1. the atom (a reminder) - atomchipatomchip.org/.../2010/10/atomlightmw_ws10_lecture1.pdf · 1. the...
TRANSCRIPT
1. The Atom (a reminder)1.1 H-Atom basics 1.2 Fine structure
1. The Atom (a reminder)1.1 H-Atom basics 1.2 Fine structure1.3 Hyperfine structure1.4 Alkali atoms (1 electron atoms)1.5 Zeeman effect, Stark shift1 6 Selection rules for optical transitions
1.3 Hyperfine structure1.4 Alkali atoms (1 electron atoms)1.5 Zeeman effect, Stark shift1 6 Selection rules for optical transitions1.6 Selection rules for optical transitions1.7 Optical pumping, preparing a 2-state system1.8 Einstein coefficients, rate equations 1.9 Additional information: alkali atom
l l h d d
1.6 Selection rules for optical transitions1.7 Optical pumping, preparing a 2-state system1.8 Einstein coefficients, rate equations 1.9 Additional information: alkali atom
l l h d datomic level schemas and Grotian diagramstransition strength of D-linesatomic level schemas and Grotian diagramstransition strength of D-lines
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Literature: Basic Atomic PhysicsLiterature: Basic Atomic Physics
1. Demtröder: Experimentalphysik III Atomphysik2 M K k k At h ik2. Mayer-Kuckuck, Atomphysik3. H. Haken und G. Wolf, Atom- und Quantenphysik, Springerverlag, Berlin4. R. Eisberg, R. Resnik; Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles,
2nd Edition J. Wiley & Sons, New York, 1985y , ,5. download
MIT: AMO Physics http://cua.mit.edu/8.421/H-Atom: http://www.pha.jhu.edu/%7ert19/hydro/orbital visualization http://www.shef.ac.uk/chemistry/orbitron/p y
6. Properties of some alkali atoms: http://george.ph.utexas.edu/~dsteck/alkalidata
Additional Books:• H. Haken und H. C. Wolf, Molekülphysik und Quantenchemie, Springerverlag, Berlin• G. Otter und R. Honecker, Atome-Moleküle-Kerne, Teubner Verlag, Stuttgart• M. Alonso und E.J. Finn, PhysikIII: Quantenphysik und statistische Physik,
Inter. Europ. Ed. AmsterdamInter. Europ. Ed. Amsterdam• A. Beiser, Concepts of Modern Physics, Mc Graw Hil
sehr schönes Buch , das sich auf das unverzichtbare Grundwissen beschränkt. Gut zur Orientierung, man wird nicht durch Nebensächliches abgelenkt. Aber nicht ausreichend für einen Diplomphysiker.
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
D plomphys ker.
Hydrogen Atomquantum description: Schrödinger equation
Hydrogen Atomquantum description: Schrödinger equation
• Schrödinger Gleichung
quantum description: Schrödinger equationquantum description: Schrödinger equation
22
2V r t r t i
r t( , ) ( , )
( , )
• Schrödinger Gleichung
Zentralpotential (Coulomb) r
erV
o
2
4
1)(
2m t( , ) ( , )
2 • Problem ist zeitunabhängig
• Central symmetric problem: transform to spherical coordinates r
)()(2
)( 2 rrVm
rE
S ti f i bls
EUmrr
rrrm
2
2
22
22
2
2
)(sin
1)sin(
)sin(
1
2
1
2
• Separation of variabls(r) = R(r)
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Hydrogen Atomeigenstates of the Schrödinger equation
Hydrogen Atomeigenstates of the Schrödinger equationeigenstates of the Schrödinger equationeigenstates of the Schrödinger equation
2
1
nRE Hn
220
4
8
h
emRH
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
for a visualisation look at: http://www.shef.ac.uk/chemistry/orbitron/
Shell structure of H-Atom statesconfiguration
Shell structure of H-Atom statesconfigurationconfigurationconfiguration
?? is that all ???? is that all ??
