An Introduction to AMO Physics

32 Pages·2007·0.19 MB·English

An Introduction to AMO
Physics
Cass Sackett
UVA
What is AMO?
= Atomic, molecular, and optical physics
Linked because share basic approach:
- Study “simple” quantum systems with high precision
- Learn to control systems for applications
- Central tool: laser
Purpose of Talk
Introduce key background ideas of AMO
Helpful for subsequent talks
Aimed at new students
Outline
I. Atoms and molecules
Hierarchy of structures, notation
II. Driving transitions
Transition rate, saturation, coherent evolution
III. Lasers
Basic theory, types of laser
IV. Frequency conversion
Nonlinear response, phase matching
V. AMO at UVA
Groups, courses
Atoms
Simplest atom: hydrogen
Energy levels have hierarchy
mc2
Highest level: Coulombic E = - a 2
n 2n2
e2 1
a = =
fine structure constant
ep h
4 c 137
0
1
= -
Often write E using atomic units
n 2n2
a
unit of energy = mc2 2 = Hartree = 27.2 eV
Label states with n, l: 3d state has n = 3, l = 2
Fine structure
Spin orbit coupling correlates L and S
Use J = L +S
Relativistic effects shift energy levels
a
Fractional shift ~(Z )2 for atomic number Z
More important for heavier atoms
Energy levels split by J
J = 5/2 (6 states)
⇒
3d
J = 3/2 (4 states)
(10 states)
Notation: n 2S+1L
J
So “3 2D ” means n = 3, S = ½, L = 2, J = 3/2
3/2
Hyperfine structure
Electronic angular momentum J coupled to
nuclear angular momentum I
via magnetic moments
⇒ Total momentum F = I+J
Hydrogen has I = ½:
F = 2
⇒
3 2D
3/2
F = 1
nuclear moment
» ·
Energy scale FS scale
electron moment
Typically about 10-3
Other atoms
Alkali atoms (Li, Na, K, Rb, Cs)
have one valence electron + core electrons
Act like H, but levels shifted due to core
Rb:
6 S -13500 cm-1
1/2
units cm-1 = wave numbers
4 D
3/2 -14300 cm-1 1 eV = 8050 cm-1
4 D
5/2
= inverse of corresponding
517 nm
wavelength
5 P -20800 cm-1
3/2
5 P -21000 cm-1
1/2
497 nm
780 nm
5 S -33600 cm-1
1/2
Multielectron Atoms
More than one valence electron = more complex
l
Multiple s ’s and ’s, couple in different ways
i i
= ∑l = ∑ = +
Typically L S s J L S
i i
Label state with L, S and J:
Calcium:
1S (4s5s)
33300 cm-1
0 31500 3S (4s5s)
0
300 nm
1P (4s4p) 23700
1
1D (4s3d) 21900
2 3D (4s3d)
20300
1,2,3
3P (4s4p)
15300
0,1,2
422 nm
653 nm
1S (4s2) 0 cm-1
0
Molecules
Put two atoms together, even more fun!
Interact via molecular potential V(R)
= energy as function of nuclear separation R
Born-Oppenheimer approximation:
- Fix nuclei at spacing R
- Find electronic energies E (R)
n
- Use E (R) as potential for nuclear motion
n
Usually valid (m << m )
e N
→
At large R, E (R) E + E atomic energies
n n1 n2
lots of quantum numbers!
Alkali diatom ground state potential:
E
Pauli exclusion
Spin triplet
R
Attractive van der Waals
bound states
Spin singlet
Nuclei move in V(r): have own eigenstates and energies
vibrational and rotational quantum numbers