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39-428: The name for the technique comes from the fact that spin exchange relaxation , a mechanism which usually scrambles the orientation of atomic spins , is avoided in these magnetometers. This is done by using a high (10 cm) density of potassium atoms and a very low magnetic field. Under these conditions, the atoms exchange spin quickly compared to their magnetic precession frequency so that the average spin interacts with

78-459: A gyromagnetic factor equal to 2 follows from Dirac's equation, it is a frequent misconception to think that a g -factor 2 is a consequence of relativity; it is not. The factor 2 can be obtained from the linearization of both the Schrödinger equation and the relativistic Klein–Gordon equation (which leads to Dirac's). In both cases a 4- spinor is obtained and for both linearizations the g -factor

117-512: A magnetic field B {\displaystyle \mathbf {B} } is T = m × B . {\displaystyle \,{\boldsymbol {\mathrm {T} }}=\mathbf {m} \times \mathbf {B} \,.} The identity of the functional form of the stationary electric and magnetic fields has led to defining the magnitude of the magnetic dipole moment equally well as m = I π r 2 {\displaystyle m=I\pi r^{2}} , or in

156-403: A truly quadratic fermion. Protons , neutrons, and many nuclei carry nuclear spin , which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is: where μ N {\displaystyle \mu _{\mathrm {N} }}

195-428: A typical SERF magnetometer, the spins merely tip by a very small angle because the precession frequency is slow compared to the relaxation rates. SERF magnetometers compete with SQUID magnetometers for use in a variety of applications. The SERF magnetometer has the following advantages: Potential disadvantages: Applications utilizing high sensitivity of SERF magnetometers potentially include: The SERF magnetometer

234-854: Is γ e = − 1.760 859 630 23 ( 53 ) × 10 11 r a d ⋅ s − 1 ⋅ T − 1 {\displaystyle \gamma _{\mathrm {e} }=\mathrm {-1.760\,859\,630\,23(53)\times 10^{11}\,rad{\cdot }s^{-1}{\cdot }T^{-1}} } γ e 2 π = − 28 024.951 4242 ( 85 ) M H z ⋅ T − 1 . {\displaystyle {\frac {\gamma _{\mathrm {e} }}{2\pi }}=\mathrm {-28\,024.951\,4242(85)\,MHz{\cdot }T^{-1}} .} The electron g -factor and γ are in excellent agreement with theory; see Precision tests of QED for details. Since

273-462: Is where q {\displaystyle {q}} is its charge and m {\displaystyle {m}} is its mass. The derivation of this relation is as follows. It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result then follows from an integration . Suppose the ring has radius r , area A = πr , mass m , charge q , and angular momentum L = mvr . Then

312-468: Is 7.622593285(47) MHz/T. The gyromagnetic ratio of a nucleus plays a role in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). These procedures rely on the fact that bulk magnetization due to nuclear spins precess in a magnetic field at a rate called the Larmor frequency , which is simply the product of the gyromagnetic ratio with the magnetic field strength. With this phenomenon,

351-411: Is a ratio of a magnetic property (i.e. dipole moment) to a gyric (rotational, from Greek : γύρος , "turn") property (i.e. angular momentum ), it is also, at the same time , a ratio between the angular precession frequency (another gyric property) ω = 2 πf and the magnetic field . The angular precession frequency has an important physical meaning: It is the angular cyclotron frequency ,

390-434: Is denoted g e : γ e = − e 2 m e | g e | = g e μ B ℏ , {\displaystyle \gamma _{\mathrm {e} }={\frac {-e}{2m_{\mathrm {e} }}}\,|g_{\mathrm {e} }|={\frac {g_{\mathrm {e} }\mu _{\mathrm {B} }}{\hbar }}\,,} where μ B

429-484: Is found to be equal to 2. Therefore, the factor 2 is a consequence of the minimal coupling and of the fact of having the same order of derivatives for space and time. Physical spin- ⁠ 1 / 2 ⁠ particles which cannot be described by the linear gauged Dirac equation satisfy the gauged Klein–Gordon equation extended by the g ⁠ e / 4 ⁠ σ F μν term according to, Here, ⁠ 1 / 2 ⁠ σ and F stand for

SECTION 10

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468-458: Is not aligned with its magnetic moment , will precess at a frequency f (measured in hertz ) proportional to the external field: For this reason, values of ⁠ γ / 2 π ⁠ , in units of hertz per tesla (Hz/T), are often quoted instead of γ . The derivation of this ratio is as follows: First we must prove the torque resulting from subjecting a magnetic moment m {\displaystyle \mathbf {m} } to

507-451: Is obtained by simply heating solid alkali metal inside the vapor cell. A typical SERF atomic magnetometer can take advantage of low noise diode lasers to polarize and monitor spin precession. Circularly polarized pumping light tuned to the D 1 {\displaystyle D_{1}} spectral resonance line polarizes the atoms. An orthogonal probe beam detects the precession using optical rotation of linearly polarized light. In

