finite classical and semiclassical correlaons in an …killian etal. prl 83, 4776 (99) prl 85, 318...

mpipks!

Finite !Systems!

Jan Michael Rost

Max-Planck-Institute

for the Physics of Complex Systems

Dresden, Germany

Classical and semiclassical correla.ons in an ultracold gas 

Thomas Pohl Andrei Lyubonko Ivan Liu Jovica Stanojevic Weibin Li

group leader predoc predoc

postdoc postdoc

Ultracold  Rydberg physics 

quantum                         semiclassical                         classical  

Many‐body  quantum interac.ons 

Ultracold chemistry:  long range molecules 

Strongly coupled  plasmas 

density: 1/a3                                       a~an                              electron excita.on: an= n2a0   

XFEL

Ultr

acol

d Pl

asm

as

Natural &  man‐made plasmas 

  Ultracold Plasmas

Strong coupling (Γ > 2) ? Crystallization (Γ > 174) ?

Natural & Temperature, size, & time-scales man-made plasmas of ultracold plasmas

Killian etal. PRL 83, 4776 (99) PRL 85, 318 (00) PRL 86, 3759 (01)

Photoioniza.on and subsequent  plasma forma.on 

  Photoionization of laser cooled atoms in a trap

t=0 t=1ns t=1µs

Ee=ω-Ι   electrons leave until global Coulomb well (potential V) is deeper than their kinetic energy Ee

➜  From Ti =10µK => Γi~30000 strongly coupled ionic component? NO, recombination and correlation heating…

Non‐equilibrium dynamics, short .mes: Ionic correla.on hea.ng 

 potential energy Ucorr converted

into kinetic energy of the ions

➜  temperature increases

  strongly coupled regime through

adiabatic expansion

➜  Γ∞≈15

Ion temperature: comparison with experiment  Pohl, Pattard & Rost PRL 94, 205003 (2005)

  How can one achieve large Γ ? (strongly coupled regime)

106 Sr atoms, ρ=2 x 109 cm-3 Te=38 K

Ultra cold plasma under con$nued laser cooling:  theore.cal descrip.on 

plasma expansion

τexp= 0.6µs

mpipks!

Finite !Systems

τexp= 3.7µs

Ion density 

τexp= 0.6µs

mpipks!

Finite !Systems

Look at the surface of one shell…

τexp= 3.7µs

Ion density 

LaNce structure on the ion shell 

Pohl, Pattard & Rost

PRL 92, 155003 (2004)

Ultracold plasmas 

  allow one to follow and observe non-trivial correlated dynamics (numerically and in the lab!)

➜  Non equilibrium plasma physics (Pohl, Pattard and Rost, PRL 54, 205003 (2005): "Relaxation to non-equilibrium")

  Review Article: Ultracold Neutral Plasmas, Killian, Pohl, Pattard and Rost, Physics Reports 449, 77 (2007)

Ultracold  Rydberg physics 

quantum                         semiclassical                         classical  

Many‐body  quantum interac.ons 

Ultracold chemistry:  long range molecules 

Strongly coupled  plasmas 

density: 1/a3                                       a~an                              electron excita.on: an= n2a0   

Diatomic molecular Rydberg orbit Rb2 (N=30):  almost separable in ellip.cal coordinates 

C H Greene et al, PRL 93, 063001 (2000)

R r 

Rydberg chemistry in the ultracold? First step: triatomic molecules (trimers)

  can one make a (linear) triatomic

molecule? (YES: Pfau group!)

  what does its electron density

look like?

R 

Triatomic molecule: Born‐Oppenheimer poten.al curve 

  Wave func.on is  symmetry adapted  linear combina.on of  two trilobites and conserves parity 

A                                B |!±! = |!n(r; r1)!± |!n(r; r2)!r1                   r2    

N12 ! "!n(r; r1)|!n(r; r2)#r

N12 =!

l "nl(r2)"nl(r1) 2l+14! Pl(r̂2r̂1) R = r1= ‐ r2 

How many ground state atoms on a circle give the deepest poten.al well? 

(N=30 Rydberg atom in the center) 

➜  58 ground state atoms

➜  corresponds to the 2(n-1) values of m for a circular Rydberg state forming 58 lobes

Rb Rydberg (NS) dimer: Comparison to experiment 

 In the experiment  excited by two photons from the (atomic) ground state to  35S, 36S, 37S  (Tilman Pfau’s talk!) 

➜  Single Rydberg wave func.on contributes (l=0) 

 But: P‐wave (resonant scaaering) in addi.on to s‐wave scaaering off the ground state atom 

Single channel  with s‐wave                             with s‐ and p‐wave 

Dimer poten.al (Rb 35S) with 35S wave func.on only 

Construc$on of the solu$on 

 Construct pseudo poten.al which leads to correct asympto.c phase of the wave func.on 

 Use Coulomb  Green func.on  + quantum defect  correc.on  to get the solu.on 

Single channel  with s‐wave                             with s‐ and p‐wave 

1200 1400 1600 1800 2000 2200R(a.u.)

-60

-50

-40

-30

-20

-10

0

Bin

din

g e

ner

gy(M

Hz)

Dimer spectrum (Rb 35S) with standard s‐ and p‐wave scaaering length 

___ full solu.on ‐‐‐‐‐ single channel 

Single channel  with s‐wave                             with s‐ and p‐wave 

1200 1400 1600 1800 2000 2200R(a.u.)

