molecular collisions in the (ultra-)cold€¦ · theory: ‚simple‘ model of elastic collisions...

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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: