Atomic magnetometry - Optical magnetometry

 

 

Alkali atom optical pumping and optical transitions

 

Alkali-metal atoms (Li, Na, K, Rb, Cs) have a single electron in the outer shell i.e. one valence electron. For example, rubidium (Z=37) has the electronic configuration 1s2, 2s2, 2p6, 3s2, 3p6, 3d10, 4s2, 4p6, 5s1 with the 5s shell having a single electron. As a result, the charge distribution of the atom is not homogeneous and a non-zero magnetic moment is generated due to which the alkali atom behaves like a natural magnetic dipole.

 

The valence electron has orbital angular momentum Le due to its orbit/rotation around the nucleus and spin angular momentum Se due to its spin (self-rotation analog in classical physics) (cf. figures of section on remote magnetometry with LGS technology). This electron will determine the direction of the vector of the total electronic orbital angular momentum L and the total electronic spin angular momentum S, and by extension their sum, the (total) electronic angular momentum J of the atom. It will also determine the direction of the vector of the atomic angular momentum F (ref.1) (ref.2) which is equal to the sum of the nuclear angular momentum (net nuclear spin) I and the electronic angular momentum J (total angular momentum of the electrons). The vector of the atomic angular momentum determines the polarization of the atom. Therefore, the alkali atom outer shell electron (valence electron) will determine the polarization of the alkali atom.

 

The 5s shell where the valence electron is found has an L of 0 (as all s shells) and is split in two substates or energy levels, depending on whether the electron is in the spin-up configuration i.e. S=½ or in the spin-down configuration i.e. S=-½. The electron angular momentum J which is the sum of L and S will be respectively J=½ or J=-½. As the nuclear spin of Rb 87 is I=3/2, the atom angular momentum F which is the sum of I and J will be respectively F=3/2+½=2 or F=3/2-½=1. Therefore, the 5S½ state can be either F=2 (spin up) or F=1 (spin down).

 

The excited state represented by the 5p shell has an L of 1 (as all p shells) and is split in two substates or energy levels, depending on whether the electron is in the spin-up configuration i.e. S=½ or in the spin-down configuration i.e. S=-½. The electron angular momentum J which is the sum of L and S will be respectively J=3/2 or J=½. 

 

The transitions from the ground state to the first excited state for alkali atoms are represented by the D spectroscopic line according to the historic designation for sodium. The wavelengths corresponding to these transitions are in the visible, infrared or ultraviolet spectrum (wavelengths seen by living organisms) and are called optical transitions. For the Rb 87 isotope we have the following D transitions (ref.): 

 

1. D1 line at 794.7 nm  corresponding to the 52S½  → 52P½  transition

2. D2 line at 780 nm corresponding to the 52S ½  → 52P3/2 transition 

 

Note on energy state label notation (ref.): the first number is the principal quantum number of the outer electron, the superscript is 2S + 1, the letter refers to L (i.e., S ↔ L = 0, P ↔ L = 1, etc.), and the subscript gives the value of J.

 

A diagram of Rb 87 can be found in Figure 1 and at this reference. (Alternative reference for D2 line.)

 

Figure 1: Transitions of Rb 87 (left from Wikipedia, right from this reference).

 

Left-circularly polarized light tuned to the D1 line excites the electrons from the spin down 2S1/2 (ms=-1/2) state into the spin up 2P1/2 (ms=+1/2) state (Wikipedia). During a transition mediated by circularly polarized light — which has a specific polarization (right or left) — photons of only one type of angular momentum are absorbed and as this angular momentum is transferred to the electrons, the spin polarization changes or in other words the spins become polarized. 

 

This is an important concept, as spin polarization can not only be mediated by a strong magnetic field but also using circularly polarized light. Additional considerations are mentioned in the section on remote magnetometry using LGS technology.

 

It is noted that use of circularly polarized light, which transfers angular momentum to the atom, leads to a state with the largest corresponding angular momentum and will tend to increase the absolute value of the magnetic quantum number mF . If for instance we consider the transition F = 2 → F΄ = 3, σ+ light will mediate the |F = 2, mF = 2 −→ |F = 3, mF = 3 transition and σ− light will mediate the |F = 2, mF = −2 → |F = 3, mF = −3 transition (reference section 4.3.1). 

 

If we consider an atomic population consisting of alkali atoms, illumination in a continuous manner with laser light induces atom excitations in a process termed optical pumping which describes the increase of the energy level of the atoms. The excitations will be followed by relaxations in a cyclical manner.

 

Optical pumping of alkali atoms is used in atomic magnetometers. Also, for some biochemical applications, the polarization of specific atoms is required such as for instance performing a lung MRI with noble gas 129Xe inhalation. In this case, the alkali atom and the noble gas are brought in a glass chamber and the alkali atom is spin-polarized via optical pumping. Subsequently, collisions of the alkali atom with the noble gas result in spin-exchange and thereby polarization transfer to the latter.

