1. The Atom (a reminder) - AtomChipatomchip.org/.../2010/10/AtomLightMW_ws10_Lecture1.pdf · 1. The...

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.


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)


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


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


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


)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


Hyperfine Structurenuclear magnetic moment

Hyperfine Structurenuclear magnetic momentnuclear magnetic momentnuclear magnetic moment

)1()1()1( 2

int

IIJJFF

BEA

IHFS


)()()(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


)1(21

JJgJ

H-Atomcomplete spectrum

H-Atomcomplete spectrumcomplete spectrumcomplete spectrum


Alkali Atomsone electron atomsAlkali Atomsone electron atomsone electron atomsone electron atoms


Rydberg AtomsRydberg AtomsRydberg AtomsRydberg Atoms


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


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


)(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


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


3043 ikik Mc

P

Transition ProbabilitiesNa 3S1/2 -> 3P3/2

Transition ProbabilitiesNa 3S1/2 -> 3P3/2Na 3S1/2 -> 3P3/2Na 3S1/2 -> 3P3/2


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)


( )

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


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


nAWBc

2121

2121

)(

32

2

3023

ikik

ik Mc

A

Other useful informationOther useful informationatomic level diagramsatomic level diagrams


Spectral lines Alkali AtomsGrotrian Diagram for Na

Spectral lines Alkali AtomsGrotrian Diagram for NaGrotrian Diagram for NaGrotrian Diagram for Na


Grotrian Diagram for KGrotrian Diagram for K


Li - atomlevel diagramsLi - atomlevel diagrams


Li - atomLi - atom


Rb - atomRb - atom

121 MHz

63.4 MHz

29.3 MHz

362.2 MHz

3.035 GHz6.835 GHz


Na - atom Cs - atom Na - atom Cs - atom


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


1s0

Atoms are detected !

I = 1/2I = 1/2


I = 1I = 1


I = 3/2I = 3/2


I = 5/2I = 5/2


I = 7/2I = 7/2


Other useful informationOther useful informationdisplaying orbitalsdisplaying orbitals


1s-Orbitals1s-Orbitalshttp://www.shef.ac.uk/chemistry/orbitron/




2p-Orbitals2p-Orbitalspphttp://www.shef.ac.uk/chemistry/orbitron/


3d-Orbitals3d-Orbitalshttp://www.shef.ac.uk/chemistry/orbitron/


3d z23d z2zzhttp://www.shef.ac.uk/chemistry/orbitron/


n=7 Orbitalsn=7 Orbitals

7g

http://www.shef.ac.uk/chemistry/orbitron/

7s 7ff

7p7d7d




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