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Inhalt WPF FortgeschritteneAtomphysik I Literatur Budker, Kimball, deMille Atomic Physics, Oxford
Woodgate Elementary atomic Structure,Oxford
Foot Atomic Physics, Oxford
Friedrich Theoretische Atomphysik, Springer
Demtröder Laserspektroskopie, Springer 1. Atomstruktur 1.1 Diracgleichung, Elektronenspin und Feinstruktur 1.2 Lamb Shift 1.3 Hyperfeinstruktur und Zeeman Effekt 1.4 Übergänge und Auswahlregeln 1.5 Helium 1.6 Mehrelektronensysteme und Zentralfeldnäherung 1.7 Alkali Atome 1.8 Hund’sche Regeln 1.9 Rydberg Atome und Stark Effekt 1.10 Geonium 2. Atom-Licht Wechselwirkung 2.1 Zwei Niveauatom 2.2 Lichtkräfte und Laserkühlung 2.3 Drei Niveauatome und elektromagnetisch induzierte Transparenz 3.Spektroskopische Methoden und Präzisionsmessungen 4. Atom-Atom Kollisionen Streutheorie Feshbach Resonanzen 5. Ultrakalte Atome
Lamb Shift in the optical spectrum
300 K100 K
Williams, R. C.The fine structure of H and D under varying dischargeconditions," Phys. Rev. 54, 558 (1938).
Feinstruktur ~10 GHz
Doppler free spectroscopy
Hänsch, T. W., I. S. Shahin, A. L. Schawlow, Optical resolution of the Lamb shift in atomichydrogen by laser saturation spectroscopyNature 235, 63 (1972)
Microwave Experiment by Lamb and Retherford
Lamb, W. E., and R. C. RetherfordFine structure of the hydrogen atom by a microwave methodPhys. Rev. 72, 241 (1947).
Milchstrasse bei 21 cm Linie im H Atom
Lebensdauer des Angeregten Zustands ~ einige Mio Jahre…Anregung thermischABER 80% d. Universums sind H Atome…21cm Linie wird nicht durch Staub absorbiert
The Hydrogen Maser
1.420405751 GHz. H. M. Goldenberg, D. Kleppner, and N. F. RamseyPRL, 8, 361 (1960)
H Spektroskopie
Hänsch MPQ, Garching
experimentelle Ergebnisse (Spektren)experimentelle Ergebnisse (Spektren)
Messung der 1SMessung der 1S--2S2S--AbsolutfrequenzAbsolutfrequenz
Vergleich mit Cs-Fontänen-AtomuhrSalomon (Paris)
Differenz zu 1999:29 (57) Hz
Lambshift Lambshift ∆∆LLund Rydbergkonstante Rund Rydbergkonstante R∞∞
Spektroskopie an H und D auf Übergängen 1S-2S, 2S-2P, 2S-8S/8D und 2S-12D ⇒ ∆∆LL = = 8 172 840(22)kHz
RR∞∞ = 109 737.315 685 50(84) cm−1 mit relativer Genauigkeit von 7.7×10-12 !!!
