1. Introduction

Optically pumped magnetometers (OPMs), despite being invented more than 50 years ago [1], have seen renewed interest and a rapid development in recent years [2], now even surpassing SQUIDs as the most sensitive magnetic field sensors [3]. An OPM relies on a measurable interaction of alkali atom vapor, usually kept in glass cells, with the external magnetic field B⃗₀. One established setup, as applied here, uses a single narrow-band laser light beam resonant on the D1 transition of the alkali atom for both preparation of the atoms by optical pumping [4], and for signal detection by monitoring the cell-transmitted light power [5]. A suitably prepared alkali atom subject to an external static magnetic field starts to precess, thereby modulating its optical properties at the characteristic Larmor frequency ω_L = γ|B⃗₀|, where γ denotes the gyromagnetic ratio of the alkali atom. This modulation becomes resonantly enhanced and all the atoms precess phase-synchronized when the frequency of an additionally applied alternating magnetic field B₁ matches the Larmor frequency, giving rise to the macroscopic measurement signal. Using a feedback loop keeping the B₁ frequency equal to ω_L a sensor can be built [6].

Basically, OPMs are inherently scalar sensors measuring the absolute value of B⃗₀ independently of its spatial direction. However, several prominent effects like the dead zones of the M_x setup, the nonlinear Zeeman effect in mediate magnetic fields (leading to asymmetic Cs magnetic resonance lines) or light shifts (i.e. AC Stark shifts) due to off-resonantly tuned, circularly polarized light [7] introduce an orientational dependence to the sensor’s readings that have to be considered and well controlled [8]. Operating the magnetometer in the light-narrowed (LN) mode (cf. Sec. 3), as published recently [9], requires the circularly polarized laser radiation frequency to be tuned away from the magnetic resonance (at the upper hyperfine groundstate level F = 4). Due to the high intensity of the detuned laser light a strong displacement of the detected Larmor frequency dependent on the relative orientation of the external magnetic field to the pumping light’s direction emerges. To remove this effect, an approach known for almost 40 years [10], using the average of two identical but oppositely circularly polarized pumped magnetometer channels, is reinvestigated. However, this approach is applied to our special case of severe laser detuning and a buffer-gas broadened cell absorption profile of overlapping hyperfine transitions. For this purpose, due to the need of as identical cells as possible, a microfabricated multi-channel array sharing a common reservoir is used.

After describing the experimental setup the sensitivity optimizations are presented, followed by the investigation of the light-shift suppression.

2. Experimental setup

The setup shown in Fig. 1(a) is similar to the one described in [9], extended to be capable of two-channel measurements. The central part of the sensor is the newly designed vapor cell array shown in Fig. 1(b) incorporating two measurement cells sharing one common Cs metal reservoir. The fabrication of the cells follows the procedure described in [11]. The cells are illuminated by narrow-band (Δν < 5MHz) circularly polarized light of a DFB laser, that is optionally amplified by a tapered amplifier and tuned to the Cs D1 line (λ = 894.6nm). The intensity of the modulated cell-transmitted laser light is monitored by silicon PIN photo diodes. The cell array is temperature-controlled by far off-resonant (λ = 977nm) heating laser radiation that is fiber-coupled onto two sooted spots of the cell array’s silicon wafer parts. The relatively good heat conductivity of silicon leads to equal measurement cell temperatures and to a slightly smaller temperature at the bigger central reservoir cavity, ensuring that Cs condensation always occurs there [12]. Coils on printed circuit boards are attached to both sides of the cell array to supply B₁ fields parallel to the pump laser’s direction being separately tunable for both channels. The B₁ fields are driven by the lock-in’s integrated oscillators that are also being used as the photo signals demodulation references. Despite the encouraging results obtained most recently by the use of an all-optical light modulation technique [13], we here stick to the ”classical” B₁ method, as with the present setup the maximum possible pump laser power is not sufficient to allow an investigation of all-optical LN operation. For future unshielded application, we characterize our sensor at earth’s magnetic field strength. The setup is placed inside a three-axis Helmholtz coil system, described more in detail in [14]. The six coils are each fed by independently controllable current sources, to supply B₀ = 50μT at an angle of 45° relative to the laser direction (used for the noise measurements) as well as enabling rotation of B⃗₀ across a full half space for the orientation-dependent investigations. External fields and disturbances are shielded using a three-fold mu-metal barrel and reduced by a factor of not less than 500. The two channels can be used as independent magnetometers or one channel, made magnetically insensitive by switching off the B₁ field, can serve to cancel technical noise [14, 15].

