cause some low-frequency noise, reflected in the magnetometer measurements.
A distributed feedback (DFB) laser provides a narrow-band (Δf < 5 MHz) laser beam that can be automatically tuned around the Cs D1 line (λ = 894.6 nm) and varied in intensity. The linearly polarized output laser beam is fed via polarization-maintaining optical fibers into an integrated lithium-niobate (LiNbO3) based Mach-Zehnder interferometer AM905HF from Jenoptik  which serves as intensity modulator. Compared to typically used acousto-optical modulators it further improves the linear polarization and is more easily incorporated into the setup via fiber coupling. The intensity modulator has a cosine dependence of the transmitted light intensity on the applied dc voltage, ranging from 4 dB damping for zero voltage to complete extinction for 2.5 V. Behind the output fiber of the modulator, the light path is split and coupled into two multimode fibers. In the measurement channel M, inside the shielding barrel, the pumping light passes another polarizer (to re-establish a good linear polarization) and a λ/4 plate to create circular polarization. In the reference channel R, the light is guided through several tight loops of the fiber, providing depolarized light. In the reference channel the degree of linear polarization was suppressed down to ≈1%. In the measurement channel the minor to major axis ratio of the elliptically polarized light was >98%. The incident and transmitted laser power ranged from about 40 to 100 and 10 to 25 µW in the various measurements, respectively.
The resulting signal behind the magnetometer cell is detected by a photo diode and amplified by a low-noise trans-impedance amplifier. The phase synchronization of the precessing atomic spins is realized either by B1 field or intensity modulation of the pumping beam. A generator provides both the modulation signal and the reference for the lock-in amplifier. All measurement parameters are controlled and recorded by computer.
3. Results and discussion
The new IM method is evaluated in three steps. First, the pure transmitted signal behind the magnetometer cell is looked at. Then, the resulting signals using lock-in detection are regarded, followed by the determination of the achievable magnetic field resolution. In each step, the parameters are compared to the common Mx method.
3.1 Magnetometer signals
In the first experiment, the alkali vapor was pumped with rectangular light pulses. This means, the intensity modulator switched the light on and off. Figure 2 shows the resulting signals behind the magnetometer cell. Since the spin precession is only visible during the switched-on times, a longer switch-on time gives more measurement time. However, the relaxation of the spin polarization leads to a damping of the signal, which counteracts the benefit of a longer switch-on time. Therefore, switching-off once per Larmor period yields the best pronounced signals. For this case, the dependence of the signals on duty cycle d (given as the fraction of the Larmor period, where the light is switched on) and modulation depth k (by changing the lower pump light level) was investigated. The results shown in Fig. 3 depict an optimum for a symmetric pumping (d = 50%) and complete modulation (k = 100%). This is independent of the switched-on pump level. Either appears plausible. Complete modulation causes strongest phase synchronization. For a symmetric pumping cycle not only pump-light switch-on but also switch-off is synchronized to the spin precession course.
The signal patterns in Fig. 3 can be explained more quantitatively using the results of Suter, Mlynek et al. [10,11]. They investigated the magnetic resonances of a sodium vapor cell with buffer gas in an experimental setup comparable to ours. The alkali vapor was pumped with a circularly polarized laser beam, which was oriented perpendicular to the magnetic field. The laser beam was switched on or off to measure the step response of the system. However, in contrast to our measurements, the authors measured the time evolution of the magnetization with a separate linearly polarized probe beam. From their results, the magnetization component parallel to the pump beam is relevant for us, because it is responsible for the change in transmission that we measure.
In our measurements, the laser is tuned on the center of the resonance line. Therefore, light-shift terms are negligible. Furthermore, our modulation frequency always equaled the Larmor frequency. Then the formulas given in Refs.  and  for the time dependence of the magnetization in pump direction can be simplified to10] and m- the free induction decay after switching off . ΩL is the angular Larmor frequency ΩL = 2π⋅fL. Amplitude A and phase φ of the oscillatory signals are given byFigs 2(b) and (c). In our measurements, the relaxation rates were Γeff = 2.2kHz and Γ0 = 480Hz (the latter was extrapolated from the light-intensity dependence to zero pumping rate). Together with the Larmor frequency fL = 17.7 kHz this results in a phase of φ = 88.9° (it would be 90° for infinitely small resonance).