non reletivistic modelno magnetic momentno magnetic moment
motion of the electron is relativisticrelativistic
magnetic moment of electron spin magnetic moment of orbit motion magnetic moment of nucleus magnetic moment of nucleus
effects of quantum field theorie
enegy level shiftsenegy level shiftslifts degeneracy
allows new physics
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
p y
Fine StructureSpin Orbit coupling
Fine StructureSpin Orbit couplingSpin-Orbit couplingSpin-Orbit coupling
8
3
20 slBE
rm
eZS
)1()1()1(21
22221
8
lljj
sljsl
rme
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
)1()1()1( 221 sslljj
Magnetic Moment from coupling L + S = J
Magnetic Moment from coupling L + S = Jfrom coupling L + S = Jfrom coupling L + S = J
z=-mJ gJz J gJ
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Hyperfine Structurenuclear magnetic moment
Hyperfine Structurenuclear magnetic momentnuclear magnetic momentnuclear magnetic moment
)1()1()1( 2
int
IIJJFF
BEA
IHFS
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
)()()(2
Atomic StatesAtomic States
St t 2S+1States: n 2S+1XJ
X: S(=0), P(=1), D(=2), ( ), ( ), ( ),F(=3), G(=4) ....
Magnetic Moments:V/G5 78MH /G1 4
e
)1()1()1()1()1()1(
JJIIFFIIJJFF
mgE FBF
B neV/Gauss 5.78 MHz/Gauss 1.42
cme
B
)1()1()1(1
)1(2
)1()1()1(
)1(2
)1()1()1(
LLSSJJg
FF
JJIIFFg
FF
IIJJFFgg
B
KIJF
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
)1(21
JJgJ
H-Atomcomplete spectrum
H-Atomcomplete spectrumcomplete spectrumcomplete spectrum
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Alkali Atomsone electron atomsAlkali Atomsone electron atomsone electron atomsone electron atoms
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Rydberg AtomsRydberg AtomsRydberg AtomsRydberg Atoms
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Atoms in Magnetic FieldZeeman and Paschen Back effect
Atoms in Magnetic FieldZeeman and Paschen Back effectZeeman and Paschen-Back effectZeeman and Paschen-Back effect
:parametertypical
eV/Gauss1078.5
MHz/Gauss 4.1
:parameter typical
9
B
B
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
K/Gauss 67
eV/Gauss1078.5
B
B
Atoms in Magnetic FieldBreit Rabi Formula for F=I+1/2
Atoms in Magnetic FieldBreit Rabi Formula for F=I+1/2Breit Rabi Formula for F=I+1/2Breit Rabi Formula for F=I+1/2
2021
12
41
24),( xx
I
mEBgm
AmIFE F
KKFFHFSB
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
)(2
21
000
IAEEE
ggx BKKBJ
Atoms in Electric FieldStark effect
Atoms in Electric FieldStark effectStark effectStark effect
2202
1 4 EU
A 24
:parameter typical3Na
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
V/AVA 034723.0][ 23 eVUPol
Selection Rules for Optical Transitionselectric dipole transitions
Selection Rules for Optical Transitionselectric dipole transitions
radiating classical dipole
electric dipole transitionselectric dipole transitions
30
42
43
2
c
pP
expectation value of dipole
ki rerep *
dipole matrix elementki re
dipole matrix element
kiik reM
radiated power2
44k
ikk MP
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
3043 ikik Mc
P
Transition ProbabilitiesNa 3S1/2 -> 3P3/2
Transition ProbabilitiesNa 3S1/2 -> 3P3/2Na 3S1/2 -> 3P3/2Na 3S1/2 -> 3P3/2
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Multi Level AtomsMulti Level Atoms
States: n 2S+1XJ X: S(=0), P(=1), D(=2) ....
