In this chapter, we overview the most sensitive contemporary atomic magnetometers (AM) that are based on high-density alkali-metal vapors. These magnetometers are considered in a broader content of other magnetometers and their applications. The principles of the operation of the AMs are explained for better understanding of this topic. One point of focus in this chapter which establishes the connection to the title of this book is about the relation between lasers and most sensitive atomic magnetometers. The chapter is organized in the following way. After general introduction to the AMs and the applications of magnetometers, the principles of the operation of optical atomic magnetometers are given. With this background information, next so-called SERF magnetometers and their features are discussed. Then, the discussion continues to the topic about the operation of “SERF magnetometers” in the non-SERF regime. Finally, after covering the principles and theory, we return to some most notable applications of atomic magnetometers.
Since their discovery, lasers have revolutionized many fields – the field of AMs or magnetometers in general is no exception. Before the advent of lasers, AMs were based on discharge lamps which though relatively simple and inexpensive light sources did not provide enough power and had some other drawbacks for the realization of maximum sensitivity that can be achieved with atomic magnetometers. In a comparison of sensitivity of the state-of-the-art Cs magnetometers based on a Cs discharge lamp and a semiconductor laser made in Ref. (Groeger et al., 2005), the lamp Cs magnetometer had sensitivity of 25 fT/Hz1/2 that was lower than that of the same but laser-based magnetometer, 15 fT/Hz1/2. For most sensitive magnetometers the difference is expected much more significant, although there is no investigation of this question in the literature. From Ref.(Groeger et al., 2005), we can estimate that the intensity of the lamp light in the Cs absorption band was below 1 mW, and such power would be suboptimal in most sensitive magnetometer based on high-density vapors, such as spin-exchange relaxation free (SERF) magnetometer (Allred et al., 2002). The absence of lasers is one of the factors that initially atomic magnetometers had been far behind superconducting quantum interference devices (SQUIDs) in sensitivity.
Although the introduction of lasers into magnetometry improved sensitivity, laser-based magnetometers are not yet commercially available. However, this can change in the near future. Diode lasers of high quality are becoming less expensive, and some lasers such as vertical cavity surface-emitting lasers (VCSELs) in addition to extremely low price allow integration into microfabricated packages. Such packages will be not only inexpensive and easy to batch produce they will also have lower power consumption, light weight and unimpeded mobility (Knappe et al., 2006).
Sensitive magnetic field measurements, for which AMs can be used, are important owing to many existing and potential applications. Magnetometers have been in wide use, for example, in geology, military, biomagnetism, space magnetic field measurements. AMs have been used because they are both relatively sensitive compared to conventional inexpensive magnetometers, such as fluxgates, and more convenient compared to SQUIDs that require cryogenic cooling. For a long time low-Tc SQUIDs had been by far the most sensitive magnetometers at low frequency. However, this has changed with the demonstration with AMs of record 0.5 fT/Hz1/2 sensitivity (Kominis et al., 2003).
High-sensitivity AMs are based on spin-polarized atomic gases or vapors, and AM research is closely related to the atomic physics subfield dedicated to the investigation of spin interactions in such media. This subfield includes the research on optical pumping and related topics such as atomic clocks, masers, hyperpolarized gases, spin-based spectroscopy, and some others. A comprehensive review of optical pumping experiments before 1972 and theory of optical pumping and various relaxation mechanisms are given by William Happer (Happer, 1972). This theory, which still stands the test of time, includes the formulation of density matrix equations, which can be directly applied to the analysis of magnetic resonances of vapors on which atomic magnetometers are based. Atomic magnetometers find many applications as other magnetometers, but they are most useful when high sensitivity and non-cryogenic operation are required. For example, AMs have been developed for submarine detection, and many other military applications are possible on similar principles. Some applications of Rb-vapor or 3He magnetometers in geophysics and space physics were mentioned as early as in 1961 by Bloom (Bloom, 1961) who did some pioneering work on the high-sensitivity measurements of magnetic fields and theory for the operation of atomic magnetometers. Theoretical analysis of early atomic magnetometers was also done by Dehmelt (Dehmelt, 1957) and by Bell and Bloom (Bell & Bloom, 1957). Although the history of atomic magnetometers is quite fascinating and they played an important role in applications where simpler and less expensive methods did not provide sufficient sensitivity, the atomic magnetometers of the past were much less sensitive than the modern ones. Most exciting results appeared only recently with the various demonstrations of performance of high-density AMs, which we would like to focus on in this chapter.
2. Principles of operation of sensitive atomic magnetometers
2.1. The interaction of spins with magnetic field
First of all, AMs are based on atomic spins which due to their magnetic moment interact with magnetic field. The Hamiltonian related to this interaction in the formalism of quantum mechanics is
magnetometers at sufficiently high frequency can be considered of very high quality. Apart from direct applications in the magnetic field measurements, these resonance properties can be also useful for building radio receivers and filters.