 

Fig. 1 (a) Experimental setup: The two magnetometer channels can be operated independently (switched to A) or channel 2 can be made magnetically insensitive to provide a noise subtraction signal for the magnetometer channel 1 (switched to B). (b) Used cell array assembly filled with 170mbar of nitrogen buffer gas.

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3. Magnetometer sensitivity optimization

The absorption spectrum of one magnetometer channel for different pump laser intensities is shown in Fig. 2(a). Due to buffer gas broadening the Cs D1 excited state hyperfine splitting is unresolved, the two ground state hyperfine levels F = 3 and F = 4 are partially overlapped. Tuning the narrow-band laser across the absorption profile results in changing the relative pumping ratio between the ground state levels. As described earlier [9] two different regimes can be observed: Pumping resonantly to F = 4 at a modest laser intensity has been labeled as the conventional operation mode, while strong pumping near the lower F = 3 level has been termed the light-narrowed (LN) operation mode, exhibiting a drastically improved shot-noise limited sensitivity compared to the conventional mode. The main effect responsible for improvement in sensitivity is the much higher signal strength due to repumping of the lower ground state level F = 3. Furthermore, due to the detuning of the high intensity laser in respect to the detected Zeeman resonances in the upper ground state level F = 4 the magnetic resonance gets not power-broadened to a large extent. On the other hand, the effect of “Light Narrowing” as suppression of spin-exchange broadening as described by Appelt et al. [16], despite being overestimated at the time we published [9], still gives an extra contribution to the sensitivity improvement to justify the label ”light-narrowed”, in our opinion. To optimize the shot-noise-limited sensitivity in both regimes, automatically controlled measurements with variation of the operational parameters namely cell temperature, pump laser power and frequency and B₁ field strength are carried out. The shot-noise-limited sensitivity of one channel is determined according to

 

Fig. 2 (a) Cell absorption profile without B₁ field, normalized to the F = 4 peak. Increasing the pump laser intensity results in reduced absorption for the F = 3 transitions caused by depletion of the lower hyperfine ground state level. Optimal laser frequency tuning points for conventional mode (black square) and LN mode (red triangle) are indicated. (b) Shot-noise-limited sensitivity optimized for each cell temperature in conventional (black squares) and LN (red triangles) operation mode.

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As a second step the real noise values were acquired for each optimal parameter set by recording the noise spectra V_n of the quadrature component lock-in output and using

The noise level evaluated at 1kHz (what is within the magnetometer’s bandwidth) for single channel conventional mode operation lies about a factor of 2 above the calculated shot-noise limited value. By application of the noise compensation method [14] the shot-noise limit is reached at high frequencies, which is a factor of $\sqrt{2}$ higher than without noise compensation due to the doubled light intensity. Noise measurements in the LN mode reveal a performance improvement by a factor of 2 compared to the conventional mode. However, in contrast to the conventional mode operation, despite the use of noise compensation, the shot-noise limit is not reached. Further investigations are necessary to shed light upon this issue.

4. Magnetometer orientational dependence

The best sensitivity values shown in the previous section were attained by tuning intense circularly polarized laser light across the cell’s absorption spectrum at the optimal pumping laser frequency near F = 3 for the LN mode, as shown in Fig. 2(a). Since the magnetic resonance signal is detected in the Zeeman transitions of the upper hyperfine ground state level (F = 4), the detuned optical radiation induces light shifts to the energy level structure [7]. The Zeeman light shift acts like a virtual magnetic field lying in the photon spin direction (i.e. always parallel or antiparallel to the light propagation vector for circularly polarized light) and adding up vectorially to the real external magnetic field B⃗₀. In this way, variations of the direction of B⃗₀ are converted into variations of the measured Larmor frequency leading to a light-shift induced heading error of the sensor. The Zeeman light shift has a dispersive dependence of the laser frequency and increases with increasing light intensity, but vanishes for pumping light tuned exactly on resonance of the isolated optical transition that involves the Zeeman splitting. In our case, due to overlapping hyperfine structure, this point does not coincide with the F = 4 absorption maximum, but is very sligthly shifted. Tuning the laser away from this point to obtain a higher pumping efficiency and better sensitivity, which is the fundamental concept of our LN method, inevitably leads to strong light-shift contributions. To eliminate this effect, a straightforward approach is to average two magnetometers with identical properties except for the sense of their pump light’s circular polarization [10]. Experimental investigations, as presented below, clarify whether this concept can be also adapted sucessfully to our LN configuration.