Marc Christian Fischer, Dissertation der Fakultät für Physik der Ludwig-Maximilians-Universität München: „Höchstauflösende Laserspektroskopie an atomarem Wasserstoff“
ZeitabhZeitabhäängigkeit fundamentaler Konstantenngigkeit fundamentaler Konstantenαα undund µµCsCs//µµBB=g=gCsCsmmee/m/mpp
Messung von fMessung von f1S1S--2S2S (d. h. Vergleich H optisch mit (d. h. Vergleich H optisch mit Cs HFS) Cs HFS) üüber lber läängere Zeit (1999,2003).ngere Zeit (1999,2003).Messung der Absolutfrequenz des Messung der Absolutfrequenz des ÜÜbergangs bergangs 5d5d10106s 6s 22SS1/21/2(F = 0) (F = 0) →→ 5d5d996s6s22 22DD5/25/2(F = 2,m(F = 2,mFF = 0) = 0) eines Hgeines Hg++--Ions in einer Falle (d. h. Vergleich HgIons in einer Falle (d. h. Vergleich Hg++
optisch (el.optisch (el.--quadr.) mit Csquadr.) mit Cs--HFS) am NIST HFS) am NIST Boulder, Colorado USA, 2 Jahre langBoulder, Colorado USA, 2 Jahre langS. Bize et al., S. Bize et al., PRL 90, 150802 (2003)PRL 90, 150802 (2003)
ZeitabhZeitabhäängigkeit fundamentaler Konstantenngigkeit fundamentaler Konstanten
setzt man: und setzt man: und ::
Reminder: Stark map of Rubidium
electrical field (V/cm)
lase
r fre
quen
cy w
ith re
spec
t to
5 P
-leve
l (TH
z)3/
2
41P
40D
42S
n=39,l>F
42P
41D
43S
39F
40Fn=40,l>FBEC exp.
0 2010electrical field (V/cm)
623.696
623.704
0
226
453
Dn
(MH
z)
n=4041D41 D5/2
41 D3/2
623.700
0 105electrical field (V/cm)
lase
r fre
quen
cy w
ith re
spec
t to
5 P
-leve
l (Th
z)3/
2
Circular Rydberg atoms forquantum optics experiments
very high electric dipole matrix element on a transition between neighboring states (scalesas n squared, 1250 atomic units for the 51 to 50 transitionVery long lifetimes (30 ms): The acceleration of the electron is minimal, and hence theradiative losses as low as possibleMillimeter-wave transitions between neighboring states (51.099 GHz for the transitionbetween 51 and 50) Perfect implementation of a two level system in a weak directing electric field. No fine orhyperfine structures. Sensitive and selective detection (field ionization method): detect single atoms and determine quantum number
Haroche, Raimond, ENS
Preparation
Three diode lasers excite the transitions from the 5S ground state of 85Rb. Through 5P and 5D levels, the 52F level is finally reached. Lasers polarizations are chosen so that only the m=2 substate is populated. The last laser step is resonant only in zero electric field, during 2µs. An electric field is the switched on, and the population transferred to a lowlying level in the Stark manifold. A radiofrequency source excites the degeneratetransitions to the circular state in an adiabatic rapid passage process.
State dependent detection
Rydberg atoms
Prepare single photon in cavity
Photon exchange with empty cavity
Interaction with classical field
n = 0.85 photons
Copy quantum state
R1,R2: prepare atomic statee.g. π/2 pulses
Copy atom state to photon state
Entanglement
π/2 pulse with cavity
send 2nd atom in g with π pulse
atom photon entanglement
atom atom entanglement
Bohr‘s Gedanken experiment
Modern version of Bohr‘s proposal
Bohr‘ experiment with circular Rydberg atoms
First beam splitter
Cryogenic experiment!
Mesoskopische Quantenphysik
Tilman PfauUniversity of Stuttgart
Interactions make life interesting
L. Hau et al., Phys. Rev. A 58, R54 (1998).
critical behaviour densityideal Bose-gas
Interacting gas
Bose Nova
JILAMIT
superfluidity
OutlineOutline
van der van der WaalsWaals blockadeblockade in in frozenfrozen RydbergRydbergmattermatterRydbergRydberg excitationexcitation of a BECof a BEC
Reminder: Stark map of Rubidium
electrical field (V/cm)
lase
r fre
quen
cy w
ith re
spec
t to
5 P
-leve
l (TH
z)3/
2
41P
40D
42S
n=39,l>F
42P
41D
43S
39F
40Fn=40,l>FBEC exp.