The Zeeman level splitting and transitions between the Zeeman levels under the action of field is the quantum-mechanical picture of the interaction of the field with the spins, which is most appropriate for quantum objects such as atomic spins. However, in practice, the classical picture can be more convenient to use. In the classical picture, the magnetic field causes torque on the spins, and their behavior is described by the Bloch equations:
Alternatively, if accurate description is desirable, the density matrix (DM) equation
can be used (Happer, 1972; Appelt et al., 1998; Alred et al., 2002; Savukov & Romalis, 2005). Here
A coupling between the oppositely rotating spins exists due to SE collisions, which can lead either to full alignment of two subsystems if the precession frequency is much lower than the rate of SE collisions or to relaxation otherwise. In the former case, a single set of the Bloch equations can be used to describe the precession of the spins.
Another important concept that allows us greatly simplify the analysis is the spin-temperature (ST) distribution. A ST density matrix is
2.2. The interaction of spins with light
The interaction of spins with light leads to a number of phenomena such as optical pumping, dependence of optical properties on spin states, light shift, light-induced spin-destruction, and light narrowing of magnetic resonances that are encountered in atomic magnetometers. Optical pumping, in particular, is an essential feature of high sensitivity atomic magnetometers. In general optical pumping, quite common process in laser physics, leads to redistribution of atomic levels. For example, many lasers are based on population inversion that is created by irradiating laser medium with light. More specifically, in the context of AMs, optical pumping means the redistribution of magnetic sublevels due to absorption of light. Optical pumping can change the total spin of initially disoriented spins and can lead to build up of spin polarization. Although magnetic field prepolarization can be in principle used to create the preferential spin orientation and non-zero magnetometer signal, the optical pumping is much more efficient. It can increase polarization by many orders of magnitude compared to thermal equilibrium values even in strong field. With sufficient pumping power (about 10 mW), the expectation value of spin can reach almost maximum value, which is ½ in the case of S=1/2. For comparison, in NMR, such levels can not be reached with the strongest polarization magnets. Only the combination of high field (10 T) and low, liquid-helium temperature (4 K) can produce similar polarization of electron spins, but this method is not practical especially for alkali-metal vapors that have to be kept at much higher temperature.
Optical pumping of atomic spins can be illustrated and estimated in the case of circularly polarizing light by using the fundamental law of conservation of angular momentum. Circularly polarized photons have spin 1. In the act of absorption, according to this law the photons transfer their spins to atoms. The selection rules is another way to understand this process: the magnetic sublevel M changes by 1 in a transition to the excited state induced by circularly polarized light, so the expectation value of the atomic spin, which depends on M, changes. From excited states, atoms decay, either spontaneously or through collisions with other atoms, to the ground state. The overall cycle results in the change of angular momentum or spin of the ground state. The efficiency of pumping can be quite high – typically in atomic magnetometers on average only 1.5 photons are required to polarize one alkali-metal atom in the ground state. The described above pumping process is called depopulation pumping, because it is arranged that the photons preferentially depopulate the atomic states of some M with higher probability than others. It is possible to arrange other schemes of optical pumping. Some of them are analyzed in the review paper [Happer 1972]. In optical pumping not only the expectation value of spin (vector) can be changed, but also the expectation values of multipoles of higher order, if the state has angular momentum greater than ½. The terms orientation and alignment are used to differentiate odd and even multipoles or just dipole and quadrupole moments [(Budker et al., 2004), appendix about atomic polarization moments]. For example, if M=-1,0,1 levels are populated in the proportion 1:0:1, the system will have alignment but no orientation. Alignment, as orientation, precesses around magnetic field and can be used for magnetic-field measurements. Sensitive magnetometers based on various multipoles have been explored extensively by D. Budker group at UC Berkeley.
To build a sensitive magnetometer such as SERF, in addition to optical pumping it is necessary to utilize optical probing. Optical probing is a high-sensitivity method to detect the states of atomic spins based on strong spin-dependent interaction of light with polarized atoms. Alternatively, a pick-up coil can be used in some cases, but its sensitivity is low at low frequency. For example, the SERF magnetometer has only frequencies below a few hundred Hz range and a coil will not be very sensitive. The optical probing signal, on the other hand, does not depend much on frequency, and the optical probing can be used for detection of DC fields. The only problem could be 1/f noise, that exists at very low frequencies owing to various reasons. To reduce this technical noise, some methods of modulation can be implemented. For example, a polarization modulator can be inserted into the probe beam path to shift the low-frequency AM signal to frequencies of a few kHz.