The most straightforward setup is to use the two oppositely circularly polarized pumped magnetometer channels of the cell array in parallel. However, this proved to be problematic for our experimental characterization method. Even though the measurement setup was trimmed to produce very homogenous magnetic fields at the place of the sensors, a residual distortion of about 2 · 10⁻³ still exists [14]. Moreover, this resulting magnetic field gradient between the two cells of the integrated setup of Fig. 1(b) depends on the applied magnetic field orientation and the actual measurement history. In order to get rid of these problems, we chose another measurement procedure. Only one magnetometer cell was used, whose pumping light’s circular polarization sign was altered (σ^±) by mechanically switching two λ/4-plates in and out the beam path. The retardation plates were carefully adjusted to give an equal minor-to-major axis ratio of the polarization ellipse of ≈ 0.98 for both positions. The magnitude of the light shift was trimmed to be identical in both configurations by carefully tuning the pump laser intensities, finally ending up with nearly equal detected photo current values. Each time before the magnetic field direction was changed, the shielding barrel was carefully demagnetized. Furthermore, to compensate for residual magnetization of the shielding barrel, imperfections of the coil system calibration and limited resolution of the magnetic field components due to the quantization limit of the coil’s current sources, the same B⃗₀ orientation variation procedure was carried out twice. Starting in the conventional mode configuration, tuning the laser frequency to the point near the F = 4 absorption maximum, where no Zeeman light shift occurs, the Larmor frequency was measured in dependence of static magnetic field orientation. Then, by subtracting these values from the ones obtained in the LN mode all deviations due to experimental imperfections should be cancelled, leading to the measurement of the pure light-shift phenomenon.

The result of this subtraction is shown in Fig. 3(a). The strong dependence of the measured Larmor frequency difference on the B⃗₀ field direction, caused by the light shift, can then be eliminated to a high degree by averaging the σ⁺ and σ⁻ light values. The residual variations, as shown in Fig. 3(b), are within the range of 14nT.

 

Fig. 3 (a) Measured Larmor frequency difference as a function of the angle of the magnetic field to the laser beam direction (−90°: antiparallel, 0°: perpendicular, 90° parallel) for the two oppositely circularly polarized configurations σ⁺ (red dots) and σ⁻ (black squares) and the average (blue triangles) of both measurements, magnified in (b).

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Except for the measurements near the dead zones of the M_x magnetometer (±90° and 0°), where the measurement resolution gets poor, a systematic but asymmetric effect in the two hemispheres is visible. Thus, the deviation is most probably due to residual experimental imperfection of the magnetic field generation with the coil system inside the magnetic shielding. To overcome these experimental limits of the characterisation system, the rotation of a suitably constructed magnetometer system in a stable homogenous external field would be necessary. This would also offer the opportunity to study the impact of the nonlinear Zeeman effect and to investigate methods for its elimination. In the measurements shown here this systematic error is virtually absent as both the LN as well as the subtracted conventional mode values are shifted in a similar manner.

5. Conclusion

After optimizing the shot-noise limited sensitivity of an optically pumped magnetometer working both in the LN mode and the conventional mode at B₀ = 50μT, the value of $50\frac{fT}{\sqrt{Hz}}$ in the LN mode represents an improvement by a factor of 4 compared to the conventional mode performance. The drawback of having to operate with an off-resonant pump laser of circular polarization, which introduces an orientational dependence to the measurement by a strong Zeeman light shift, can be suppressed by averaging two channels pumped by light of inverse circular polarzation sense. With this method the residual error was made to be within the range of 14nT, experimentally limited by the reproducibility of the used characterisation setup.