546-541: Is the Bohr magneton . The gyromagnetic ratio due to electron spin is twice that due to the orbiting of an electron. In the framework of relativistic quantum mechanics, g e = − 2 ( 1 + α 2 π + ⋯ )   , {\displaystyle g_{\mathrm {e} }=-2\left(1+{\frac {\alpha }{\,2\pi \,}}+\cdots \right)~,} where α {\displaystyle \alpha }

585-545: Is the fine-structure constant . Here the small corrections to the relativistic result g = 2 come from the quantum field theory calculations of the anomalous magnetic dipole moment . The electron g -factor is known to twelve decimal places by measuring the electron magnetic moment in a one-electron cyclotron: g e = − 2.002 319 304 361 18 ( 27 ) . {\displaystyle g_{\mathrm {e} }=-2.002\,319\,304\,361\,18(27).} The electron gyromagnetic ratio

624-470: Is the nuclear magneton , and g n {\displaystyle g_{\rm {n}}} is the g -factor of the nucleon or nucleus in question. The ratio γ n 2 π g n , {\displaystyle \,{\frac {\gamma _{n}}{\,2\pi \,g_{\rm {n}}\,}}\,,} equal to μ N / h {\displaystyle \mu _{\mathrm {N} }/h} ,

663-417: Is the ratio of its magnetic moment to its angular momentum , and it is often denoted by the symbol γ , gamma. Its SI unit is the radian per second per tesla (rad⋅s ⋅T ) or, equivalently, the coulomb per kilogram (C⋅kg ). The term "gyromagnetic ratio" is often used as a synonym for a different but closely related quantity, the g -factor . The g -factor only differs from

702-417: Is the "slowing-down" constant to account for sharing of angular momentum between the electron and nuclear spins: where P {\displaystyle P} is the average polarization of the atoms. The atoms suffering fast spin-exchange precess more slowly when they are not fully polarized because they spend a fraction of the time in different hyperfine states precessing at different frequencies (or in

741-618: Is the relaxation rate due to collisions with the cell walls and R s d , X {\displaystyle R_{sd,X}} are the spin destruction rates for collisions among the alkali metal atoms and collisions between alkali atoms and any other gasses that may be present. In an optimal configuration, a density of 10 cm potassium atoms in a 1 cm vapor cell with ~3 atm helium buffer gas can achieve 10 aT Hz (10 T Hz) sensitivity with relaxation rate R t o t {\displaystyle R_{tot}} ≈ 1 Hz. Alkali metal vapor of sufficient density

780-519: Is the time between spin-exchange collisions, I {\displaystyle I} is the nuclear spin, ν {\displaystyle \nu } is the magnetic resonance frequency, γ e {\displaystyle \gamma _{e}} is the gyromagnetic ratio for an electron. In the limit of fast spin-exchange and small magnetic field, the spin-exchange relaxation rate vanishes for sufficiently small magnetic field: where Q {\displaystyle Q}

819-460: The precession of a gyroscope. The earth's gravitational attraction applies a force or torque to the gyroscope in the vertical direction, and the angular momentum vector along the axis of the gyroscope rotates slowly about a vertical line through the pivot. In place of a gyroscope, imagine a sphere spinning around the axis with its center on the pivot of the gyroscope, and along the axis of the gyroscope two oppositely directed vectors both originated in

SECTION 20

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858-556: The Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while A is the electromagnetic four-potential . An example for such a particle is the spin ⁠ 1 / 2 ⁠ companion to spin ⁠ 3 / 2 ⁠ in the D ⊕ D representation space of the Lorentz group . This particle has been shown to be characterized by g = ⁠− + 2 / 3 ⁠ and consequently to behave as

897-480: The Wikimedia System Administrators, please include the details below. Request from 172.68.168.151 via cp1112 cp1112, Varnish XID 379059822 Upstream caches: cp1112 int Error: 429, Too Many Requests at Fri, 29 Nov 2024 05:29:39 GMT Gyromagnetic ratio In physics , the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system

936-430: The alkali metal atoms. SERF magnetometers are among the most sensitive magnetic field sensors and in some cases exceed the performance of SQUID detectors of equivalent size. A small 1 cm volume glass cell containing potassium vapor has reported 1 fT/ √ Hz sensitivity and can theoretically become even more sensitive with larger volumes. They are vector magnetometers capable of measuring all three components of

975-391: The atom and F z {\displaystyle F_{z}} is the average polarization of total atomic spin F = I + S {\displaystyle F=I+S} . In the absence of spin-exchange relaxation, a variety of other relaxation mechanisms contribute to the decoherence of atomic spin: where R D {\displaystyle R_{D}}

1014-502: The center of the sphere, upwards J {\displaystyle \mathbf {J} } and downwards m . {\displaystyle \mathbf {m} .} Replace the gravity with a magnetic flux density B   . {\displaystyle \,\mathbf {B} ~.} d ⁡ J d ⁡ t {\displaystyle {\frac {\,\operatorname {d} \mathbf {J} \,}{\,\operatorname {d} t\,}}} represents