The high sensitivity of optical detection is due to both strong interaction of light with spins and high sensitivity of polarization angle measurements (or absorption measurements) that can reach quantum limit of photon fluctuations. This limit is extremely small, on the order of nrad/Hz1/2. Note that one nrad is the angular size of a 1-mm object at the distance 1000 km! The interaction of light with atoms is strong because atoms, especially in gas phase, have very narrow optical absorption resonances and large transition amplitudes. For example, alkali-metal atoms of concentration of 1014 atoms/cc can absorb resonant light in the path length on the order of 1 mm. Quantitatively, the absorption coefficient
In the center of the resonance, the absorption coefficient
Both absorption and light polarization rotation (Faraday effect) can be used for detection of spins. In most sensitive magnetometers, such as SERF, light polarization rotation measurements were chosen over absorption measurements. One drawback of the absorption method is that the probe laser has to be tuned close to the center of absorption line, and this leads to stronger spin-destruction as well as to strong attenuation of the probe beam, especially in optically thick high-density vapors. In the Faraday detection method, on the other hand, the probe laser is tuned away from the resonance, which facilitates the propagation of light through optically thick medium and reduces the spin destruction.
According to the rules of optics, the plane of polarization of linearly polarized light will be rotated by non-zero angle
if the refractive indices for right and left circularly polarized light components
The rotation of polarization by optically-pumped vapors, which can be evaluated with Equation 8, exceeds by many orders of magnitude usual Faraday rotation in other substances.
In theory of AMs, the questions about spin-destruction and light shifts by pump and probe beams also arise. The mechanism of light-induced spin-destruction is similar to that of spin pumping: when light is absorbed it changes the spin states, or in other words perturbs the spins. In the light-induced spin destruction the change in the spin state leads to the loss of coherence and longitudinal polarization. Both circularly polarized and linear polarized light can induce spin destruction, but only circularly polarized component of light builds up the orientation of spins. Hence if the degree of circular polarization is smaller than 1, the maximum polarization level will be less than 1 for arbitrary light intensity. This result can be written as
Light shift is the AC Stark effect, i.e. the shift of atomic energy levels in AC electric field produced by light. An unperturbed atom has zero electric moment (extremely small electric moment might exist, but its effect is hardly detectable), so Stark effect appears only in the second order of perturbation theory in
Thus the maximum magnitude of light shift is on the order of the pumping rate that will be obtained at the center of the absorption line. Light shift follows dispersion Lorentzian, while the pumping rate follows absorption Lorentzian, both having the same prefactor. Light shift can be expressed in the units of frequency as the pumping rate, but by dividing light-shift frequency by gyromagnetic coefficient, it can also be expressed in the units of magnetic field. Actually, the effect of light shift on the spins is equivalent to that of a magnetic field and it can be included into the Bloch equations or in the density matrix equation on the equal footing as usual magnetic field. However, if there is more than one type of atom in the cell, the light shift “field” will be different for different atoms. The direction of the light-shift “field” is along the direction of the beam and the sign depend on the sign of circular polarization. Circularly polarized light creates light shift, but linear polarization does not except for very small light-shift noise arising from fundamental fluctuations in the difference of the number of photons of two circularly polarized components of which the linearly polarized light is composed.
Light shift is a parasitic effect in AMs which can add noise to the AM signal and lead to the broadening of magnetic resonances. Because light shift depends on the wavelength as the dispersion Lorentzian, it can be minimized by tuning the laser to the center of absorption resonance. However, this cannot be done for the probe beam, which is deliberately tuned off the resonance to avoid strong absorption. Although the probe beam is linearly polarized, due to imperfections, for example birefringence of glass cell walls, light-shift from the probe beam is always present. By minimizing its intensity, stabilizing wavelength, light shift can be made small and quite constant, so it won’t lead to a large noise in the magnetometer.
As we mentioned above, optical pumping and optical probing are essential features of most sensitive AMs. Although it is possible to use very simple light sources for pumping and probing such as discharge lamps, their intensity over the absorption spectrum of atoms used in AMs is not sufficient for reaching best sensitivity and lasers have to be used. A question arises, then, what are requirements for the lasers to be good candidates for AMs? The primary parameter is the wavelength. The wavelength selection depends on the atoms that are used in the magnetometer. Ultra-sensitive magnetometers in order of their sensitivity are based on K, Rb, and Cs vapors. Usually D1 lines of these atoms are preferable, but D2 lines or other lines, which are less convenient from point of view of wavelength availability, in principle can be used. The D1 line (ns1/2-np1/2, where n=4,5,6 for K, Rb, Cs, respectively) has the advantages over D2 line (ns1/2-np3/2, the same n) that the pumping on the D1 line by circularly polarized light makes the vapor transparent to this light, so the pump beam can propagate over distances greatly exceeding the (low-intensity) absorption length. The intensity propagation equation for D1 line is
In addition to the wavelength selection, the requirement for power is also important to consider. For relatively small cells employed in single-channel magnetometers, the power on the order of 50 mW is sufficient. The pump power requirements can be simply estimated from the analysis of the magnetometer sensitivity as the function of the pumping rate. For example, the signal of the SERF magnetometer scales as
Many semiconductor lasers can provide enough power for the SERF magnetometers. However, multi-channel operation, important for magnetoencephalography (MEG) and magnetocardiography (MCG) applications, requires much higher power, on the order of 1W or more. This can be achieved with systems that have laser amplifiers or arrays of laser diodes.
While any diode laser with the required wavelength and power can be used, for best sensitivity additional requirements such as laser stability, single-frequency operation, and the absence of mode-hops have to be satisfied. In experiments with atomic magnetometers, it was discovered that so-called (distributed feedback) DFB lasers are almost ideal. These lasers are quite a novelty, with US patent issued on June 22, 2004. They work without mode hops and have low intensity noise. However, one problem exists that these lasers need additional cooling below freezing point for reaching the D1 line wavelength of K, 770 nm. In this respect, Rb magnetometers might have advantage for which the DFB laser is available for the D1 line without cooling. Alternative lasers based on tuning by mechanical rotation of a diffraction grating are quite unstable: they can change wavelength during experiments, can suddenly increase their intensity noise to high level, when modes jump. Another interesting laser type is VCSEL. These lasers are quite inexpensive and can perform well if the current is stable. Contrary to edge-emitter, VCSEL can operate only in a single mode. It is also possible to use apparently inexpensive lasers that are commonly found in CD players that have wavelength matching the Rb D2 line (about 780 nm).
The central question in the theory of atomic magnetometers is about noise and sensitivity. There are many sources of noise, some of which are of fundamental nature and cannot be avoided, and other technical noises that can be reduces by careful choice of components and experimental arrangement. Fundamental sources of noise are spin projection noise, photon-counting noise, and light-shift noise. Technical noise arises due to probe beam intensity fluctuations, environment magnetic field, pump intensity and wavelength fluctuations, vibration, air flow, etc. Some sources of noise can be tested separately: the environment field noise and noise from the pump beam can be turned off by blocking the pump beam. The residual noise in the magnetometer signal is frequently called the probe beam noise. The probe beam noise is due to intensity fluctuations of the probe beam, as well as due to wavelength instabilities and beam steering, which can occur due to vibration, temperature drifts, or air flow. This noise directly penetrates the probe beam detection photodiodes. The intensity fluctuation noise can be reduced using either a polarizing beam splitter (PBS) or with modulation methods. The PBS if well balanced has equal intensity fluctuations in its two channel and they can be removed from the signal. The subtraction level of 100 can be achieved, which is often sufficient to reach photon shot noise performance with a good laser. The alternative technique is based on the modulation of light polarization orientation, which is especially useful for detecting low-frequency (a few Hz) magnetic field. When the probe beam passes through one polarizer, a polarization angle modulator, an atomic vapor cell, and the second polarizer with polarization axis at 90 degree angle to the light polarization, the signal will be proportional to
Noise due to a pump laser is also important to consider and minimize. The intensity and wavelength fluctuations of the pump laser can penetrate to the atomic magnetometer signal due to various coupling mechanisms. One such a mechanism is light-shift. Light shift in an atomic magnetometer affects its signal similarly to the applied magnetic field, as we discussed earlier. The effect of light shift can be modeled with the Bloch equations which contain effective light-shift “magnetic field.” The circularly polarized light of pump beam, when it is not exactly tuned to the center of the line, creates light shift field in the direction of its propagation. The change in the intensity as well as in wavelength on which light shift depends will result in the change of amplitude of the effective field, resulting in magnetometer noise. One solution to this problem developed in SERF magnetometers, which is based on the SERF signal output equation
is to zero the
At high frequency the magnetometer signal is not described by Equation 9. Instead, the response of the magnetometer is linear to small oscillating Bx and By fields and the magnetometer exhibits resonance which is the function of the applied Bz field. Light shift from the pump laser, does not enter directly into the signal, but merely changes resonance frequency. Thus if there are no large oscillating fields the rf magnetometer will be immune to light shift fluctuations of pump beam. However, it is not immune to the probe beam light shift fluctuations, which is equivalent to Bx noise. Thus apart from noise that can be directly seen in the detection system arising from probe beam intensity fluctuation, addition noise with characteristic ringing of AM magnetic resonance (because it is capable of exciting the spin resonances), can be present due to these fluctuations.
Environment field noise can be reduced by magnetic shielding and with gradiometers. Vibration noise can be minimized by building magnetometes on optical tables that are floated. To achieve best sensitivity, many noise reduction strategies are combined, and the magnetometers become state-of-the-art.
3. Spin-exchange free atomic magnetometer
Among various atomic magnetometers, the so-called spin-exchange-relaxation-free (SERF) magmetometer introduced by Princeton group have the highest sensitivity at low frequency for a small cell size. (In general, for comparison, it necessary to specify the size, because many magnetometers can improve their sensitivity with the size as
Although the SERF regime can be achieved at low densitities, the most beneficial densities are on the order of 1014 cm-3. To achieve such densities the heating of alkali cells to relatively high temperatures is needed. Potassium cells require heating to about 180 C, Rb to 150 C, and Cs to 120 C. Thus one drawback of the SERF regime is relatively high temperature of operation requiring building ovens. Initially ovens of SERF magnetometers were based on hot air flow to avoid any magnetic field noise, and their design was quite cumbersome. The power efficiency of heating is also very low, with power on the order of 1 kW required. Apart from this, the air flow is arranged with an inconvenient hook-up to compressed air outlet. More recently, electrical oven designs were introduced for SERF magnetometers. While electrical current produces significant magnetic noise and can disorient atomic spins in the magnetometer, there are several ways to deal with it. The simplest method to reduce this noise is to turn off the power during measurements. While the noise becomes quite small with power off, the measurement is not continuous, which is probably the major drawback of the method. The interruptions also lead to periodic temperature variations which cause correlated variations of the AM signal. The heater element has to be chosen carefully to avoid ferromagnetic and highly conductive materials, which can cause field distortions and noise. In general, with the solution of these problems the electric oven design will be invaluable in out-of-the-lab applications where power consumption and portability are at premium.
Potassium SERF magnetometers set the record of the sensitivity, but from the comparative analysis of the noise (practical and fundamental) of SERF magnetometers for different alkali-metal atoms, which is dominated often by technical noise, it can be found that they can be used with similar results. The ratios of fundamental noise that scale as 1/Rsd1/2 in the sequence of K,Rb, Cs are about 1:3:10 for the corresponding approximate ratios of the SD rates
One important motivation for developing atomic magnetometers is owing to applications which have to be done outside the lab. In such applications, portability, small weight, low-power consumption, and vibration stability are highly desirable. The most sensitive SERF magnetometer (Kominis et al., 2003) was implemented on a special non-magnetic optical table with a multi-layer mu-metal shield reducing the ambient magnetic field by a factor of 1 million and due to the complexity of experimental arrangement and high price, such magnetometers would have only limited use, in the lab with the aim to demonstrate highest possible sensitivity or in fundamental experiments. For external applications the design has to be simplified and miniaturized, and for successful commercialization, the price also has to be greatly reduced.
With the goal of commercialization of AMs in mind, a NIST group has been working on the micro-fabrication of miniaturized atomic vapor cells motivated also by miniature atomic clock applications (Knappe et al., 2005). The NIST group showed that the clock package can be adapted to magnetic field measurements with sensitivity of 50 pT/Hz1/2 at 10 Hz. The clocks or the magnetometer modules consisted of many layers of various functional components: lasers, filters, lenses, quartz waveplates, ITO heaters, atomic cells, and photodiodes. The components, thin wafers, were stacked on the top of each other to form a compact assembly. Although the demonstration of a miniature AM was a real breakthrough in the magnetometer technology, the performance of the first microfabricated magnetometer was not optimal. One reason of low sensitivity was that this magnetometer was not configured as the SERF magnetometer. However, in a following experiment, a microfabricated atomic cell was tested in the SERF configuration in the SERF regime, and dramatic improvement in sensitivity, almost 1000 times, to the level of 65 fT/Hz1/2 was achieved [Shah et al 2007]. According to fundamental noise analysis, even higher sensitivity should be possible. One problem with microfabricated cells is that they have significant spin-destruction rate due to diffusion to the walls, so linewidth is much greater than in larger-cell SERF magnetometers. Perhaps in future if high-temperature coating is developed, the diffusion to the wall can be reduced and sensitivity of microfabricated SERF magnetometer can receive further boost.
In parallel, at Princeton small-scale magnetometers (quite larger than the microchip type) have been created and sensitivity on the order of a few fT/Hz1/2 has been demonstrated (result is not yet published). Thus probably by converging these two approaches of NIST and Princeton groups, both inexpensive and highly sensitive magnetometers can emerge soon. The commercialization of this magnetometer will be important in many applications based on sensitive and portable magnetic-field measurements.
4. “SERF magnetometer” in non-SERF regime
The SERF magnetometer is a great advance in magnetometer technology. However, the operation in the SERF regime is limited in a frequency range and in the range of ambient fields. Thus a question arises about the performance of the “SERF magnetometer” – or high-density magnetometer with the arrangement of pumping and probing as well as of other elements similar to the SERF magnetometer– outside the SERF regime; in particular, about how sensitivity changes with a frequency and applied field. The investigation of the non-SERF regime of “the SERF magnetometer” was done in Ref. (Savukov & Romalis, 2005), which resulted later in discovery of rf magnetometer (Savukov et al., 2005) and rf-based scalar magnetometer (Smullin et al., 2009). One characteristic feature in operation outside the SERF regime is the effect of SE collisions on the magnetic resonance of the magnetometer. As we mentioned SE collisions have much higher cross section than SD collisions, and the broadening due to SE collisions can be on the order several kHz for typical temperatures of vapors used in SERF magnetometers, exceeding orders of magnitude a typical SERF bandwidth of several Hz. Because the bandwidth and the signal amplitude are inversely related in the AM, the bandwidth investigation is very important for the analysis of the sensitivity. The bandwidth of high-density magnetometers and the broadening due to SE was investigated in detail (Savukov & Romalis, 2005) experimentally and numerically by solving the DM equation.
Typically, the SERF magnetometer is operated with all fields close to zero, and the magnetometer has its frequency sensitivity profile similar to that of the first-order low-pass filter, with the bandwidth equal to the width of the magnetic resonance. The profile has the shape of Lorentzian centered on zero frequency. When the frequency of the measured field
The transitions between Zeeman levels are excited with the change of magnetic number by 1, which is due to the term
The case when the SE rate dominates other rates in the atomic spin system, including the rate of spin precession, is most simple for analysis. However, in practical situations Zeeman precession rate can exceed the SE rate. One consequence of this is that different Zeeman components can decouple in their motion. In particular the lower hyperfine components and the higher hyperfine components can evolve independently. Then SE collisions will “try” to bring these components into coherent motion causing relaxation.
For strong enough field, the Zeeman splitting between different levels can also become substantially unequal, and multiple magnetic resonances can be observed if the distances between them exceed the resonance widths. This can happen in the Earth field in atomic cells with low pressure of buffer gases and anti-relaxation coating. One consequence of these multiple resonances is that a magnetometer based on measurements of the position of this resonances (the field and the position are almost linearly related) will have heading error, that is the signal at a given modulation frequency will depend not only on the field strength as would be expected for a true scalar magnetometer but also on the direction. Thus the signal of the AM exposed to a large ambient field, such the Earth field, will fluctuate when its orientation changes and this can be a problem in mobile applications.
In the non-SERF regime, the SE broadening can reach levels of several kHz for typical SERF magnetometer operating temperatures. Good understanding of SE effects is essential for designing sensitive magnetometers at arbitrary frequency. For example, the SE broadening can be suppressed with light narrowing. Light narrowing was discovered and explained in Ref.(Appelt et al, 1998& 1999). In very simple terms, light narrowing can be explained as follows. The SE broadening occurs due to the collisions between oppositely precessing spins of F=I+1/2 and F=I-1/2 hyperfine levels. Strong pumping populates the majority of atoms into the stretched state (F=I+1/2, M=F) and the number of atoms in the lower manifold (F=I-1/2) is small. Thus there will be not many SE collisions between oppositely precessing groups and relaxation due to SE will be suppressed. More detailed explanation is provided in Refs.(Appelt et al., 1998; Savukov & Romalis, 2005; Savukov et al., 2005) where also equations are given for calculations of light narrowing. In magnetometer experiments, light narrowing leads to more than 10 time reduction in bandwidth and similar improvement in magnetic field sensitivity because in practice it is limited by probe beam noise. Although high pump rate can suppress SE broadening completely, it also broadens resonance, more or less linearly with power, so there is an optimal rate to minimize the bandwidth and to maximize sensitivity. In Ref. (Savukov et al., 2005) it was found that the transverse relaxation rate or bandwidth are related to the magnetometer parameters as
Tuning to resonance and light narrowing are two main features of high-density rf atomic magnetometers. Another interesting feature is that laser noise, as well as many other technical noises, goes down with frequency, so the rf AM can be more sensitive than the SERF magnetometer, at least in terms of real experimental noise performance. Fundamental limit of the SERF might be by several orders better, but the rf magnetometer can approach its fundamental limit closer while SERF will be by far dominated by technical noise. The fundamental noise of the rf magnetometer has been investigated in Ref. (Savukov et al., 2005). After optimization of various parameters, such as the pumping rate and the probe laser intensity, this noise can be expressed in terms of fundamental quantities of atomic vapors, such as SE and SD cross sections:
Because the rf magnetometer sensitivity exhibits resonance behavior with resonance frequency being a function of the applied DC magnetic field, this magnetometer can be converted to a scalar magnetometer by applying an rf modulation field near resonance frequency. One advantage of this approach is that the magnetometer can be used in the Earth-field environment, without mu-metal shielding or field compensation, unlike SERF. In the Earth field, the resonance frequency is about 350 kHz (I=3/2 atoms). Small variations in the Earth field can be readily observed as the shifts in the resonance. The in-phase and out-of-phase responses near the magnetic resonance have absorption and dispersion Lorenzian dependencies on frequency. It is convenient to use the dispersion component. Then the signal of the scalar magnetometer is proportional to the deviation of the field from the resonance condition. The lock-in amplifier can be used to convert DC magnetic field changes to the high-frequency rf magnetometer signal. The sensitivity to the DC field is determined by the slope of the dispersive component. The slope of the rf magnetometer was investigated in upcoming paper about scalar magnetometers (Smullin et al., 2009). Because the signal initially grows with the rf field excitation amplitude and then falls off, the optimal excitation amplitude exists. The fall off happens due to broadening of magnetic resonances, which consists of the conventional broadening that can be explained with the Bloch equations and the broadening due to SE collisions. The fundamental limit of the sensitivity of the scalar magnemeter can be derived from that of rf magnetometer in which the effects of large-excitation amplitude broadening are incorporated. Due to the additional SE broadening at the large excitation amplitude required for maximum sensitive, the fundamental noise of the scalar magnetometer has different dependence on the SE and SD rates than the rf magnetometer. The scalar magnetometer fundamental noise is mostly determined by the SE rate, while the rf magnetometer has
