Ultracold Polar Molecules in Gases and Lattices Paul S. Julienne
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Ultracold Polar Molecules inGases and Lattices
Paul S. JulienneJoint Quantum Institute, NIST and The University
of Maryland
Quantum Technologies Conference: Manipulating photons, atoms, and moleculesAugust 29 - September 3, 2010, Torun, Poland
Experiments by
K.-K. Ni, S. Ospelkaus, D. Wang, M. H. G. de Miranda, A. Pe’er, B. Neyenhuis, J. J. Zirbel, D. S. Jin, J. Ye (JILA/NIST)
Thanks toZbigniew Idziaszek (Warsaw)
Andrea Micheli, Guido Pupillo, Peter Zoller (Innsbruck)John Bohn, Goulven Quéméner (JILA)
Svetlana Kotochigova (Temple), Robert Moszynski (Warsaw)
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Evaporative cooling BEC (K-nK)
Trapped quantum gases, lattices
Precision control, measurement (atomic clocks)
Well-characterized
Laser cooling, an enabling technology (mK-K)
Controlling collisions and inter-species interactions are a key:
Coherent interactions (scattering length)
Decoherence, loss (rate constant, time scale)
Building blocks for quantum science and technology for the future
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7Li 6Li
Interactions: a = scattering length
Truscott, Strecker, McAlexander, Partridge, Hulet, Science 291, 2570 (2001)
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s-wave scattering phase shift
Wavelength 2/k
Noninteractingatoms
R
R = 0
Interactingatoms
Phaseshift
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S. Inouye, M. R., Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and W. Ketterle, “Observation of Feshbach resonances in a Bose-Einstein condensate,” Nature 392, 151–154 (1998).
Change Scattering length
(relative sale)
Number of Atoms(x105)
Atom loss
ChangeMean field
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From Greiner and Fölling, Nature 435, 736 (2008)
Optical trap 1D Lattice (“pancakes”)
40K87Rb
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From I. Bloch, Nature Physics 1, 23 (2005)
2D Lattice (“tubes”)
3D Lattice (“dots”)
133Cs2
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Dipoles: 1/R3 interaction
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Similar method had been proposed by Jaksch, Venturi, Cirac, Williams, and Zoller, Phys. Rev. Lett. 89, 040402(2002) for making non-polar Rb2 in a lattice.
Example with KRb molecule
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40000 40K87Rb moleculesv=0, J=0, single spin level200 to 800 nKDensity ≈ 1012 cm-3
KRb
1. Prepare mixed atomic gas1
2. Magneto-association to Feshbach molecule
2
3. Optically switch to v=0 ground state
3
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Cs2
1
23
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Molecular collisions: simple or complex?Collisions are a key to the control and stability of ultracold gases and
lattices.
"Quantum-State Controlled Chemical Reactions of Ultracold KRb Molecules," S. Ospelkaus, K.K. Ni, D. Wang, M.H.G. de Miranda, B. Neyenhuis, G. Quéméner, P.S. Julienne, J.L. Bohn, D.S. Jin, and J. Ye. Science 327, 853 (2010).
“Universal rate constants for reactive collisions of ultracold molecules,” Z. Idziaszek and P. S. Julienne, Phys. Rev. Lett. 104, 113204 (2010)
Add an optical lattice:“Universal rates for reactive ultracold polar molecules in reduced dimensions,” A. Micheli, Z. Idziaszek, G. Pupillo, M. A. Baranov, P. Zoller, and P. S. Julienne, Phys. Rev. Lett. (to be published) arXiv:1004.5420.
Simple but adequate theoretical models for the next generation of experiments.
