|
Like atomic clocks, atomic magnetometers based on a measurement of the atomic spin precession or Larmor frequency can be run in either passive or active modes. In the passive (or "unlocked") mode, the atomic spin precession is excited with a frequency generated by an external, driving oscillator. The response of the atoms is measured as a function of the driving oscillator frequency by monitoring the absorption of an optical field as it passes through the atomic sample. The atomic response signal can then be used to lock the frequency of the driving oscillator to the Larmor frequency of the atoms; the output of the magnetometer in this case is the driving oscillator signal, whose frequency is proportional to the magnetic field seen by the atoms. Active, or "self-oscillating," magnetometers do not contain a driving oscillator. In the active mode, the atom response signal, which is proportional to the light absorbed by the atoms as in the passive case, is simply fed back to the mechanism that drive the atoms. With the correct filtering, when the loop gain becomes larger than unity, oscillation occurs at the Larmor frequency. The filtering can be done either with a simple analog low-pass or band-pass filter, or with a digital phase-locked loop. The device output then becomes the oscillating loop signal, which is proportional to the atomic Larmor frequency. The active mode is advantageous in that it is potentially simpler to implement since it does not require a separate driving oscillator.
Although our first chip-scale atomic magnetometer (CSAM) performed well with a sensitivity of 50 pT / Hz1/2 at 10 Hz, there is much room for improvement in terms of sensitivity, power consumption, and simplicity of operation. The CSAM measured the hyperfine splitting between two magnetically sensitive Zeeman. By measuring the Larmor frequency directly, a CSAM should improve its sensitivity and long-term stability since the hyperfine frequency does not need to be subtracted from the measurement to determine the magnetic field. By switching our local oscillator frequency from gigahertz to kilohertz, we should reduce the power consumption and expense of the local oscillator. Further simplification can be achieved if the magnetometer can be made to self-oscillate, eliminating the need for a local oscillator.
Here, we show how a magnetometer using a nonlinear magneto-optic rotation (NMOR) can be made to self-oscillate using analog and digital feedback in magnetic fields ranging up to the Earth’s field. Buker et al. have shown that frequency modulated (FM) light can be used to excite an NMOR resonance, extending the field range of NMOR-based magnetometers [1]. The FM NMOR technique eliminates the need for an RF coil to excite the magnetic resonance and uses linear polarized light rather than circularly polarized light. Both make the magnetometer simpler and eliminate some sources of systematic error.
In this table-top experiment, we use a vertical cavity surface emitting laser (VCSEL) tuned to the D1 line to illuminate a vapor cell (diameter 3.5 cm) filled with isotopically enriched 87Rb. The interior of the cell is coated with an anti-relaxation paraffin layer. The cell is placed between a linear polarizer and an analyzer oriented at with respect to each other. Each output beam of the analyzer is directed to a separate photo detector, and the signals from the two detectors are subtracted in a balanced receiver to provide a measure of the polarization rotation caused by the atoms. Use of a balanced receiver to detect the optical rotation eliminates much of the AM and FM-AM noise from the VCSEL.
The FM NMOR resonance is produced by a simultaneous pump/probe interaction of the linearly polarized light with the atomic vapor. To excite the resonance, we modulate the VCSEL injection current at twice the Larmor frequency such that the peak-to-peak amplitude of the modulation of the laser frequency is 1.38 GHz, roughly three times the Doppler width of the optical resonance. The center frequency of the laser is optimally tuned to the low frequency side of the transition such that the laser is approximately on resonance when it reaches its maximum frequency during the modulation cycle. When the laser frequency is on resonance, an atom in the laser beam is optically pumped by the linearly polarized light into an aligned state along the direction of the light’s polarization. After the atom exits the laser beam, the atomic alignment precesses at the Larmor frequency due to the magnetic field. Because the state of atomic polarization is symmetric, the atomic alignment returns to the same state after half the Larmor precession period. Thus, with light modulated at twice the Larmor frequency, the atomic alignment is resonantly driven as the atom moves in and out of the laser beam. We probe the atomic alignment with the light by detecting a rotation of the light polarization at the output of the cell. Optical rotation occurs when the atomic alignment is at an angle to the light polarization, and the light is maximally rotated when both the light is on resonance and the atomic alignment is at a angle relative to the light polarization. The FM NMOR signal shows optical rotation in opposite directions depending on the sign of the angle between the atomic alignment and the laser polarization.