5. Applications of ultra-sensitive magnetometers
Research on atomic magnetometers is strongly motivated by many current and potential future applications. Among such applications, MEG is probably the most invaluable because no other device than the atomic magnetometer can rival low-Tc SQUIDs in sensitivity at low frequency, in the range of interest to MEG:
5.1. - MEG
History of MEG begins in 1968 when the first magnetic recordings of brain activity were registered with a Faraday coils (Cohen, 1968). Although the sensitivity of the coils in the initial demonstration was quite low, soon significant improvement was achieved when the coil was replaced with a SQUID magnetometer (Cohen, 1972). Later on, multi-channel systems have been developed to enable practical MEG source localization. Such systems became the basis for MEG research and clinical applications. However, the cost of multi-channel systems, of their maintenance, and of magnetically shielded rooms required for MEG measurements has been very high, restricting the clinical and research applications of this exciting technology. Consequently, some research has been done in the direction of cost reduction. For example, SQUID gradiometers were tested that could reduce ambient noise 1000 times to eliminate the requirement of expensive high-quality multi-layer shielded rooms. Some other ideas were tested, such as noise suppression based on open superconducting shield and reference channels (Volegov et al., 2004). However, until recently all practical MEG systems had been based on SQUIDs that required liquid helium supply, which is the major drawback.
Alternatively, MEG systems can be based on atomic magnetometers and requirements for cryogens can be eliminated. Recently, it was demonstrated that a SERF magnetometer can be successfully used for the detection and imaging of brain activities (Xia et al., 2006). Moreover, it was argued that a commercial multi-channel system can be built at a fraction of cost of a multi-channel SQUID system, so not only the AM MEG system would be more convenient in operation it would be less expensive as well. An inexpensive multi-channel operation is possible because a large atomic cell filled with a buffer gas can independenly measure magnetic field in different locations. Thus instead of building many separate magnetometers, it is sufficient to build a few large atomic cells to realize hundreds of channels. In Ref. (Xia et al., 2006) it was also demonstrated that a low cost shield can be designed for lying position consisting of mu-metal cylinders. With all these features, overall cost reduction is expected quite significant to make AM MEG system commercially viable and to extend the applications of the MEG method in research and hospitals. However, the currently demonstrated design is not suitable for building a full-head MEG system and requires further investigation.
Owing to rapid progress in AM technology and its novelty, it has to be noted that some even recent review books contain outdated notions about AMs with regard to MEG applications. For example, it is stated [see p. 273, (Clarke & Braginski, 2006) or (Wikswo, 2004), the original source] that one of the difficulties with atomic magnetometers in MEG applications is that they must be operated with a shielding factor about 104 times larger than that of magnetically shielded rooms currently used for biomagnetic measurements. This conclusion was drawn from the fact that shielding factor in Ref. (Kominis et al., 2003) was on the order of 106, but this was not essential. Actually, it was shown in a different paper (Seltzer & Romalis, 2004) that the SERF magnetometer can operate even in unshielded environment, if due field compensation is provided with a system of coils. Moreover, it was shown that with the gradiometric noise reduction technique based on multi-channel detection a relatively inexpensive shield can be used to conduct MEG experiments (Xia et al., 2006). Another outdated statement was about greater difficulty in thermal insulation of the hot oven, heated to 180 C, from the head compared to that of cryogenic systems such as SQUIDs. However, this problem was solved as well in Ref. (Xia et al., 2006). In addition to effective thermal insulation, a water cooling pad was added to make the subject comfortable during MEG sessions. The thermal insulation measures did not increase much distance from the sensor to the head or sources of the brain activity compared to that of the MEG SQUID Dewar. With regard to greater magnetic noise of the hot oven compared to that of the cold Dewar (Wikswo, 2004), it is the fact that the hot oven made of non conductive and non magnetic material does not create any magnetic noise, while in helium Dewars conductive materials are used for reflecting IR radiation to achieve minimal helium consumption, and such conductive materials produce significant noise.
5.2. - Fundamental experiments
Another possible application of AMs where high sensitivity is in demand is in fundamental physics. An example of such an application is the measurement of electric dipole moments (EDM) of atoms. There are several schemes for EDM experiments. The basic idea is to apply a strong electric field and to measure with high sensitivity a weak magnetic field arising due to EDM. Because the hypothetical atomic EDMs are extremely small, it is necessary to use sensors of highest sensitivity. Some schemes are based on unique properties of atomic spins and such experiments cannot be done with arbitrary magnetic sensors. Others do not necessarily need atomic magnetometers, and low-Tc SQUIDs can be used as well. A comprehensive review of EDM research is given in a book by Khriplovich and Lamoreaux (Khriplovich & Lamoreaux, 1997). Atomic magnetometers can be also used in other fundamental experiments such as the setting limits on CPT violation (Kornack & Romalis, 2002).
