Post on 17-Jun-2020
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Molecular collisions in the (ultra-)cold
Matthias W Gempel
RTG - Goslar 3013-02-11
Molecules
Vdd=d2
R31−3cos2𝜃
long-range anisotropic
+ can tune (effective) interactions
+ can handle them (might not be easy)
To give you an idea…
AB (n) + AB (m) AB (p=n) + AB (q=m)
AB (n) + AB (m) AB (p≠n) + AB (q≠m)
AB (n) + AB (m) A2 (p) + B2 (q)
AB (n) + AB (m) A2B + B
AB + A …
or…
etc.
or…
What happens in a trap filled with molecules?
elastic
inelastic
chemical
Theory v.s. Experiment
Theory Experiment
T→0 T≈1
Some single quantum state
Some quantum states
What makes Experiment so difficult ?
… vastly different energy scales.
and same reason why theory is difficult…
room: 300 K
0.1 μK
chemical: 1000 K
vibration: 100 K
rotation: 0.1 K
resonance spacings: 1 nK
no direct (laser)cooling to uc
Theory
Chem Rev 112,4949 (2012)
long-range
r
p r’
• Coupled channel • Internal vibrational relaxation • Unimolecular dissociation • Statistical
• Coupled channel • Quantum defect theory • Quantum Langevin • Born
Theory: ‚Simple‘ model of elastic collisions
NJP 11,055039
−ℏ2
2𝜇Δ + 𝑑1𝑑2
1−3cos2𝜃
𝑅3 + 𝑉𝑠𝑟 Ψ = 𝐸 Ψ
aligned dipoles short range: hard core (interested in long range → ‘ignore’ it)
Natural scales:
𝑎𝑑𝑑 =𝜇𝑑1𝑑2
ℏ2
𝑈𝑑𝑑 = ℏ6
𝜇3𝑑12𝑑2
2 𝐸
12
𝐸0
Theory: ‚Simple‘ model of elastic collisions
NJP 11,055039
s-wave scattering
phase shifts at short range potential average out over multiple partial waves
𝜎𝑒𝑣𝑒𝑛 = 1.117 𝑎𝑑𝑑2 + 4𝜋𝑎2
𝜎𝑜𝑑𝑑 = 3.351 𝑎𝑑𝑑2
𝜎𝑒𝑖𝑘 = 8𝜋3 𝑎𝑑𝑑
𝜇
2𝐸
Theory: Statistical approach
PRA 87,012709
𝑅 < 𝑅0 : is hard →
look for sth. ‚simple‘
many (dense) scattering resonances
mean decay width: Γ𝑅𝑅𝐾𝑀 =𝑁𝑜
2𝜋𝜚
average obervables
𝑎 𝑖
Random Matrix Theory Multichannel
Quantum Defect Theory
Theory: Statistical approach
PRA 87,012709
𝐽 = 𝐿𝑖𝑛 𝐽 = 𝐿 + 𝑁1 + 𝑁2
many (dense) scattering resonances: rotational – vibrational - chemical
𝑁𝑂 = 1 𝜚 ≫ 1
𝑁𝑂 > 1 𝜚 ≫ 1
RbCs
KRb
long complex lifetimes:
broad resonances
𝜏~102ms
Compute short range K-Matrix match MQDT at R0
compute scattering matrix
Theory: Statistical approach
PRA 87,012709
RbCs:
The group
Thanks!
Prof. Silke Ospelkaus
Torben Schulze
Matthias Gempel
Torsten Hartmann
Maurice Petzold
Janis Wöhler Dr. Alessandro Zenesini
Theory: Statistical approach
PRA 87,012709
KRb: