Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)

Rydberg atoms

Tobias Thiele

References

• T. Gallagher: Rydberg atoms

Content

• Part 1: Rydberg atoms

• Part 2: A typical beam experiment

Introduction – What is „Rydberg“?

• Rydberg atoms are (any) atoms in state with high principal quantum number n.



• Rydberg atoms are (any) atoms with exaggerated properties



• Rydberg atoms are (any) atoms with exaggerated properties

equivalent!

Introduction – How was it found?

• In 1885: Balmer series:

– Visible absorption wavelengths of H:

– Other series discovered by Lyman, Brackett, Paschen, ...

– Summarized by Johannes Rydberg:

42

2

n

bn






42

2

n

bn






42

2

n

bn

2

~~

n

Ry

Introduction – Generalization




– Quantum Defect was found for other atoms:

42

2

n

bn

2)(

~~

ln

Ry

Introduction – Rydberg formula?

• Energy follows Rydberg formula:

2)( ln

hRyEE

Introduction – Rydberg formula?


2)( ln

hRyEE

13.6 eV


22)( n

hRy

n

hRyEE

l

Introduction – Hydrogen?

0

0

13.6 eV

Ener

gy

0


2)( ln

hRyEE

Quantum Defect?

Quantum Defect

Ener

gy

0

Rydberg Atom Theory

• Rydberg Atom

• Almost like Hydrogen

– Core with one positive charge

– One electron

• What is the difference?

A

e

Rydberg Atom Theory

• Rydberg Atom



– One electron


A

e

Rydberg Atom Theory

• Rydberg Atom



– One electron


A

e

Rydberg Atom Theory

• Rydberg Atom



– One electron


– No difference in angular momentum states

A

e

Radial parts-Interesting regions W

r

rrV

1)(

0


r

rrV

1)(

0

)(1

)( rVr

rV core


r

rrV

1)(

0

)(1

)( rVr

rV core

0rr Ion core


r

rrV

1)(

0

)(1

)( rVr

rV core

0rr Ion core

Interesting Region For Rydberg Atoms


r

rrV

1)(

0

)(1

)( rVr

rV core

0rr Ion core

H


r

rrV

1)(

0

)(1

)( rVr

rV core

0rr Ion core

nH

H


r

rrV

1)(

0

)(1

)( rVr

rV core

0rr Ion core

lδ

nH

H

(Helium) Energy Structure

• usually measured

– Only large for low l (s,p,d,f)

• He level structure

• is big for s,p

2)(2

1

lnW

l





• is big for s,p

2)(2

1

lnW

l





• is big for s,p

2)(2

1

lnW

l

l





• is big for s,p

2)(2

1

lnW

l

l

Excentric orbits penetrate into core. Large deviation from Coulomb. Large phase shift-> large quantum defect





• is big for s,p

•

2)(2

1

lnW

l

l

3)(

1

lndn

dW

Electric Dipole Moment

• Electron most of the time far away from core

– Strong electric dipole:

– Proportional to transition matrix element

3)(

1

lndn

dW

2)(2

1

lnW





red

3)(

1

lndn

dW

2)(2

1

lnW





red

3)(

1

lndn

dW

2)(2

1

lnW

ififif rered )cos(





• We find electric Dipole Moment

–

• Cross Section:

red

ififif rered )cos(

2)cos(1 nllrd if

3)(

1

lndn

dW

2)(2

1

lnW

2

0nad





• We find electric Dipole Moment

–

• Cross Section:

red

ififif rered )cos(

2)cos(1 nllrd if

42nr

3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n

Stark Effect

• For non-Hydrogenic Atom (e.g. Helium)

– „Exact“ solution by numeric diagonalization of

in undisturbed (standard) basis ( ,l,m)

FdHH ififif

0

n~

3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n

EFdHH

0




FdHH ififif

0

n~

2)(2

1

lnW

3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n

Stark Effect EFdHH

0




FdHH ififif

0

n~

2)(2

1

lnW

Numerov

3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n

Stark Effect EFdHH

0

n=12

n=11

n=13

Stark Map Hydrogen

Levels degenerate

n=12

n=11

n=13

Stark Map Hydrogen

n=12

n=11

n=13

k=-11 blue

k=11 red

Stark Map Hydrogen

Cross perfect Runge-Lenz vector conserved

Levels degenerate

n=12

n=11

n=13

Stark Map Hydrogen

n=12

n=11

n=13

Stark Map Helium

Levels not degenerate

n=12

n=11

n=13

Stark Map Helium

n=12

n=11

n=13

k=-11 blue

k=11 red

Stark Map Helium

n=12

n=11

n=13

k=-11 blue

k=11 red

s-type

Stark Map Helium

Do not cross! No coulomb-potential

Levels degenerate

n=12

n=11

n=13

Stark Map Helium

Stark Map Helium

n=12

n=11

n=13

Inglis-Teller Limit n-5

• Rydberg Atoms very sensitive to electric fields

– Solve: in parabolic coordinates

• Energy-Field dependence: Perturbation-Theory

k

nn 21k

nn 21

Hydrogen Atom in an electric Field

EFdHH

0

)(199)(31716

)(2

3

2

1 522

21

24

212nOmnnnn

FnnnF

nW


• When do Rydberg atoms ionize?