In contrast to the investigations of Suter, Mlynek et al., where well-resolved single responses to a switch-on  or switch-off  of the pump laser were examined, in our experiments both are repeated alternatingly. The effect of this continuous switching up and down we simply took into account by a superposition of m+(t) and m-(t) with some phase difference δ between them. However, some further adaption of the original formulas to our situation had to be made. In Ref , a stationary value m∞ approached infinite time after switch-on is used in the m+ equation. We get a stationary magnetization ms after many successive switch-on and -off cycles. After switch-on, magnetization builds up due to . It then decays much more slowly after switch-off withfrom the value reached during illumination. After several cycles, in this way a stationary value ms is created, which depends on the duty cycle d in good approximation to
In order to describe the experiments with varying duty cycle d, we introduced the phase shift between switch-on and switch-off pulses into Eq. (2). Therefore, any deviation of the duty cycle from 0.5 (corresponding to a phase difference of 180°) harms the constructive superposition of the magnetizations m+ and m-, what leads to smaller resulting modulation. In Fig. 4(a) , left graph, the resulting magnetization is shown in dependence on duty cycle d. The experimentally observable light signal (Fig. 4(a), right graph) simply reproduces this magnetization, taking into account the vanishing visibility in the switched-off time.
In Fig. 4(b), left and right graph, the resulting magnetization and photo signal for various modulation depths k are shown (performed with optimum duty cycle d = 0.5), respectively. The measurements with varied modulation depth k correspond to a switching between a fixed higher pumping level (k = 0) and a varied lower one (k = 1 for complete switch-off). This has several consequences for the adaption of the Eq.s (1) – (5): (1), the step height of switching is reduced. Therefore, the amplitude A of both oscillatory magnetizations m+ and m- is weighted with k. (2), now also the low-level magnetization has a stationary value. The weight of this ms is (1-k). (3), the exponential decay of the oscillation after switch-down does not proceed with the relaxation rate Γ0 anymore, but at a rate Γk = Γ0 + (1-k)⋅P+ between Γ0 and Γeff. (4), because the pumping light strength also determines the visibility of the magnetization in our measurement configuration, the signals in the switch-down period have to be multiplied with (1-k).
For all dependencies, the calculations reflect the experimental curves reasonably well.
In the following experiment, a “smoother” kind of pump modulation was investigated, in order to see, whether an incomplete switching off of the observable light during half the period results in any advantages. A smoothed top-hat intensity profile was achieved by sinusoidally varying the applied voltage across the modulator with respect to time. In combination with the cosinusoidal dependence of the transmission on the applied voltage this smoothed top-hat function results. Figure 5 shows the effect of variation of the pumping modulation frequency around the Larmor frequency fL on the signal. For both IM methods, with rectangular and smoothed light pulses, the pronounced signal at fL combined with a phase change in its vicinity can be seen distinctly. No preference of one or the other IM method can be found here. In Fig. 6 the resulting light modulation signals at Larmor frequency are compared with B1-field modulation.
All the IM experiments were performed with the measurement field B0 perpendicular to the pump light direction, because in this arrangement the best sensitivity is achieved. This is shown in the polar diagram in Fig. 7 . In contrast to the Mx method with two dead zones (polar and equatorial) the IM method has just one like any BB magnetometer.
3.2 Lock-in signals
In Fig. 8 the signals after lock-in demodulation are shown. The absorptive signals Ua showing the resonance, exhibit a distinct difference between the Mx and the IM technique. Detuning far from the Larmor frequency, the B1-field modulation does not produce any signal. For IM operation the signal still occurs, causing a high base floor. In the dispersive signal Ud (which may be regarded as the derivative of the absorptive one) this floor is cancelled. The phase signal φ, given by φ = arctan(Ud/Ua), exhibits smaller steepness around the Larmor frequency for the IM method than for the Mx one, because of the absorptive signal’s offset. However, it is still sufficient for phase detection and adjustment, which is a prerequisite for a proper discrimination between absorptive and dispersive signals.
Elaborated experimental investigations of the lock-in signals’ dependence on the operational parameters confirmed, that the steepest slope of the dispersive signal is obtained for modulation depth k = 100% and duty cycle d = 50%.
3.3 Magnetic field resolution
Figure of merit for a magnetometer is its noise-limited magnetic field resolution. Here, two parameters are important. The principal potential of the magnetometer is given by the shot-noise limited magnetic field resolution Bsn [7,26]. Next, the question is how close the real noise measurement value Bn can approach this shot-noise value.
The shot-noise limited magnetic field resolution Bsn is calculated according toTable 1 together with the other parameters. They are the result of an individual optimization for each method aiming at lowest Bsn value. For this, the B1-field strength in the Mx method and the pump light intensity for all methods was varied. The latter is reflected in the resulting dc photo current Idc.
It should be remarked that in the Mx method Idc is given as the rms-value of the signal modulated at the Larmor frequency . This would make no sense in the IM method, however, because a substantial part of the modulation is generated by the pumping itself. For that reason, here we used the value at the full illumination to determine Idc. Due to the 100% modulation depth it is about twice the rms-value.
The resonance widths (half-width at half-maximum) and the steepness |dUd/df| are extracted from the dependencies shown in Fig. 8. The widths Γd and Γφ of the dispersive and the phase signal were determined as the frequency difference between signal maximum and zero crossing and the frequency difference between 45° and 0° phase, respectively.