-60

-50

-40

-30

-20

-10

0

Bin

din

g e

ner

gy(M

Hz)

Dimer spectrum (Rb 35S) with standard s‐ and p‐wave scaaering length 

___ full solu.on ‐‐‐‐‐ single channel 

  Complicated spectrum of bound states:  in outer well as well as localized inwards 

  Lower energies from full solu.on 

➜  Scaaering length cannot be determined  with a simple model from experiment 

  but: effec.ve scaaering length (s‐and p)  will produce reasonable approxima.on 

-40 -30 -10 10-45 -35 -25 -15 -5 50-20+Rb2

relative frequency / MHz

75007000600050004000300020001000

0500

150025003500450055006500

5001000

0Ion signal / a

rb. units

Theory

+Rb

36s state

Dimer spectrum (Rb 36S) V. Bendkowsky etal., Nature 458, 1005 (2009)

Et(ν=1)? 

Trimer: Et(ν=0)=  2 x Ed(0) 

-40 -30 -10 10-45 -35 -25 -15 -5 50-20+Rb2

relative frequency / MHz

75007000600050004000300020001000

0500

150025003500450055006500

5001000

0Ion signal / a

rb. units

Theory

+Rb

36s state

Dimer spectrum (Rb 36S) V. Bendkowsky etal., Nature 458, 1005 (2009)

Et(ν=1)? 

Trimer: Et(ν=0)=  2 x Ed(0) 

-40 -30 -10 10-45 -35 -25 -15 -5 50-20+Rb2

relative frequency / MHz

75007000600050004000300020001000

0500

150025003500450055006500

5001000

0Ion signal / arb.

units

Theory

+Rb

36s stateTheore.cal spectrum shiged by 0.55 MHz rela.ve to experiment: 

Main (Rydberg) peak posi.on shiged due to excita.on blockade? 

1200 1400 1600 1800 2000 2200R(a.u.)

-150

-100

-50

0

Binding energy(M

Hz)

Dimer spectrum (Rb 35S) 

Rydberg chemistry in the ultracold has  unexpected proper.es 

 Molecule forma.on also possible with repulsive atom‐Rydberg atom interac.on  (posi.ve scaaering length) 

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a

.u.)

Dimer

Ne‐Ne* dimer: repulsive interac.on (Ne*: n=30) 

r1 

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a

.u.)

Dimer

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a.

u.)

GeradeUngerade

Ne‐Ne* dimer: repulsive interac.on (Ne*: n=30) 

r1 one more ground state atom... 

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a

.u.)

Dimer

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

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2.0

2.5

3.0

3.5

4.0

V (

10

-7 a.

u.)

GeradeUngerade

Ne‐Ne*‐Ne trimer: strong modula.ons in the poten.al 

E2(r1 = R) = L1N11

E±3 (r1 = R, r2 = !R) = 12 (L1N11+L2N22)(1± N12!

N11N22)

r1 R

2R 

r2 

r1 r2 

N12 ! "!n(r; r1)|!n(r; r2)#r =!

l "nl(r2)"nl(r1) 2l+14! Pl(r̂2r̂1)

N12 ! "!n(r; r1)|!n(r; r2)#r =!

l "nl(r2)"nl(r1) 2l+14! Pl(r̂2r̂1)

Normal mode analysis of Ne‐Ne*‐Ne trimer 

R

2R 

r1 r2 

R = (ρ,z) 

R:   symmetric stretch 

ρ:   bending (degenerate) 

z:    asymmetric stretch 

H = ! 14M

d2

dR2 ! 34M"

2R + V (r1, r2)

Symmetric stretch mode 

  Two vibra.onal levels    Tunneling in  

 v0 negligible 

ESS = 0.811 x 10‐7 au 

τSS = 240 s 

(τss(v1) = 11 µs) 

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a

.u.)

GeradeUngerade

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a

.u.)

GeradeUngerade

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a

.u.)

GeradeUngerade

400 600 800 1000 1200 1400 1600 1800 2000

R (a.u.)

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

V (

10

-7 a

.u.)

GeradeUngerade

Asymmetric stretch 

  mo.on on top of the  barrier (highly excited) 

  decay by  “rolling down the hill” 

➜  akin to “tradi.onal” ABA molecules 

  EAS = 0.73 x 10‐7 au 

          = V(r1= R0, r2= ‐R0) 

τAS ~ 0.5µs  

z

  ENormalMode= 1.43 x10‐7 au = 940 MHz 

      (blue detuned from Rydberg level n=30) 

  life .me: τ = 0.5 µs   influence of the series of conical 

intersec.ons? 

  increasing n decreases τSS and  increases τAS 

  realiza.on in a 1D laNce ? 

Summary: Rydberg Borromean Trimer (n=30) Liu, Stanojevic and Rost, PRL 102, 173001 (2009)

Thanks! 

Ultracold gases: Cenap Ates . Ivan Liu . Andrei Lyubonko Jovica Stanojevic . Thomas Pohl Alex Eisfeld . Alex Jurisch

Ultracold gases: Cenap Ates . Ivan Liu . Andrei Lyubonko Jovica Stanojevic . Thomas Pohl

Interac.on of finite (atomic) systems  with laser light 

Single photon absorption: Ulrich Galster Agapi Emmanouilidou Jan Roden

Attosecond physics: Paula Riviere Olaf Uhden

Intense field physics: Ionut Georgescu Alexey Mikaberidze Kamal Singh Anatole Kenfack

Time resolved X-ray physics Ulf Saalmann . Roland Guichard Christian Gnodtke

For pre/reprints see hap://www.pks.mpg.de/~rost/publ1.html