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Научни трудове на Съюза на учените в България-Пловдив. Серия В. Техника и технологии, естествен ии хуманитарни науки, том XVI., Съюз на учените сесия "Международна конференция на младите учени" 13-15 юни 2013. Scientific research of the Union of Scientists in Bulgaria-Plovdiv, series C. Natural Sciences and Humanities, Vol. XVI, ISSN 1311-9192, Union of Scientists, International Conference of Young Scientists, 13 - 15 June 2013, Plovdiv.
An absolute, high precision combined 3He /Cs magnetometer
Hans-Christian Koch(1'2), Antoine weis(1), werner Heil(2)
(1): University of Fribourg, Department of Physics, Ch. du Musée 3, 1700
Fribourg (Switzerland)
(2): University of mainz, Physics Department, Staudingerweg 7, 55124
mainz (Germany)
e-mail: hans-christian.koch@unifr.ch
Abstract
Many experiments in fundamental science, such as the search for the neutron electric dipole moment at PSI, Switzerland, demand precise measurement and control of an applied magnetic field. Here, we report on a combined 3He-Cs magnetometer for absolute measurement of a ^T magnetic field with a precision of better than 10-6. The measurement principle relies on the detection of the precession frequency of polarized Cs and 3He atoms.
Introduction
It is known that a magnetic moment, which can be visualized as a spinning bar magnet, performs a precession around the axis of an applied external magnetic field to which it is exposed. The frequency of this precession, the Larmor frequency,
B
(1)
involves the modulus of the magnetic field and the gyromagnetic ratio, y, of the concerned magnetic moment. If y is known, one can determine the field by measuring the Larmor frequency. This principle is applied in the optically pumped cesium magnetometers (CsOPM) developed by the FRAP group at University of Fribourg as well as in magnetometric measurements with polarized 3He nuclei carried out by the QUANTUM group of the University of Mainz. Each method exhibits individual strengths and weaknesses as summarized in Fig. 1 which can be overcome by fusing both types of measurement in a combined device.
Larmor У
Properly
high sensitivity higi\ accuracy long coherence time optical detection
3Ke cs
Of) *
X
X
X ✓
Figure 1: Advantages and disadvantages of different types of magnetometers.
Theory
a) Polarized 3He
3He is an isotope of helium which contains only one neutron instead of two. This results in each 3He atom carrying a residual nuclear magnetic moment which produces a small magnetic field. By default the magnetic moments of the individual atoms of a 3He gas sample are randomly oriented and the sum of their fields cancels out on average: there is no macroscopic magnetization. By using appropriate methods, the magnetic moments of a 3He gas sample can be oriented along a common direction. This process is called optical pumping and the ensemble of nuclei in the gas becomes polarized. A more detailed description of the complicated process of 3He optical pumping of can be found in [1].
Such a polarized 3He gas sample will produce a macroscopic field since the contributions of the individual atoms now sum up constructively. In the described work, a spherical 3He cell of ~50 cm3 volume filled at a pressure of ~1 mbar was used which, when polarized at ~80%, produces a magnetic field on the order of 10 pT close to the surface of the cell. For a spherical cell the produced macroscopic far-field is dipole-like.
lr J*-Lii'
fcWÖni
™n!a>yi
4
Figure 2: Optical pumping.
If the polarized gas is brought into a transverse homogeneous external magnetic field, the magnetic moments will precess coherently, leading to a precession of the macroscopic magnetization around the external field. In this work, the applied magnetic field is on the order of
1^T resulting in a 3He precession frequency of (0E / 2n ~32.4 Hz. The magnetization of the gas will exponentially decay with time t according to
M <x e _Tr (2)
due to inhomogeneities of the magnetic field and depolarizing wall collisions. Since the nuclear magnetic moments are basically not interacting with their environment anymore after optical pumping (except for the magnetic field), one speaks of a free induction decay (FID) of the magnetization. Under good conditions the decay constant T2 can easily be on the order of several hours which allows long measurement times, as shown for example in [2].
b) CsOPM
The CsOPMs used in this work were developed by the FRAP group of the University of Fribourg. They rely on optical detection of the feedback-driven precession of polarized Cs vapor
in an external magnetic field. The measurement output is a sinusoidal signal at the Cs-Larmor
frequency C0S . For an applied field of 1^T, d)e /2n~3.5kHz. In this mode of operation, they offer high sensitivity but their absolute accuracy is affected by systematic effects. More information on the working principle, strengths and limitations of these sensors can be found in [3].
c) Combined 3He / Cs magnetometer
In the presented work, a cell of polarized 3He gas is surrounded by several CsOPMs, all exposed to an external magnetic field B0 which one seeks to measure. For simplicity, we assume a single CsOPM in the vicinity of the 3He cell.
r l i T/2l
(a) (b) (c) Figure
3: FID of 3He magnetization and effect on nearby CsOPM.
