Course schedule Lectures: Monday 15.15-17.00, H322 Tuesday 10.15-12.00, H322 Exercises Thursday 10.15-12.00, H322 (Stefan Kröll) Course literature: Foot, Atomic Physics, available at KFS. Two assignments (part of the exam) Two laboratory exercises: Quantum information Atoms in strong laser fields with preparation assignment Short written exam Responsible for the course: Anne L’Huillier (222 7661) A221 (e-mail anne.lhuillier@fysik.lth.se).

Light-Matter Interaction (7.5 hp) FAFN05

Repetition Basic Atomic Physics – Quantum Mechanics

Chapter 7: The interaction of atoms with radiation

Chapter 9: Laser cooling and trapping

Introduction to Chapter 10: Magnetic trapping, evaporative cooling and Bose-Einstein condensation

Introduction to Chapter 12 and 13: Ions traps, Atoms in cavity and Quantum Computer

Introduction to atoms in strong laser fields

Lectures

Laboratory exercises including an assignment

Quantum information Atoms in strong laser fields

ω ω0

1

2

Monday 21/1 Repetition Atomic Physics Tuesday 22/1 Repetition Atomic Physics Thursday 24/1 Repetition Atomic Physics Monday 28/1 Chap. 7 Interaction light – atom Tuesday 29/1 Chap. 7 Interaction light – atom Thursday 31/1 Exercise Repetition Monday 4/2 Chap. 7 Interaction light – atom Project 1 (Deadline 18/2) Tuesday 5/2 Lecture: Atoms in strong laser fields (Johan Mauritsson) Thursday 7/2 Exercises Chap 7 / Project 1 w 7 Laboratory exercises; Atoms in strong laser fields Monday 11/2 (Chapter 13) Lecture Quantum computers (Stefan Kröll) Tuesday 12/2 Chap. 9 Laser cooling and trapping Thursday 14/2 Exercises Chap 7 / Project 1 w 8 Laboratory exercises; Quantum Control Monday 18/2 Chap. 9 Laser cooling and trapping Project 2 (Deadline 4/3) Tuesday 19/2 Chap 10 Magnetic Trapping Thursday 21/2 Exercises Chap 9 /Project 2 Monday 25/2 Chap 10 Lecture BEC (Stephanie Riemann) Tuesday 26/2 Chapter 12 Ion Traps / CQED Thursday 28/2 Exercises Chap 10 + 12 /Project 2 Monday 4/3 Lecture Atoms in very strong fields (Claes-Göran Wahlström) Tuesday 5/3 Repetition Thursday 7/3 Project Tuesday 12/3 8-13 H421 Exam

Repetition

• Quantum Mechanics • Hydrogen atom (energies, wave functions) • Fine structure, Lambshift, hyperfine

structure • Atoms in magnetic field • Selection rules • Atoms in electric field • Multielectron atoms

Quantum Mechanics Postulates

Postulate 1: A physical state is represented by a wavefunction . The probablility to find the particle at within is .

Postulate 2: Physical quantities are represented by Hermitian operators acting on wavefunctions.

Postulate 3: The evolution of a wavefunction is given by the Schrödinger equation .

Postulate 4: The measurement of a quantity (operator A) can only give an eigenvalue an of A.

Postulate 5: The probability to get an is . After the measurement, the wavefunction collapes to (corresponding eigenfunction).

Postulate 6: N indistinguishable particles. The wavefunctions are either symmetrical (bosons) or antisymmetrical (fermions).

),( trΨr rd rdtr 2|),(| Ψ

Ψ=∂Ψ∂ Ht

i

2|),(|| >Ψ< trnψ

nψ

Spherical coordinates

),,( πϕθπ +−r×

re)r(V

0

2

4πε−=

22

613n

eV.n

hcREn −=−= ∞

( )φθ ,Y)r(R mn

Hydrogen atom

Energies Wave functions

[ ] Ψ=Ψ+ EVT

ρ=Zr/na0

http://homepages.ius.edu/kforinas/physlets/quantum/hydrogen.html

n=50

29< <37

n=50 =32 m=

Na

Circular states

17 states n=180

Wave packet

j

l

s

H n=3

Fine structure, hyperfine structure, Lamb shift

{ })1()1()1(2

+−+−+= JJIIFFAEHFS{ })1()1()1(2

+−+−+= SSLLJJESOβ

Atoms in a magnetic field

zzzB BSLSLr

re

mH )2(.)(

42 0

22

+++−∆−=

µξπε

JJBLSJM MBgEJ

µ=∆

)1(2)1()1()1(1

++−+++

+=JJ

LLSSJJgJ

Selection rules for electric dipole transitions

1,0 ±=∆J1,0 ±=∆ JM

1±=∆

1,0 ±=∆L0=∆S

Parity changes

)0'0( =↔= JJ

)0'0( =↔= LL

)000( ' =∆=↔= JifMM JJ

angradrad JJ|e.re| >=< 12

φθθφθφθππ

ddsin),(Ye.r),(YJ mrad*

mang 11220

2

0 ∫∫=

dr)r(Rr)r(RJ nnrad ∫+∞

=0

31122

Time-independent perturbation theory

VHH += 0000

0 kkk EH φφ = known

? Approximation ?

Non-degenerate level

kkk VE =1 ∑

∑

≠

≠

−=

−=

km mk

mkk

kmm

mk

mkk

EEVE

EEV

00

22

000

1

||

φφ

Degenerate level (s times) First diagonalize V in the subspace corresponding to the degeneracy

10 ,ss kk Eφ

kkk EH φφ =

...

...210

10

+++=

++=

kkkk

kkk

EEEEφφφ

Atom in an electric field

∑

∑

>

≠

−><

=

−><

=

100

1

2222

1

01000

1

1100

|100||10|

100||10

n n

mkz

kmn

n

mkz

EEznEeE

EEzneE φφ

zeEr

em

H z+−∆−=0

22

42 πε

00000000000000

vv

0121−φ0

211φ0210φ0

200φ

0200φ

0210φ

0211φ

0121−φ

03 aeEv z−=

1=

)( 0210

02002

1 φφ −

021mφ

0,1=

0,1= )( 0210

02002

1 φφ +

Na

Symmetric/Antisymmetric wave functions

H, L2, Lz commute

L,ML,S,MS good quantum numbers

H, L2, S2, J2, Jz commute

L,S,J,MJ good quantum numbers

21

+=L