In the unlocked (passive) mode an external driving oscillator modulates the VCSEL current, and the FM NMOR signal from the balanced receiver is sent to a lock-in amplifier with the original modulation as the reference. When frequency of the oscillator is swept about the FM NMOR resonance frequency, a dispersive line shape is observed at the in-phase output of the lock-in amplifier. The measured sensitivity of the magnetometer in the unlocked mode is ~0.15 pT / Hz1/2 at 1 Hz bandwidth. In the unlocked mode we manually tune the driving oscillator to the nominal FM NMOR resonance to measure the magnetic field. A magnetometer using lock-in detection that automatically acquires and locks to the FM NMOR resonance would require the additional complication of a microprocessor, especially in light of the fact that there is another, lower amplitude FM NMOR resonance when the VCSEL is driven at the Larmor frequency.
If the magnetometer is made to self-oscillate, its control system can be greatly simplified. To make FM NMOR system self-oscillate, the output waveform from the balanced receiver needs to emulate the input waveform before it is fed back to the VCSEL. The output waveform is not a simple replication of the input modulation, and in the analog self-oscillating mode we use a four-pole low-pass filter to attenuate all harmonics but the fundamental frequency. The roll-off frequency is set to 1.25 times the frequency of the driving oscillator, and the phase shift and gain are set so that the system self-oscillates when the analog components provide the feedback to the VCSEL. The magnetic field is then determined by simply counting the frequency of the analog output. We observe self-oscillation in fields ranging from 35 nT to 35,000 nT, and the sensitivity of the magnetometer in the analog self-oscillating mode is ~0.15 pT / Hz1/2 at 1 Hz bandwidth in a 143 nT field.
A comparison of the noise spectra of the magnetometer shows that at frequencies above 20 Hz the noise in the analog self-oscillating mode increases proportionally to the frequency, while the noise in the unlocked mode is approximately white. This frequency corner corresponds to the linewidth of the FM NMOR resonance, 27 Hz. At higher frequencies, the response of the magnetometer in the unlocked mode decreases proportionally to the inverse of the frequency, and thus the signal-to-noise ratio decreases at the same rate. In the analog self-oscillating mode the gain in the feedback loop keeps frequency response flat, but the noise increases with frequency so the signal-to-noise ratio at any given frequency remains the same for the two cases. However, the flat frequency response of the self-oscillator is an advantage that allows straightforward detection of high frequency magnetic signals. Below 0.3 Hz the noise in the digital and analog self-oscillating mode is shown to decrease sharply, which is an artifact of the noise measurement system when the magnetometer is self-oscillating.
An obvious disadvantage of the present analog self-oscillating mode is that the low-pass filter needs to be tuned as the magnetic field changes because when the oscillation frequency surpasses the roll-off frequency, there is not enough gain in the loop to allow oscillation. To avoid this problem, we implemented a digital phase-locked loop (PLL) to lock a voltage controlled oscillator (VCO) to the FM NMOR signal. With the VCO tracking the FM NMOR oscillation frequency we can digitally synthesize a sine wave at the oscillation frequency with the appropriate phase shift. We find that with the magnetometer in the digital self-oscillating mode the PLL can acquire and track the FM NMOR oscillation frequency over the full locking range of the PLL (1 kHz to 6.9 kHz or 71 nT to 490 nT in this case). The magnetic field is found by counting the frequency of the VCO, and the sensitivity is ~0.8 pT / Hz1/2 at 1 Hz bandwidth. The sensitivity of the digital self-oscillating mode is degraded somewhat because the PLL was not properly optimized. The PLL and sine generator are easily implemented with five low-cost, off-the-shelf integrated circuits. With more carefully designed electronics, the sensitivity should be equivalent to the other two methods, and the size and power consumption of the electronics could be greatly reduced for use in a CSAM.
Practical magnetometry is frequently done in the Earth’s field, which ranges from approximately 20 to 70 , and we have performed a limited study of the operation of our magnetometer at these fields. We have observed self-oscillation up to 500 kHz (35 ) in the analog mode, but the sensitivity is reduced. This is mainly due to the nonlinear Zeeman effect. In the Earth’s field the frequency splitting between each Zeeman state is no longer equal due to quadratic terms in the Zeeman splitting that become important at these fields. With our goal being to develop a CSAM, the size of the cell will be reduced to a volume of ~1 mm3. At this cell size the resonance linewidth will be on the order of 1 kHz compared to the sub-10 Hz linewidth for a large wall coated cell. Therefore, the contribution of the nonlinear Zeeman terms to the resonance width will be a much smaller fraction of the resonance width in the Earth’s field range allowing the magnetometer to operate in the Earth’s field without a significant decrease in sensitivity.
Contact: Dr. Peter Schwindt References: D. Budker, D. F. Kimball, V. V. Yashchuk, M. Zolotorev, Phys. Rev. A 65, 055403 (2002).
|
||||||||||||||||||||||
