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 [email protected]).
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
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