finite classical and semiclassical correlaons in an …killian etal. prl 83, 4776 (99) prl 85, 318...
TRANSCRIPT
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
1.5
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