0 2010electrical field (V/cm)
623.696
623.704
0
226
453
Dn
(MH
z)
n=4041D41 D5/2
41 D3/2
623.700
0 105electrical field (V/cm)
lase
r fre
quen
cy w
ith re
spec
t to
5 P
-leve
l (Th
z)3/
2
0 1 2 3 4elektrisches Feld (V/cm)
0
20
40
60
80
100
120
14043S1/2
rela
tive
Freq
uenz
(MH
z)
Rydberg Rydberg interaction
ener
gy
r=x-x‘Ω
g,g
g,r
r(x '),r(x)
Simplest case: van der Waals
66( ) CV r
r= −
blockade condition
66 ( , )
c
c
C Maxrr few mµ
≈ Γ Ω
>
h
rc
11n∝
Rydberg Rydberg interaction
ener
gy
r=x-x‘Ω
g,g
g,r
r(x '),r(x)
blockade condition
66 ( , )
c
C Maxr
≈ Γ Ωh
rc
5
5
10c
BEC
r m
N
µ
20 100
1Kepler
BEC
r n a nmN
∝
MOT work: Storrs, Michigan, Freiburg, Paris,…
Mesoscopic quantum dynamics
cr∅ <<
g gg g gg
g
g gg g gryd g
G
E?Ω
collectivestates
1 , , ,..., , , ,..., ... , , ...,
, , ...,
E g g g g g g g g gN
G g g g g
ryd ryd ryd= + + +
=0NΩ = Ω
Collective coherent time scale
Related mesoscopic systems: excitons in quantum dots
V
CEF
X2X
Related mesoscopic systems: excitons in quantum dots
1 , , ,..., , , ,..., ... , , ...,
, , ,...,
E v v v v v vc c v v vN
G v v
c
v v
= + + +
=0NΩ = Ω
Collective coherent time scale
V
CEF
Mesoscopic quantum dynamics
0 0g
blockaderyd
nN
nΩ = Ω Ω
Collective coherent time scale
cr∅ >
ryd
ryd
rydryd
rydryd
ryd
rydn
satrydn
t
vdW blockade in thermal cloudChange density by microwave Change Ω0
Coherent collective excitation
Blockade time scale: 0 gnΩ ∝Ω
Strong blockade regime
Saturation value: 0
,0 0( )sat gN n∝ Ω
Simplyfied model
Assume dense packing : 6cr mµ=18π
9 3710rydn cm−=
Scaling behaviour of rc
606#nn meso
c
C Nr
≈ Ωh
??
What about the BEC?
Rydberg excitation of a BEC
T>Tc
BEC
Tc
Rydberg excitation in a BECBEC survives Rydberg excitation
τ~100 µsec
Rydberg lifetime in BEC
Rydberg atoms survive in BEC
Note: sofar BEC just serves as a dense small well defined mesoscopic sample!but in the future exp. it can serve as a phase reference
• strongly interacting Rydberg Matter• scalable mesoscopic quantum system• measured blockade radius & collective coherent scaling behaviour• first Rydberg excitation of a BEC• general technique for all quantum gases!
Next steps:• Decoherence & Coherent manybody physics• Phase sensitive measurements• Rydberg molecules? biexcitons?• Control interactions by Förster resonance• Gate operations?
Rydberg conclusion & outlook
D. Jaksch et al., PRL 85, 2208; Lukin et al., PRL 87, 037901
87Rb
780 nm
480,5 nm
n=40
5S 1/2
5P 3/2
qubitF=1
F=2 |1>
|0>
87Rb
780 nm
480,5 nm
n=40
5S 1/2
5P 3/2
qubitF=1
F=2 |1>
|0>
87Rb
780 nm
480,5 nm
n=40
5S 1/2
5P 3/2
qubitF=1
F=2 |1>
|0>
Hans G. Dehmelt* 9 September 1922 in Görlitz
http://nobelprize.org/nobel_prizes/physics/laureates/1989/dehmelt-lecture.pdf
Boiling electrons by RF
Detecting Spin flipsby magnetically inducedshift of axial frequency