– No field applied

– Electric Field applied

– Classical ionization:

– Valid only for

• Non-H atoms if F is

Increased slowly

3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT






– Valid only for


Increased slowly

3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT






– Valid only for


Increased slowly

4

2

16

1

4

1

n

WF

Fzr

V

cl

416

1

nFcl

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT





– Valid only for


Increased slowly

416

1

nFcl


4

2

16

1

4

1

n

WF

Fzr

V

cl

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT





– Quasi-Classical ioniz.:

2

20

2

2

2

4

44

12)(

Z

WF

FmZV

m

416

1

nFcl

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT






4

2

20

2

2

2

9

1

4

44

12)(

nZ

WF

FmZV

m

416

1

nFcl

49

1

nFr

red

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT





416

1

nFcl

49

1

nFr


4

4

2

2

2

2

2

9

29

1

4

44

12)(

n

nZ

WF

FmZV

red

blue

49

2

nFb

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT


classic

Red states

Blue states

Inglis-Teller

Lifetime

• From Fermis golden rule

– Einstein A coefficient for two states

– Lifetime

2

3

3

,,,

2

,,,12

),max(

3

4nlrln

l

ll

c

eA

lnln

lnln

lnln ,,

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT

Lifetime



– Lifetime

2

3

3

,,,

2

,,,12

),max(

3

4nlrln

l

ll

c

eA

lnln

lnln

lnln ,,

1

,,

,,,,

lnln

lnlnln A

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT

Lifetime



– Lifetime

2

3

3

,,,

2

,,,12

),max(

3

4nlrln

l

ll

c

eA

lnln

lnln

lnln ,,

1

,,

,,,,

lnln

lnlnln A

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT

Lifetime



– Lifetime

2

3

3

,,,

2

,,,12

),max(

3

4nlrln

l

ll

c

eA

lnln

lnln

lnln ,,

1

,,

,,,,

lnln

lnlnln A

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT

For l0: Overlap of WF

23

n

30, nn

Lifetime



– Lifetime

2

3

3

,,,

2

,,,12

),max(

3

4nlrln

l

ll

c

eA

lnln

lnln

lnln ,,

1

,,

,,,,

lnln

lnlnln A

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT

For ln: Overlap of WF

2n

53, ,nnln

For ln: Overlap of WF

3 n

Lifetime 2

3

3

,,,

2

,,,12

),max(

3

4nlrln

l

ll

c

eA

lnln

lnln

1

,,

,,,,

lnln

lnlnln A

State Stark State

60 p small

Circular state 60 l=59 m=59

Statistical mixture

Scaling (overlap of )

Lifetime 7.2 ms 70 ms ms

3n 5n 5.4n

)1,1(),( lnln)l,n(

23

n2nr

416

1 nFcl3)(

1

lndn

dW

2)(2

1

lnW

2

0nad

4n 5 nFIT53

, , nnln

Part 2- Generation of Rydberg atoms

• Typical Experiments:

– Beam experiments

– (ultra) cold atoms

– Vapor cells

ETH physics Rydberg experiment

Creation of a cold supersonic beam of Helium. Speed: 1700m/s, pulsed: 25Hz, temperature atoms=100mK


Excite electrons to the 2s-state, (to overcome very strong binding energy in the xuv range) by means of a discharge – like a lightning.


Actual experiment consists of 5 electrodes. Between the first 2 the atoms get excited to Rydberg states up to n=inf with a dye laser.

Dye/Yag laser system


Experiment


Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!) Provides energy for dye laser

Experiment


Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!) Provides energy for dye laser

Dye laser with DCM dye: Dye is excited by Yag and fluoresces. A cavity creates light with 624 nm wavelength. This is then frequency doubled to 312 nm.

Experiment

Dye laser

Nd:Yag pump laser

DCM dye

cuvette

Frequency doubling


Detection: 1.2 kV/cm electric field applied in 10 ns. Rydberg atoms ionize and electrons are Detected at the MCP detector (single particle multiplier) .

Results TOF 100ns

Results TOF 100ns Inglis-Teller limit

Results TOF 100ns Adiabatic Ionization- rate ~ 70% (fitted)

41

0

161250

F

cmV

nd

41

0 2

91250

F

cmV

nd

Adiabatic Ionization- rate ~ 70% (fitted) )exp( t

Pure diabatic Ionization- rate:

41

0

161250

F

cmV

nd

Results TOF 100ns

Results TOF 100ns 32 nr

41

0 2

91250

F

cmV

nd

Adiabatic Ionization- rate ~ 70% (fitted) saturation )exp( t

Pure diabatic Ionization- rate:

41

0

161250

F

cmV

nd

From ground state

Results TOF 15ms

lifetime

41

0 2

91250

F

cmV

nd

41

0

161250

F

cmV

nd

3n

32 nr

From ground state

Documents

Rydberg atoms - Quantum Device Lab · ... Rydberg atoms Content •Part 1: Rydberg atoms •Part 2: A typical beam experiment . ... Stark Effect •For non-Hydrogenic Atom (e.g. Helium)