The IM method requires a higher pumping light level (reflected in the higher photo current Idc) than the Mx method, because the light modulation has to synchronize the spin phases. On the other hand, in the Mx method the B1-field broadens the resonance width Γd [2,9,28,29] (shown by a comparison with the value Γφ of the phase signal, which is free from that broadening). At the end both methods yield comparable ultimate magnetic field resolution Bsn.
To determine the real noise Bn, the voltage Ud of the dispersive signal at or (due to noise) around the Larmor frequency was measured. Additionally to the experiments using only the measurement channel M, reduction of the noise by implementing a reference channel R was investigated, which is pumped by the same laser source. Therefore, noise contributions coming from laser amplitude and frequency variations should be eliminated to a high degree. This was already shown for the Mx method , where it was sufficient to assure similar pumping conditions for measurement and reference channel with the exception, that only the measurement channel’s spins are phase-synchronized with a B1-field. In the new IM method, pumping and phase synchronization are performed both with the same laser beam. Therefore, a new way to desensitize the reference channel to magnetic fields had to be incorporated. For that reason, the reference pumping beam was depolarized before passing a second Cs cell of the array. First, the light intensities of the two beams were trimmed to be equal. Then the reference signal magnitude was adjusted with a tunable amplifier to minimize noise. In accordance with the results reported in Ref , the lowest noise values in the Mx method were achieved with equal magnitudes of both signals. In the new IM method, however, a value of about 0.6 was optimal for the gain Gref of the reference signal. Apparantly this is because up to that value the differential measurement signal is free from artifacts (Fig. 9 ).
This holds both for rectangular and smoothed pulses. However, in the following measurements a better noise reduction with the reference channel was achieved with the rectangular pulses. Figure 10 shows the measured noise spectra for this IM variant and the Mx method, both using only the measurement channel as well as an additional subtraction of the reference channel. The additionally plotted shot-noise levels as the ultimate values are larger by a factor of and than those given in Table 1 for the Mx and IM method, respectively, because of the different shot-noise contributions from the reference channel.
With the additional laser noise reduction using a reference channel, in the IM method the white noise approaches the shot-noise level. In order to classify this value, Table 2 shows a comparison with those given in the literature (to our knowledge, the best magnetometer in its class was chosen). The selection is exclusively focused on magnetometers working in the Mx method or BB with phase synchronization. SERF (spin-exchange-relaxation-free) magnetometers are not included, because they are restricted to zero field operation [30,31]. A more comprehensive comparison (including operational methods beyond the scope of this paper) can be found in Ref . The figure of merit in Table 2 is Bn√V, where the magnetic field resolution is weighted with the active cell volume V. In this way, magnetometers of different size can be compared, because Bn depends on the cell volume according to
Accordingly, our IM magnetometer shows the best results amongst those using small buffer gas cells.
For frequencies below 100 Hz the white noise of the IM magnetometer in Fig. 10 is superimposed by 1/f noise. This will most likely be due to external noise sources (viz. chapter 2). Further investigations, for example with gradiometer setups, have to be undertaken to verify this assumption. The noise peaks between 10 and 20 Hz are originated by residual microphonic effects in the setup.
In our Mx magnetometer configuration the 1/f noise dominates the complete spectrum up to several kHz. A satisfactory explanation cannot as yet be given. However, because all parameters in the magnetometer operation, except the phase synchronization method, were completely identical to the IM measurements, this impairment can only be due to the B1-field action, perhaps in combination with the buffer gas. In fact, with large B1-field coils and vacuum cells good results have been achieved in the Mx configuration [20,27,28,33,34]. Clearly, the IM method avoids any problems connected with the B1-field a priori, thus reaching the ultimate shot-noise limit in the measurement.
3. Summary and conclusion
The pumping-light intensity-modulation (IM) method enables a very convenient and valuable magnetometer operation. Like the original BB method, it has only one dead zone. It is an all-optical technique, combining pumping, phase synchronization and signal detection with one laser beam. The shot-noise limited magnetic field resolution is identical to that obtained with the Mx method. However, in the IM technique this ultimate value is also reached in real noise measurement, if an additional noise-reducing reference channel is used. Furthermore, the omission of B1-field coils in the IM method not only simplifies the setup, but also abolishes any crosstalk between different channels in an array. Finally, in the Mx method, even small misalignments between the pumping light and the B1-field axis cause phase shifts, resulting in errors of the measured magnetic field. The combination of pumping and phase synchronization in the IM method avoids this problem.
We thank Alex Brown for his careful proofreading of the article. This work was supported by the state of Thuringia/Germany under contract number B714-10043 with participation of the European Union Fund for Regional Development.
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