Maykel L. González-Martínez

A New Method for Efficient Calculations On Sympathetic Cooling

http://www.dur.ac.uk/m.l.gonzalez-martinez Jan 31, 2013. MMQA'13, London

MMQA: Main goal

MicroKelvin Molecules in a Quantum ArrayMicroKelvin Molecules in a Quantum Array

Create polar molecules with sufficiently high density¹ & low enough temperature²

to form interacting quantum arrays

¹ ⩾ 10⁷ molecules/trap volume ~ 1010 molecules/cm3

² ⩽ 10 ⁶ K⁻

Dec. 16, 2010. Imperial College, London.

Jan 31, 2013. MMQA'13, London

Collisions

Evaporative coolingBuffer-gas cooling

Sympathetic cooling

THERMALIZATION

Lifetimes in trapsTrap losses

TRAP DYNAMICS

Reproduce, Understand, Predict

Jan 31, 2013. MMQA'13, London

'Traditional' coupled-channel methodology

Problem

N coupled (differential) equations

Observables!

(SS/TT matrix)

effort (time) ∝ N3

interpretation

effort/calc. Low anisotropy Large anisotropy

Rotation N ≈ 1–10 t ∝ (m)seconds

N ≈ 102–104

t ∝ mins, hours...

Fine(electronic spin)

N' ≈ N 2–10; ✕ t' ≈ t ✕10–103

Hyperfine(nuclear spin)

N' 2–10✕ 2; t' ✕10–106

Jan 31, 2013. MMQA'13, London

1Basis size

DS Jin and Y Je; Phys. Today 27 (2011)

FrustrationFrustration

Jan 31, 2013. MMQA'13, London

Field strengthCollision energy

Collisions take place in traps...... at a given 'temperature'.

Potential 'survey'

Well... and potentials are not 100% accurate

+ field strength '2'+ angle f

1/f

2

...

Hmm... if we really need to make it 'real'...

2Parameters

Jan 31, 2013. MMQA'13, London

Uff... do we really have to?

I know... but how far can we go 'if'...?

... sure there are other ways, aren't there?

Bohn's (et al.) statistical approach: No (if it's difficult!) Phys. Rev. A 85, 062712 (2012)

Tsherbul's (et al.) total-J approximation J. Chem. Phys. 133, 184104 (2010) Phys. Rev. A 84, 040701 (2011) J. Chem. Phys. 137, 024103 (2012) Phys. Rev. A 85, 052710 (2012)

James' (et al.) Multichannel Quantum Defect Theory Phys. Rev. A 84, 042703 (2011) Phys. Rev. A 86, 022711 (2012) arXiv:1212.5290 (2012)

George (Optimisations, approximations)Maykel (Approximate hyperfine)

1 2

1

1

To 'CC' or not to 'CC'...

'1'Jan 31, 2013. MMQA'13, London

Jan 31, 2013. MMQA'13, London

'Small' RE

tot ≫ E∞

Fully coupledeffort ∝ N3

'Large' RE

tot ≈ E∞

Fully uncoupledeffort ∝ N

Rmin

Rmatch

Just once! ... a few times?

Rmax

As many as you want!

YY SS/TTFull CC + MQDT parameters =

Jan 31, 2013. MMQA'13, London

Test case 1 (low anisotropy)

Mg(1S) + NH(3S-) in magnetic fields

Jan 31, 2013. MMQA'13, LondonMQDT: JFE Croft et al.; Phys. Rev. A 84, 042703 (2011)

Mg(1S) + NH(3S-). YY(E) (fixed B).

Jan 31, 2013. MMQA'13, LondonMQDT: JFE Croft et al.; Phys. Rev. A 84, 042703 (2011)

Mg(1S) + NH(3S-). YY(B) (fixed E).

Jan 31, 2013. MMQA'13, LondonMQDT: JFE Croft; PhD Thesis (2012)

Mg(1S) + NH(3S-). Feshbach resonances.

Jan 31, 2013. MMQA'13, London

Test case 2 (large anisotropy + long-range spin-spin)

Li(2S) + NH(3S-) in magnetic fields

Jan 31, 2013. MMQA'13, LondonCC: AOG Wallis et al.; Eur. Phys. J. D 65, 151 (2011)MQDT: JFE Croft and JM Hutson; arXiv:1212.5290 (2012)

Li(2S) + NH(3S-). CC vs MQDT (204 vs 5).

Jan 31, 2013. MMQA'13, LondonMQDT: JFE Croft and JM Hutson; arXiv:1212.5290 (2012)

Li(2S) + NH(3S-). MQDT(converged basis 1,800 vs 900).

Summary

Jan 31, 2013. MMQA'13, London

“Coupled-channels” have taken us this far...

MQDT provides the best(?) solution to the “parameters” problem (and we've optimized it!)

... a solution to the “basis size” problem is needed

Many Thanks!