 

 

 

Classic SERF atomic magnetometer

 

An atomic magnetometer of superior sensitivity is the spin-exchange-relaxation-free (SERF) magnetometer. It is noted that it requires zero ambient magnetic field. Its principle of operation is described below and in Figure 2.

 

A droplet of alkali metal e.g. rubidium in a glass chamber is heated to produce a vapor (gaseous phase). A laser beam of circularly polarized light tuned at the D1 line aligns the spins of the rubidium atoms via optical pumping in the direction of propagation of the light (pump beam). The polarization fraction of the spins and by extension of the atoms depends among others on the pump power and the atom density.

 

Upon the effect of a magnetic field perpendicular to the pump beam, the spins are rotated and reorient. As a result the refraction index of the gas changes. A beam of linearly polarized light, termed the probe beam, which is typically perpendicular to the pump beam, is used to detect these events by the rotation of its polarization, which constitutes the magneto-optical phenomenon termed the Faraday effect/rotation. The rotation of the polarization is linked to the differential behavior of the right and left circularly polarized components which compose a linearly polarized beam. It is considered that the spin polarization is imprinted on the light polarization. The rotation is proportional to the magnetic field strength and therefore can be used to measure it. 

 

 

Figure 2: Principle of operation of a SERF magnetometer (image from "Atomic Magnetometer for Human Magnetoencephalograpy" by SANDIA Labs )

 

 

 

The sensitivity of an atomic magnetometer operating with density n in a volume V due to shot noise is:

where γ is the gyromagnetic ratio, t is the measurement time and T2 is the relaxation or decoherence time of the atomic population. Relaxation is due among others to collisions with chamber walls and inter-population collisions. Collisions are linked to spin-exchange or spin destruction. By using conditions such as a high-density population it is possible to remove spin-exchange relaxation. Magnetometers which operate in these conditions are termed spin-exchange-relaxation-free (SERF) magnetometers.

 

 

An atomic SERF magnetometer for Magnetoencephalography (MEG) was developed by Sandiai National Laboratories in 2010 (ref. - Figure 2 is derived from this reference). Following the publication of the development of the sensor (Colombo et al 2016), Sandia Labs reported the generation of a 20-channel MEG system using SERF optical magnetometers and a magnetically shielded chamber (Borna et al 2017archiv link). A press release by Sandia Labs is found at this link.

 

 

In 2018, Boto et al published in Nature their study of a MEG portable helmet with SERF magnetometers (PMC link). It is noted that a zero ambient magnetic field regime is required. This study was cited in the NIH’s director blog (ref.). A presentation of the authors is found at this link. Information on the sensor is available at the QuSpin site and also at the publication by Shah et Wakai 2013*.

 

*includes magnetic field cancellation protocol using coils

 

 

Figure 3: NIH Facebook post referring to NIH's director article on a wearable magnetoencephalography (MEG) scanner

 

 

 

Magnetometry with diamond NVcenters and optically-detected Electron Spin Resonance (ESR)

 

Depolarization of the NV- center as a wideband magnetometer

 

Illumination with a green laser induces an electron transition whose decay/relaxation emits red light. (Optical transition)

 

Microwave irradiation induces Electron Spin Resonance (ESR) transitions of the two unpaired electrons to two ground energy states whose splitting or energy difference (gap/spacing) is proportional to the magnetic field strength (5.6 MHz splitting per 1 Gauss field). (ESR transition)

 

Illumination with a green laser when electrons occupy these ground states induces a transition whose decay/relaxation is associated with emission of less red light.

 

By determining the difference in red light emission, we can calculate the ground state spacing and by extension the magnetic field.

 

 

Diamond is a solid form of the carbon element with its atoms arranged in a crystal (another form is graphite). It is common for nitrogen to be integrated in the crystal and substitute the carbon atoms thereby forming a crystallographic defect which is considered a substitutional impurity (substitutional nitrogen).

 

Another crystallographic defect is the vacancy defect which corresponds to a vacant or empty site (vacancy) in the lattice. When a substitutional nitrogen (N) is adjacent to a vacancy (V), it creates a nitrogen vacancy defect, termed NV defect or NV center. An NV defect can be positively, negatively charged or neutral. The NV- center is of interest to magnetometry due the fact that it can be detected with ODMR (optically-detected magnetic resonance) (ref.). 

 

Figure 4: "Simplified atomic structure of the NV- center". Legend and image from Wikipedia (by Materialscientist - Own work, CC BY-SA 3.0).

 

The NV- center is a color center as it absorbs photons of visible wavelength e.g. green at 532 nm and emits photons of a broad wavelength range e.g. red and more generally 632–800 nm. The negatively charged NV- center has six electrons i.e. three electrons from three carbons, two electrons from the substitutional nitrogen and one electron from the diamond lattice. Four of them form pairs and the remaining two are unpaired electrons. The two unpaired electrons define the energy level structure of the NV- center. Specifically, an NV- center has ground and excited states with triple spin degeneracy i.e. a triplet ground state and a triplet excited state, as well as two intermediate singlet states (Figure 4). 

 

A triplet state is a state with total spin S=1 such that there are three allowed values of the spin component, ms = −1, 0, and 1 and therefore three sublevels. The singlet state is a state with total spin S=0 and therefore ms = 0 and only one sublevel.

 

Excitation occurs from the triplet ground state to the triplet excited state with absorption of green light and relaxation occurs mainly to the triplet ground state with the emission of red light. There is also the possibility of relaxation to the intermediate singlet states which preferentially relax to the ms = 0 ground state (electrons will fill this state). A weaker emission band at 1042 nanometers is associated with decay between the singlet states.

 

 

Figure 4: "Excitation with green light places the NV- in the triplet excited state. Relaxation then emits either a red or (undetected) infrared photon, placing the centre in the ms=0 state. Microwave pumping raises the centre to ms=  ± 1 where Zeeman splitting can occur". Legend and image from Wikipedia (by Brunolucatto - Own work, CC BY-SA 4.0).

 

 

 

The separation of the triple ground state is approximately 2.9 GHz at room temperature. The ms= ± 1 states are split further in the presence of a magnetic field (Zeeman splitting). Magnetic field sensing (sensing of component along the NV axis) is performed by measuring the amount of Zeeman splitting (e.g. 5.6 MHz splitting per 1 Gauss field).


Illumination of an NV- center with green laser light induces a transition of the unpaired electrons to an excited state followed by decay/relaxation to the ground state with emission of red light. Microwave irradiation induces Electron Spin Resonance (ESR) transitions of the two unpaired electrons to two ground energy states (ms=  ± 1) whose splitting or energy difference (gap/spacing) is proportional to the magnetic field strength (5.6 MHz splitting per 1 Gauss field).

 

Illumination with a green laser when electrons occupy these ground states induces a transition whose decay/relaxation is associated with emission of less red light. By determining the difference in red light emission, we can calculate the ground state spacing and by extension the magnetic field.

 

It is noted that electron spin resonance (ESR) is observed for electrons in different cases. Among these are: (i) electrons localised at impurity atoms in the lattice of a solid, and (ii) unpaired electrons localised in orbitals at defect sites in solids. These electrons are not free but are described by specific wavefunctions. Their paramagnetism is due to their interaction with the lattice and is described in terms of the ‘spin Hamiltonian’ (ref).  

Prior to ODMR, in the 1940s all-microwave electron spin resonance (ESR) was developed and then used to study defects in diamond but its reliance on thermal polarization and microwave detection prevented its extended use in magnetometry.

 

 

 

Cycles of optical excitation and decay produce optically induced spin polarization, due to which nitrogen vacancy centers find many applications in magnetic field sensing, biological imaging and quantum information processing. The magnetic field sensitivity for a single NV- center is on the order of 1nT/√Hz which is about 105 smaller than the typical Earth’s magnetic field.

 

A comprehensive reference can be found at this link.


 

 

"Detecting tiny magnetic fields with diamond sensors"

 

 

Figure 5: Video entitled "Detecting tiny magnetic fields with diamond sensors" (from the Fraunhofer Institute for Applied Solid State Physics).

 

Transcript starting at https://youtu.be/Z6OX88jrTKc?t=46:

“Two electrons from this nitrogen vacancy center form a triplet state which we can stimulate on to a higher energy level by using a green laser. They directly return to their ground states by emission of a photon resulting in red light. With microwave radiation we lift the electrons up into the degenerated state m(s)=±1. When exposing the electrons in this state to a green laser beam, they recombine back into the m(s)=0 state. Here they emit less red light. The diamond thus appears darker. We are able to measure this variation of the photoluminescence intensity. If a magnetic field is applied a Zeeman effect occurs. The degenerated m(s)=±1 states splits into two distinct levels which can be occupied through microwave stimulation. Two measurable resonance dips in photoluminescence occur. The stronger the magnetic field the greater the splitting will be. By measuring the frequency of the double minima we can determine the magnetic field strength. Two electrons therefore facilitate the detection of smallest magnetic fields and data structures while making a diamond even more precious.”
 
 
 

 

"Magnetic nanoscopy with nitrogen-vacancy color centers in diamond" 

 

 

Figure 6: Video from Professor Budker's lab, expert in optical magnetometry.