1053-460: The desired formula comes up. d ^ {\displaystyle {\hat {\mathbf {d} }}} is the unit distance vector. The spinning electron model here is analogous to a gyroscope. For any rotating body the rate of change of the angular momentum J {\displaystyle \,\mathbf {J} \,} equals the applied torque T {\displaystyle \mathbf {T} } : Note as an example

1092-402: The field and is not destroyed by decoherence. A SERF magnetometer achieves very high magnetic field sensitivity by monitoring a high density vapor of alkali metal atoms precessing in a near-zero magnetic field. The sensitivity of SERF magnetometers improves upon traditional atomic magnetometers by eliminating the dominant cause of atomic spin decoherence caused by spin-exchange collisions among

1131-520: The following way, imitating the moment p of an electric dipole: The magnetic dipole can be represented by a needle of a compass with fictitious magnetic charges ± q m {\displaystyle \pm q_{\rm {m}}} on the two poles and vector distance between the poles d {\displaystyle \mathbf {d} } under the influence of the magnetic field of earth B . {\displaystyle \,\mathbf {B} \,.} By classical mechanics

1170-468: The gyromagnetic ratio in being dimensionless . Consider a nonconductive charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment due to the movement of charge and an angular momentum due to the movement of mass arising from its rotation. It can be shown that as long as its charge and mass density and flow are distributed identically and rotationally symmetric, its gyromagnetic ratio

1209-419: The linear velocity of the pike of the arrow J {\displaystyle \,\mathbf {J} \,} along a circle whose radius is J sin ⁡ ϕ , {\displaystyle \,J\sin {\phi }\,,} where ϕ {\displaystyle \,\phi \,} is the angle between J {\displaystyle \,\mathbf {J} \,} and

SERF - Misplaced Pages Continue

1248-427: The magnetic field simultaneously. Spin-exchange collisions preserve total angular momentum of a colliding pair of atoms but can scramble the hyperfine state of the atoms. Atoms in different hyperfine states do not precess coherently and thereby limit the coherence lifetime of the atoms. However, decoherence due to spin-exchange collisions can be nearly eliminated if the spin-exchange collisions occur much faster than

1287-425: The magnitude of the magnetic dipole moment is An isolated electron has an angular momentum and a magnetic moment resulting from its spin . While an electron's spin is sometimes visualized as a literal rotation about an axis, it cannot be attributed to mass distributed identically to the charge. The above classical relation does not hold, giving the wrong result by the absolute value of the electron's g -factor, which

1326-423: The opposite direction). The sensitivity δ B {\displaystyle \delta B} of atomic magnetometers are limited by the number of atoms N {\displaystyle N} and their spin coherence lifetime T 2 {\displaystyle T_{2}} according to where γ {\displaystyle \gamma } is the gyromagnetic ratio of

1365-696: The precession frequency of the atoms. In this regime of fast spin-exchange, all atoms in an ensemble rapidly change hyperfine states, spending the same amounts of time in each hyperfine state and causing the spin ensemble to precess more slowly but remain coherent. This so-called SERF regime can be reached by operating with sufficiently high alkali metal density (at higher temperature) and in sufficiently low magnetic field. The spin-exchange relaxation rate R s e {\displaystyle R_{se}} for atoms with low polarization experiencing slow spin-exchange can be expressed as follows: where T s e {\displaystyle T_{se}}

1404-429: The sign of γ determines the sense (clockwise vs counterclockwise) of precession. Most common nuclei such as H and C have positive gyromagnetic ratios. Approximate values for some common nuclei are given in the table below. Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a nucleus , or an electron , when placed in an external magnetic field B (measured in teslas) that

1443-506: The torque on this needle is T = q m ( d × B ) . {\displaystyle \,{\boldsymbol {\mathrm {T} }}=q_{\rm {m}}(\mathbf {d} \times \mathbf {B} )\,.} But as previously stated q m d = I π r 2 d ^ = m , {\displaystyle \,q_{\rm {m}}\mathbf {d} =I\pi r^{2}{\hat {\mathbf {d} }}=\mathbf {m} \,,} so

1482-433: The vertical. Hence the angular velocity of the rotation of the spin is Consequently, f = γ 2 π B   . q.e.d. {\displaystyle f={\frac {\gamma }{\,2\pi \,}}\,B~.\quad {\text{q.e.d.}}} This relationship also explains an apparent contradiction between the two equivalent terms, gyromagnetic ratio versus magnetogyric ratio: whereas it

1521-521: Was developed by Michael V. Romalis at Princeton University in the early 2000s. The underlying physics governing the suppression spin-exchange relaxation was developed decades earlier by William Happer but the application to magnetic field measurement was not explored at that time. The name "SERF" was partially motivated by its relationship to SQUID detectors in a marine metaphor. Atomic spin Too Many Requests If you report this error to

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