Magnetic Moments:
)1()1()1()1()1()1(
JJIIFFIIJJFF
mgE FBF
B neV/Gauss 5.78 MHz/Gauss 1.42
cm
e
eB
)1(2
)1()1()1(1
)1(2
)1()1()1(
)1(2
)1()1()1(
JJ
LLSSJJg
FF
JJIIFFg
FF
IIJJFFgg
J
B
KIJF
Matrix Elements:
)1(2 JJ
mIJJSLeg
FFIFJSJL
FFJJF
1)12)(12)(12)(12()1( 1
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›rr
FF
rmqmJFLJ
11
Are Atoms always so complicated?prepare a 2 state system
Are Atoms always so complicated?prepare a 2 state systemprepare a 2-state systemprepare a 2-state system
• Atoms interacting with a laser field can in many cases be regarded as a two state system
• line width and the frequency width of the laser radiation are much smaller then the level spacinglevel spacing
• optical pumping can prepare: specific atomic hyperfine states
ifi ti t tspecific magnetic state• selecting a specific polarization
one can prepare a l d t t t tclosed two state system
• this preparation is simple in ‘one electron atoms’ (alkali atoms)
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
( )
Bloch Kugel im ZustandsraumBloch Kugel im ZustandsraumK g m mK g m m
2 Zustandssystem wird durch die Bloch 2 Zustandssystem wird durch die Bloch Kugel beschrieben.
Die möglichen reinen Quantenzustände li f d Ob flä h d Bl hk lliegen auf der Oberfläche der Blochkugel.
In der Atomphysik kann ein Atom in einer Überlagerung der atomaten Eigenzustände Überlagerung der atomaten Eigenzustände sein
Beispiele für atomare 2-Zustandssysteme:Üb ä d S kt lli i• Übergänge der Spektrallinien
• Hyperfine Zustände
Achtung:AchtungIm allgemeinen müssen beim Aussuchen des relevanten 2-Zustandssystem alle benachbarten Atomzustände (Feinstruktur, H fi t kt ) i B t ht
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 2 ‹Nr.›
Hyperfinestruktur ...) in Betracht gezogen werden.
Einstein – Relationsrate equations
Einstein – Relationsrate equationsrate equationsrate equations
Rate equations in 2-state system
Occupation of levels in thermal equilibrium
Rate equations in 2 state system
)()( 21212121221 WBNWBNAN
dt
dN
dt
dN
AB
BBgg
2121
2112
32
3
2
1
232 ik
ikikiik
MA
ANP
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
nAWBc
2121
2121
)(
32
2
3023
ikik
ik Mc
A
Other useful informationOther useful informationatomic level diagramsatomic level diagrams
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Spectral lines Alkali AtomsGrotrian Diagram for Na
Spectral lines Alkali AtomsGrotrian Diagram for NaGrotrian Diagram for NaGrotrian Diagram for Na
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Grotrian Diagram for KGrotrian Diagram for K
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Li - atomlevel diagramsLi - atomlevel diagrams
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Li - atomLi - atom
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Rb - atomRb - atom
121 MHz
63.4 MHz
29.3 MHz
362.2 MHz
3.035 GHz6.835 GHz
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Na - atom Cs - atom Na - atom Cs - atom
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
He - atom Ar - atom He - atom Ar - atom
excitedexcited state
2p4
2p92p8
2%56% 28%5%
metastablestate
groundstate
715 nm795 nm 811 nm
801 nm1s
67%42%
28%5%state
1s41s21s3
1s5
1s0Only metastable
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
1s0
Atoms are detected !
I = 1/2I = 1/2
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
I = 1I = 1
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
I = 3/2I = 3/2
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
I = 5/2I = 5/2
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
I = 7/2I = 7/2
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
Other useful informationOther useful informationdisplaying orbitalsdisplaying orbitals
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
1s-Orbitals1s-Orbitalshttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
2s-Orbitals2s-Orbitalshttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
2p-Orbitals2p-Orbitalspphttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
3s-Orbitals3s-Orbitalshttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
3p-Orbitals3p-Orbitalspphttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
3d-Orbitals3d-Orbitalshttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
3d z23d z2zzhttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
n=7 Orbitalsn=7 Orbitals
7g
http://www.shef.ac.uk/chemistry/orbitron/
7s 7ff
7p7d7d
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›
7p-Orbitals7p-Orbitalspphttp://www.shef.ac.uk/chemistry/orbitron/
Atoms – Light and Matter Waves J. Schmiedmayer, A. Rauschenbeutel Lecture 1 ‹Nr.›