5.3. - NMR and MRI
High sensitivity of atomic magnetometers can be important for applications in unconventional low and ultra-low field (ULF) NMR and MRI. One motivation for exploring ULF MRI is that it is not based on bulky and expensive superconducting or permanent magnets and many applications supplemental to conventional MRI can be developed. For example, it is possible to combine MEG and MRI (Zotev et al., 2008) to reduce the corregistration error, or make a portable and inexpensive MRI scanner at a fraction of the cost of conventional MRI machines. Such scanners can lead to wider spread of MRI diagnostics around the world. Normally in NMR/MRI simple pick-up coils are used, but the coils, which output signal according to Faraday’s law is the time derivative of the magnetic flux, loose sensitivity at low frequency and do not perform well in the ULF regime. Apart from this, the polarization of NMR and MRI spins is also weak in this regime. On the other hand the standards of MR imaging are set very high with resolution on the order of 1 mm and SNR on the order of 30, setting demands on the sensitivity.
To enhance a weak NMR signal in the ULF regime, the method of prepolarization was proposed (Macovski & Conolly, 1993). In this method, relatively large field (whichever is practical to generate with a coil) is applied to polarize protons or other nuclear spins and is turned off during the NMR/MRI measurements. The process is repeated many times. With prepolarization method, the NMR signal is enhanced more than 1000 times compared to that would be generated in microTesla fields at which MRI enconding and readout are actually carried out. One advantage of the ULF readout and encoding is that gradients arising from the ULF coil are quite small and no shimming is necessary. Still even with prepolarization enhancement the SNR and resolution are quite inediquate if simple pick-up coils are used at low frequency, and some solution of this problem is necessary. One solution is to replace the coil with SQUIDs or AMs to achive additional gain in sensitivity. ULF MRI with SQUIDs is now a conventional way to do ULF MRI. For example, recently an airport security scanner have been built and tested based on a multi-channel SQUID detector. However, in all low-Tc SQUID applications the main drawback the requirement for cryogenics exists. The alternative solution to avoid cryogenics can be an atomic magnetometer.
The most potentially useful AM magnetometer for MRI applications (Savukov et al., 2007) is the high-density rf atomic magnetometer (Savukov et al., 2005) discussed in this chapter which not only has very high sensitivity (fundamental limit about 0.1 fT/Hz1/2 for 1 cm3 cell and practical noise was demonstrated 0.2 fT/Hz1/2) but also has sufficient bandwidth, on the order of 1 kHz which is needed in MRI detection. The minimum bandwidth for efficient scanner is estimated as the product of tissue relaxation rate and the number of pixels in readout direction.
The demonstration of MRI with AM suitable for in situ imaging is the important step in the direction of developing non-cryogenic ULF-MRI system, which was done in Ref. (Savukov et al., 2009). The achieved sensitivity was on the order of 10 fT/Hz1/2, but further significant improvement of the sensitivity is possible. Even without much modification of the system with which the demonstration was done the sensitivity on the order of 1 fT/Hz1/2 can be achieved just by raising frequency from 3 kHz to 30 kHz, and with ultimate optimization the sensitivity limits on the order of 0.1 fT/Hz1/2 are possible, which would make the MRI system suitable for clinical applications. This can be inferred from the scaling arguments given in Ref. (Savukov et al., 2009).
5.4. - Other potential applications based on similar sensitivity as low-Tc SQUIDs
There are many other potential application of AMs which can be developed following pioneering work on low-Tc SQUID applications. In biomedical imaging AMs can be applied to multi-channel MCG imaging. Since heart anomalies are among leading causes of death, their diagnostic is extremely important, and AM MCG can become a invaluable tool for saving millions of lives. Multi-channel MCG provides reach information on electrical activities in the heart non-invasively, and hence this modality can be crucial for revealing heart anomalies and the analysis of their localization. In addition to biomedical applications, AMs can be also used in submarine detection, geology, archeology, military applications, and many other fields as we have already discussed in the introduction. However, currently, high-sensitivity AMs are not available commercially, and this is the main impediment for applications. We expect that in the near future the situation will dramatically change, so all these applications will receive a significant boost.
We have considered the most sensitive atomic magnetometers based on high-density alkali-metal vapors. This chapter covered the principles of the operation of ultra-sensitive magnetometers and their applications. Among applications MEG and ULF MRI have been considered in some detail. Because low-Tc SQIUDs have been known as the most sensitive magnetometers for a long time and are still considered such by many researchers, the important conclusion from this chapter should be that atomic magnetometers can provide similar sensitivity and can be used instead of SQUIDs in their applications.
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