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