Magnetoencephalography (MEG) with optical/atomic magnetometers, SERF magnetometers
Principle of measurement of the magnetic field of the brain using an optica/atomic magnetometer, a SERF magnetometer
Personal notes based on the reference "Atomic Magnetometer for Human Magnetoencephalograpy" by SANDIA Labs
Polarization: We consider an alkali atom population in vapor form in a glass cell. Under zero magnetic field conditions, if we direct towards the atoms circularly
polarized light of frequency corresponding to the spectral resonance line of the spins, its magnetic field component will polarize the precessing spins in the direction of propagation of the
Detection upon Faraday rotation: Upon the effect of a magnetic field e.g. from the brain, applied perpendicularly to the beam, the spins are tipped from alignement
and reorient. As a result the refraction index of the vapor changes and the polarization of the light that is directed towards the atoms will be rotated. The rotation will be proportional to the
applied magnetic field from the brain. This is known as the Faraday rotation effect and constitutes a magneto-optic effect.
(Above are personal notes based on the following reference)
The NIH Director writes on his blog about the new wearable Magnetoencephalography (MEG) scanner
Francis S. Collins @NIHDirector (2018-03-27)
"A #brain scanner that looks like a futuristic cross between a helmet and hockey mask is pushing functional brain
imaging into the future. Find out how on my blog. #NIH"
NIH on Facebook: https://www.facebook.com/nih.gov/posts/10156009236911830
Figure: From the NIH Director's Blog: wearable MEG with atomic/optical magnetometers
The publication (Nature) is mentioned below.
Magnetoencephalography with optical/atomic magnetometry
SERF magnetometers (Spin Exchange Relaxation-Free regime)
"Moving magnetoencephalography towards real-world applications with a wearable system"
Use of an atomic population of rubidium (alkali-metal) in a glass cell sensor and circular polarized light at the D1 Rb transition of 795 nm. Upon the effect of the
magnetic field of the brain, the spin polarization changes the light diffraction index and the light polarization is rotated via the Faraday rotation effect, a magneto-optic effect. The spin
polarization is considered to be imprinted on the light polarization. The rotation of the light polarization is measured and the strength of the magnetic field of the brain is determined.
This study has been featured at the NIH director's blog.
(SERF magnetometers vs SQUID magnetometers)
Earth magnetic field cancellation used in the study of the MEG wearable with optically pumped magnetometers
The measurement is conducted in a magnetically-shielded room. However, there is a remnant magnetic field of about 25nT which is spatially inhomogeneous.
Excerpt: "To ameliorate this problem, we constructed a set of bi-planar electromagnetic coils designed to generate fields equal and opposite to the remnant Earth’s field, thereby cancelling it
out. The coils were designed [25,26] on two 1.6 × 1.6 m^2 planes, placed either side of the subject with a 1.5 m separation (Fig. 3a). Three coils generated spatially uniform fields (Bx, By and Bz)
while two additional coils were used to remove the dominant field variations (dB(x)/dz and dB(z) /dz). In this way, unlike standard field-nulling technologies (for example, tri-axial Helmholtz
coils), our system can account for spatial variation of the field over a 40 × 40 × 40 cm^3 volume of interest enclosing the head. Furthermore, we were able to cancel all components of the field
vector using coils confined to just two planes, hence retaining easy access to the subject. Four reference OPM sensors were coupled to the coils in a feedback loop to null the residual static field
in the volume of interest. We achieved a 15-fold reduction in the remnant Earth’s field and a 35-fold reduction in the dominant field gradient (Fig. 3b)
Publication on the sensor used for the wearable MEG
(Includes magnetic field cancellation with coils)
Excerpt: "The frequency response of the AM is given by the square root of a Lorentzian function, s(f)= s0/[1+(2 π f T2)2]1/2, where the width is determined by the inverse of the spin
coherence time, T2. The 3-dB bandwidth of our AM was roughly 100 Hz, corresponding to a T2 ~ 2 ms."
Reference link: https://quspin.com/
Optical Magnetic Resonance - Optical polarization/Optical detection (all-optical MR)
Optical pumping of a Rb (alkali-metal) atomic population (used in atomic/optical magnetometers)
"the fact that the electrons are being pumped into a state of maximal mF means that their magnetic dipole moments orient themselves parallel to the external magnetic
"rubidium atoms behave like a single electron in the 5s ground state."
Excerpts and reading notes from:
Light consists of photons which carry energy E, momentum p and angular momentum j=1 (two degrees of freedom are defined i.e. mj=±1). The angular momentum eigenstates
are called σ+ (mj=+1) and σ− (mj=−1). Photons of right circular polarization or positive helicity are σ+ and photons of left circular polarization or negative helicity are σ-. Linearly polarized
light is a combination of two circular polarizations, right and left corresponding to σ+ and σ− respectively.
Alkali-metal atoms (Li, Na, K, Rb, or Cs) have a single electron in the outer shell. For example, rubidium (Z=37) has the configuration 1s, 2s, 2p, 3s, 3p, 3d, 4s,
4p, 5s with the 5s shell having one single electron.
"The spin-orbit interaction pushes the 5s shell lower than the 4d and 4f shells, so that the rubidium atoms behave like a single electron in the 5s ground
Orbital angular momentum is represented by the orbital quantum number l. Spin angular momentum or spin (s) is represented by the spin quantum number ms, which takes
the values +1/2 for "spin up" and -1/2 for "spin down". The total angular momentum is represented by the total angular momentum number j which is equal to j=l+s and therefore for the electron it is
Fine structure - Spin-orbit interaction
The 5 state with l=0 (s shell) is the ground state and has j=1/2. It is termed 5s(1/2).
The 5 state with l=1 (p shell) is split due to the spin-orbit interaction in two states (energetic levels), one with j=1+1/2=3/2 termed 5p(3/2) and the other with
j=1-1/2=1/2 termed 5p(1/2).
Hyperfine structure - Zeeman interaction
The total angular momentum of the atom F is given by F=J+K where J and K are the angular momenta of the electrons and the protons/neutrons respectively.
The 5s(1/2) state is split in two states, F1 and F2, with magnetic quantum numbers mj=+1/2 and mj=-1/2.
The 5p(1/2) state is split in two states, F1 and F2, with magnetic quantum numbers mj=+1/2 and mj=-1/2.
The 5p(3/2) state is split in four states, F0 to F3, with magnetic quantum numbers mj=+1/2, mj=-1/2, mj=+3/2, mj=-3/2.
Energetic Transitions - Selection rules
The D1 transition of Rb: From 5s(1/2) to 5p(1/2) by absorption of photons of 794.7nm
The D2 transition of Rb: From 5s(1/2) to 5p(3/2) by absorption of photons of 780 nm
"When atoms absorb light, they must absorb both energy and angular momentum in the transition from the ground state to an excited state. The most basic, leading
order process is called the electric dipole, or E1, transition and has the selection rules for the atom ∆l = ±1, ∆F = ±1 and ∆m = 0, ±1, depending on the polarization of the light. For circularly
polarized photon absorption ∆m = mj. For linearly polarized photons ∆m = 0. These restrictions of ∆l, ∆F, etc. are called selection rules. Emission of light by F1 radiation has the same selection
rules. Also if ∆m = ±1, the photon emitted is circularly polarized, and if ∆m = ±0, the emitted photon is linearly polarized, that is a superposition of σ+ and σ−."
"σ+ photons can affect 2S1/2 →2 P1/2 transitions according to the following dipole selection rules (these give the dominant transition processes):
∆L = ±1 ∆J = 0, ±1 ∆F = 0, ±1 ∆mF = +1
Note that σ+ photons can only cause ∆mF = +1 transitions. Likewise, photons of negative helicity - so-called σ− photons - can only cause ∆mF = −1 transitions, with
otherwise identical selection rules. So when a σ+ photon hits a Rubidium 87 atom, it not only excites the electron to the 2P1/2 level, but also raises its mF by one unit. Of course, the excited state
is unstable and spontaneously decays back to the ground state by emitting another photon. However, the spontaneously emitted photon has arbitrary polarization and the decay can have ∆mF = 0, ±1.
Thus, on average we have ∆mF = +1 for the excitation by σ+ photons, but ∆mF = 0 for the spontaneous decay, giving a net average ∆mF = +1: on average, the electrons will migrate into states of higher
and higher mF . This phenomenon is referred to as optical pumping."
"Physically, the fact that the electrons are being pumped into a state of maximal mF means that their magnetic dipole moments orient themselves parallel to the
external magnetic field.
In a state of maximal mF , dipole selection rules prohibit the atoms from absorbing any more σ+ photons, and thus these photons pass through the Rubidium vapor bulb
unaffected: in its fully pumped state the bulb is transparent.
Now imagine that there was - loosely speaking - a way to disorient the magnetic moments we just talked about. Then the Rubidium gas would not be in its fully pumped
state anymore and could again absorb σ+ photons: it would temporarily become opaque.
By monitoring the depletion of the incident beam of σ+ photons using the optical detector behind the Rubidium vapor bulb, we can thus tell when the Rubidium vapor is
in its fully pumped state and when it has become temporarily disoriented: temporary opacity shows up as a dip in the intensity of the incident photon beam measured by the optical detector.
This is the key idea which makes optical pumping a powerful experimental technique: we can use it to tell when the Rubidium vapor becomes temporarily
Figure: On the left from Wikipedia (https://en.wikipedia.org/wiki/Hyperpolarization_(physics)_- on the right from second reference
Optical Magnetic Resonance - Spin Exchange Relaxation
Atomic optical magnetometry with visible/near-infrared light
Spin Exchange Relaxation-Free (SERF) magnetometers
 "Alkali atoms couple in a resonant fashion to light, with frequency in the visible and near-infrared spectrum. The transitions between the ground state and
excited state energy levels are often called optical transitions. The transitions that couple the ground state to the P1/2 and P3/2 excited states are often referred as the D1 and D2 optical
"In the absence of external fields, the hyperfine energy spectrum of alkali atoms is determined by the interaction between the nucleus, with angular momentum I, and
the unpaired electron of the atom, with angular momentum J."
 "Magnetic resonance involves the coupling of energy from the applied magnetic field to the atomic spin system, which has a natural frequency due to the Zeeman
splitting of spin up and spin down atoms in the presence of an applied, static magnetic field B0.
The energy levels for an atom with J = 1/2 and two hyperfine levels F = I ± 1/2 are given by the Breit–Rabi formula (...) .
"The magnetic resonance transitions correspond to ∆F = 0 and ∆m = ±1. For B0 of a few Gauss, x <<1, and the Breit Rabi formula can be used to show, for example
corresponding frequency is:
where γA is a gyromagnetic ratio for each isotope 85Rb with I85 = 5/2 and 87Rb with I87=3/2."
"The phenomenon of magnetic resonance is observed by changing the frequency and magnitude of the applied RF magnetic field. The mathematics is identical to that of a
driven LRC oscillator, where the damping rate constant is Γ = R/2L."
 "The dynamics of a spin coupled to a magnetic field Bo through the Zeeman interaction consists of the precession of the spin about the field. In the absence of a
driving field, spin relaxation mechanisms restrict the synchronous precession of the spins about the magnetic field, which results in dephasing. In the presence of spin decoherence and optical
pumping the response of the atomic spin ensemble to magnetic fields can be modeled phenomenologically through Bloch equations as described in chapter 2.”
When a pair of rubidium atoms move past each other "the magnetic dipole moment of one atoms causes a rapidly changing magnetic field in the rest frame of the other
leading to spin flips and the phenomena of spin exchange. Spin exchange is an important effect because it is very rapid and affects the electron spins of atoms that may be in different hyperfine
levels or even different isotopes."
Also "when a rubidium atom moves near the wall, the rapidly varying field in the atom’s rest frame can cause transitions between mj = +1/2 and mj = −1/2. This is
called “wall relaxation.”"
[e-page 32] "Figure 2.2: (a) A single atom interacting with a magnetic field. All degrees of freedom are frozen, but its spin. The effect of the interaction is
the precession of the spin about the magnetic field. In the real world the atom cannot be completely isolated from its environment. The spin will interact with this environment resulting in effects
such as the sudden change in its precession phase.
(b) An ensemble of atoms interacting with the same magnetic field as in (a). Here all degrees of freedom of the atoms are unfrozen. Thus in addition to interacting
with the magnetic field B, the atoms move within the cell, collide and interact with each other and with the cell walls, which in turn causes the dephasing of the precession in the spin
 Thesis by R. Jimenez Martinez, University of Colorado at Boulder (in collaboration with NIST)
[e-page 32] Figure 2.2: (a) A single atom interacting with a magnetic field. All degrees of freedom are frozen, but its spin. The
effect of the interaction is the precession of the spin about the magnetic field. In the real world the atom cannot be completely isolated from its environment. The spin will interact with this
environment resulting in effects such as the sudden change in its precession phase. (b) An ensemble of atoms interacting with the same magnetic field as in (a). Here all degrees of freedom of the
atoms are unfrozen. Thus in addition to interacting with the magnetic field B, the atoms move within the cell, collide and interact with each other and with the cell walls, which in turn causes the
dephasing of the precession in the spin ensemble.
DARPA's Program "Atomic Magnetometer for Biological Imaging In Earth’s Native Terrain (AMBIIENT)" - Magnetoencephalography and
"The AMBIIENT program is challenging the research community to devise new types of magnetic gradiometers that can detect picoTesla- and femtoTesla magnetic signatures out in the open, without
shielding and with whatever the ambient magnetic field environment might be. To do so will require researchers to, in Lutwak’s words, “exploit novel atomic physics techniques and architectures to
directly measure extremely tiny gradients in magnetic fields without having to compare the difference between absolute field measurements from two sensors separated along a baseline.” One
physics-based approach AMBIIENT performers are likely to pursue is to monitor changes in the polarization or other measureable features of a small laser beam as it passes through vapor cells hosting
atoms that respond in laser-beam-altering ways to even femtoTesla magnetic fields."
"Traditionally, measuring small magnetic signals in ambient environments has relied on pairs of high-performance sensors separated by a baseline distance and then measuring the small
field-strength differences between the two sensors,” said Robert Lutwak, AMBIIENT’s program manager in DARPA’s Microsystems Technology Office. “This gradiometric technique has worked well for
applications in geophysical surveying and unexploded ordnance detection,” Lutwak added, “but due to the combination of the sensors’ limited dynamic range and the natural spatial variation of the
background signals, this approach falls several orders of magnitude short of being able to detect biological magnetic signals.”
Optical Magnetometry - Faraday Rotation Magnetometry
Detection of brain activity/neural activity: Magneto-optical sensor based on the Faraday effect i.e. Faraday rotator (https://en.wikipedia.org/wiki/Faraday_rotator
with 20fT/√Hz sensitivity (noise-equivalent power)
Magnetic fields in the human brain are on the order of 50 to 500 fT.