The magnetization of the polarized 3He precesses around the B0 field-direction. Figures 3a and 3b show the instantaneous magnetic dipole field produced by 3He FID at times t and t+T/2, where T is the period of the 3He Larmor precession. In Fig. 3a the contribution of the 3He field to the B0 field, meaning its projection onto the B0 axis at the position of the CsOPM, is positive: the total field at the CsOPM's position is thus increased. In Fig. 3b the contribution of the 3He field to the B0 field at the position of the CsOPM is negative: the total magnetic field there is decreased. One sees that the magnetic field at the CsOPM's position is periodically increased and decreased by the 3He FID, resulting in a periodic increasing and decreasing of the CsOPMs Larmor frequency. The output from the CsOPM is thus a frequency modulated signal with carrier
C0e /2n~3.5kHz and modulation frequency C0S /2n~32.4Hz. This modulation frequency contains information about the absolute magnetic field value.
Measurements and results a) The experimental setup
Figures 4a and 4b show a drawing and photograph of the combined magnetometer.
(a) (b)
Figure 4: 3He / Cs combined magnetometer.
(a): The large sphere in the middle is the 3He cell, surrounded by 8 CsOPMs. One corner and two CsOPMs are left away for better view. The whole unit has dimensions ~(10cm)3.
(b): The combined magnetometer as used for the experiments. Also visible are additional
271
components for optical pumping of the 3He and starting of the 3He FID by a n/2 spin flip. The whole setup is contained inside a magnetic shielding to suppress the earths magnetic field.
b) Measurement data and analysis
Figure 5 shows the Fourier spectrum of the recorded CsOPM output and reveals the characteristic appearance of a frequency modulated signal. As indicated before, we are mainly
interested in the 3He created modulation frequency (Os / 2n of the Cs signal.
Figure 5: FFT-spectrum of Cs-OPM signal.
The Cs carrier with amplitude A is shifted to 0Hz, here. The 3He frequency-modulation sidebands with amplitudes a around the carrier are visible. The magnitude of the 3He field can be derived from the ratio a/A of the amplitudes. The information on the absolute magnitude of the magnetic field B0 is contained in the separation between carrier and sidebands.
To obtain this information, the data is digitally filtered and the frequency and its error f ±Af. are extracted by fitting a (decaying) sinusoidal function to it. Thus the magnetic field B0±AB0 can be calculated using equation 1.
The information contained in a data set depends on the signal to noise ratio (SNR) and the measurement time TM. The higher the information content, the higher will be the precision with which one can extract a measurement parameter, in our case the frequency of the noisy sinusoidal signal. Quantitatively, this relation is described by the Cramér-Rao lower bound (CRLB), a formalism which indicates the best possible precision with which a parameter can be extracted from a data set. For the frequency of a sinusoidal signal with white Gaussian noise recorded with
a bandwidth fBW, the CRLB limit is
A/ = o-( f ) =
6
(2^)2 SNRT fw
(3)
This sets a fundamental limit to the magnetometric sensitivity which can be reached. For more information on the CRLB formalism, refer to [4].
c) Results:
Figure 6 shows a 3He FID signal, extracted from the Cs signal by digital filtering, measured over 10'000s.
Figure 6: 3He FID signal.
The inset is a zoom into the data at the position denoted by the vertical line and reveals the 32Hz precession frequency of the 3He.
By fitting a (damped) sinusoidal function to chunks of increasing length taken from the data displayed in Fig. 6 and plotting the corresponding field-estimation error as a function of measurement time, one can determine the sensitivity of the magnetometer. Figure 7 shows the result.
Filled limr It]
Figure 7: Estimation error of magnetic field as function of measurement time.
The points represent measured data, the upper line is a fit to the data which shows nicely the
agreement with the T/ 2 dependence expected from estimation theory. The lower line displays the CRLB for this device which represents the fundamental theoretical limit of sensitivity. One sees, that the measured sensitivity is still approximately a factor of three worse than the CRLB. This is due to imperfections of the measurement device, like electrical noise-pickup and fluctuations of the measured field.
Conclusion and outlook:
It has been shown that a combined 3He / Cs magnetometer can be used to precisely and accurately measure small magnetic fields. The recorded sensitivity of the device is close to the fundamental limit predicted by estimation theory. The fundamental limit can only be reached in a very stable magnetic environment since the stability of the measured field sets a limit on the sensitivity determination. Measurements under optimal conditions in the magnetically shielded room of the PTB, Berlin, are planned for this year and will reveal the true performance limit of
the device.
References
M. Leduc, "Kinetics of helium-3 laser optical pumping", Hyperfine Interactions 127,443449 (2000).
C. Gemmel, "Ultra-sensitive magnetometry based on free precession of nuclear spins", University of Mainz.
S. Groeger, "Comparison of discharger lamp and laser pumped cesium magnetometers" Appl. Phys. B 80, 645-654 (2005).
David C. Rife, "Single-tone parameter estimation from discrete-time observations", Transactions on information theory, vol. IT-20, No.5, September 1974.