Add an electric field:“A Simple Quantum Model of Ultracold Polar Molecule Collisions”, Z. Idziaszek, G. Quéméner, J.L. Bohn, P.S. Julienne, Phys. Rev. A 82, 020703R (2010)
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Two kinds of collisions
Elastic: bounce off each other
Loss: go to different products
Example: KRb + KRb K2 + Rb2
Elastic cross section:
Loss cross section:
= S-matrix element for the entrance channel
Rate constant:
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40K87Rb v=0, N=0
I(40K) = 4 (9 levels) + I(87Rb) = 3/2 (4 levels) makes 36 levels total
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Apply to 40K87Rb collisions
KRb + KRb’ 0.8x10-10 cm3/s1.9(4)x10-10 cm3/s s-wave
Measured Universal
KRb + KRb 1.1(3)x10-5 cm3/s/K 0.8(1)x10-5 cm3/s/K p-wave
K + KRb 1.1x10-10 cm3/s1.7(3)x10-10 cm3/s s-wave
Universal rate limit, van der Waals potentialsC6 from S. Kotochigova and R. Mosyznski a = 6.2(2) nm
Non-identical (s-wave):
Identical fermions (p-wave):
S. Ospelkaus et al., Science 327, 853 (2010)Z. Idziaszek and P. S. Julienne, Phys. Rev. Lett. 104, 113204 (2010)
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Add an electric field
Numerical coupled channels at large RQDT universal boundary conditions at small R
Universal K for 40K87Rb mass, C6
Z. Idziaszek, G. Quéméner, J.L. Bohn, P.S. Julienne, Phys. Rev. A 82, 020703R (2010)
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Scales of various interactions
Energy Length
Chemical
van der Waals
Dipolar
TrapKRb at 50 kHz
Kinetic
KRb at 200 nK
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1. Pick a reference problem we can solvee.g. van der Waals potential, B. Gao, 1998-2009
2. Parameterize dynamics by a few “physical” parametersand apply QDT tools
3. Take advantage of separation of energy, length scalesPreparation, control: E/h ≈ kHzLong range: GHzShort range (chemical): > THz
Quantum defect theory
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Our approach
“Hybrid” quantum defect theory (QDT)QDT theories are not uniqueToolbox of pieces to assemble
Short range
2 QDT parameters: s, phase, scattering lengthy, reaction, flux loss
Long range
Numerical, coupled channels or approximationsReduced dimension effects (quasi-2D, quasi-1D)
Special case: y=1, “universal” rate constants (independent of s).Collision rates controlled by quantum scattering by the long range V.
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200 THz
AB
Chemistry:ReactionsInelasticevents
Short range
R0
1 nm
Long range
-C6/R6
Analyticlong-range
theory(B. Gao)
a_
20 GHz
6 nm
Experimentally preparedseparated species
Properties ofseparated species
20 kHz (1 K)
A+B
dB > 500 nm
Trap: ah ≈ 50 nm
Dipole: ad
Explosionhappens
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Long range Asymptotic
Cold speciesprepared
Chemistry
Scatter offlong-rangepotential
“Universal” van der Waals rate constants
Lost
Reflect
“Black hole”model
A+B
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QDT model
PartialAbsorption0 ≤ y ≤ 1 s = a/a and y
Parameterised by
R0
1 nm
a_
6 nm
Universal(vdW):
Dipole: numerical(coupled channels)
vdW: analytic
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s-wave collision summary
Complex scattering length a-ib
If only a single s-wave channel,
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S. Ospelkaus, K.-K. Ni, D. Wang, M. H. G. de Miranda, B. Neyenhuis, G. Quéméner, P. S. Julienne, J. L. Bohn, D. S. Jin, and J. Ye, Science 327, 853 (2010).
JILA Experiment
MQDT universal rateMQDT non-universal ratey=0.4
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Add an electric field
KRb hasy =0.8
Hypotheticalless reactive
molecule
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Reactive collisions in an electric field
E/kB=250 nK
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Elastic collisions in an electric field
E/kB=250 nK
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From Piotr S. Zuchowski and Jeremy M. Hutson, arXiv:1003.1418
All reactions making a trimer + an atom are energetically uphill.
Dimer reactions AB + AB A2 + B2
U = likely Universal, reactive loss
NR = Non-Universal, non-reactive
What about other species?
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d=0.2 Debyed=0
Like fermions m=1
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Quasi-2D KRb fermions
50 kHz trap
dashed:unitarized
Borndashed:
semiclassical(instanton)
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Physicaldipole
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Quasi-2D KRb E/kB = 240 nK
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Some ultracold reactions can be understood simply
QDT = versatile and powerful theory for molecular collisions:Takes advantage of scale separation of long and short rangeAnalytic or numerical implementationsMore can be built into the model (e.g., threshold exit channels)Include effects of E, B, EM fields
Predicts different classes of molecules, e.g.,Universal, no resonances: KRbNon-reactive, lots of resonances: RbCs, also Cs2
QDT extends to reduced dimension (with numerical long-range for dipoles)Stable 2D and 1D dipolar gases should be possible
even for strongly reactive species.