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NMR Nobel Prize 1952 Bloch & Purcell NMR Frequencies Abundance - - PowerPoint PPT Presentation
NMR Nobel Prize 1952 Bloch & Purcell NMR Frequencies Abundance - - PowerPoint PPT Presentation
NMR Nobel Prize 1952 Bloch & Purcell NMR Frequencies Abundance in Humans NMR aka MRI NMR aka MRI Larmor Precession | = cos( / 2) e i t/ 2 | + sin( / 2) e i t/ 2 | | S x | = 2 sin(
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Abundance in Humans
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NMR aka MRI
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NMR aka MRI
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Larmor Precession
|ψ = cos(θ/2)eiωt/2| ↑ + sin(θ/2)e−iωt/2| ↓
ψ|Sx|ψ =
- 2 sin(θ) cos(ωt)
ψ|Sy|ψ =
- 2 sin(θ) sin(ωt)
ψ|Sz|ψ =
- 2 cos(θ)
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Precessing Spin
|ψ = cos(θ/2)eiωt/2| ↑ + sin(θ/2)e−iωt/2| ↓
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Precessing Spin
|ψ = cos(θ/2)eiωt/2| ↑ + sin(θ/2)e−iωt/2| ↓
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Precessing Spin
|ψ = cos(θ/2)eiωt/2| ↑ + sin(θ/2)e−iωt/2| ↓
represent any two level system
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Dephasing
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Dephasing
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Dephasing
T2
decoherence time
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Population Decay
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Population Decay
T1
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Quantum Computing
| | |ψ1 = c0|0 + c1|1 |c0|2 + |c1|2 = 1
|ψ2 = c00|00 + c01|01 + c10|10 + c11|11 |ψ3 = c000|000 + c001|001 + c010|010 + c100|100 +c011|011 + c101|101 + c110|110 + c111|111 N particles → 2N states
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Quantum Computing
examples: NMR - specific nuclei in a molecule each has different resonant frequency Ion traps - hyperfine levels each ion has a different location Superconductor - Cooper pair controlled by voltage across a tunneling junction
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