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!