Quantum Technologies Conference: Manipulating photons, atoms, and molecules
August 29 - September 3, 2010, Torun, Poland
Ultracold Polar Molecules in
Gases and Lattices
Paul S. Julienne
Joint Quantum Institute, NIST and The University of
Maryland
Thanks to
Zbigniew Idziaszek (Warsaw)
Andrea Micheli, Guido Pupillo, Peter Zoller (Innsbruck)
John Bohn, Goulven Quéméner (JILA)
Svetlana Kotochigova (Temple), Robert Moszynski (Warsaw)
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)
Laser cooling, an enabling technology (mK-mK)
Evaporative cooling  BEC (mK-nK)
Trapped quantum gases, lattices
Precision control, measurement (atomic clocks)
Well-characterized
Building blocks for quantum science and technology for the future
Controlling collisions and inter-species interactions are a key:
Coherent interactions (scattering length)
Decoherence, loss (rate constant, time scale)
7Li
6Li
Truscott, Strecker, McAlexander, Partridge, Hulet, Science 291, 2570 (2001)
Interactions:
a = scattering length
s-wave scattering phase shift
Wavelength 2/k
Noninteracting
atoms
R
Phase
shift
Interacting
atoms
R=0
Number of Atoms
(x105)
Change
Scattering length
(relative sale)
Atom loss
Change
Mean field
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).
1D Lattice (“pancakes”)
Optical trap
40K87Rb
From Greiner and Fölling, Nature 435, 736 (2008)
2D Lattice (“tubes”)
133Cs
2
3D Lattice (“dots”)
From I. Bloch, Nature Physics 1, 23 (2005)
Dipoles: 1/R3 interaction
Example with KRb molecule
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.
40000 40K87Rb molecules
v=0, J=0, single spin level
200 to 800 nK
Density ≈ 1012 cm-3
1. Prepare mixed atomic gas
2
2. Magneto-association to
Feshbach molecule
3. Optically switch to
v=0 ground state
3
KRb
1
1
Cs2
2
3
Molecular collisions: simple or complex?
Collisions are a key to the control and stability of ultracold gases and lattices.
Simple but adequate theoretical models for the next generation of experiments.
"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 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)
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.
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:
40K87Rb
v=0, N=0
I(40K) = 4 (9 levels) + I(87Rb) = 3/2 (4 levels) makes 36 levels total
Apply to 40K87Rb collisions
Universal rate limit, van der Waals potentials
C6 from S. Kotochigova and R. Mosyznski  a = 6.2(2) nm
Identical fermions (p-wave):
Non-identical (s-wave):
Measured
Universal
1.1(3)x10-5 cm3/s/K
KRb + KRb’
1.9(4)x10-10 cm3/s
0.8x10-10 cm3/s
s-wave
1.7(3)x10-10 cm3/s
1.1x10-10 cm3/s
s-wave
K + KRb
0.8(1)x10-5 cm3/s/K
p-wave
KRb + KRb
S. Ospelkaus et al., Science 327, 853 (2010)
Z. Idziaszek and P. S. Julienne, Phys. Rev. Lett. 104, 113204 (2010)
Add an electric field
Numerical coupled channels at large R
QDT 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)
Scales of various interactions
Energy
Length
Kinetic
KRb at 200 nK
Chemical
van der Waals
Trap
KRb at 50 kHz
Dipolar
Quantum defect theory
1. Pick a reference problem we can solve
e.g. van der Waals potential, B. Gao, 1998-2009
2. Parameterize dynamics by a few “physical” parameters
and apply QDT tools
3. Take advantage of separation of energy, length scales
Preparation, control: E/h ≈ kHz
Long range: GHz
Short range (chemical): > THz
Our approach
“Hybrid” quantum defect theory (QDT)
QDT theories are not unique
Toolbox of pieces to assemble
Short range
2 QDT parameters:
s, phase, scattering length
y, reaction, flux loss
Long range
Numerical, coupled channels or approximations
Reduced 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.
Long range
Short range
Experimentally prepared
separated species
AB
A+B
1
nm
6 nm
_
a
R0
Chemistry:
Reactions
Inelastic
events
Explosion
happens
20 kHz (1 mK)
20 GHz
200 THz
dB > 500 nm
Trap: ah ≈ 50 nm
-C6/R6
Dipole: ad
Analytic
long-range
theory
(B. Gao)
Properties of
separated species
“Universal” van der Waals rate constants
Chemistry
Long range
Asymptotic
Reflect
A+B
Scatter off
long-range
potential
Lost
“Black hole”
model
Cold species
prepared
QDT model
Partial
Absorption
0≤y≤1
Parameterised by
s = a/a and y
1
nm
R0
Universal(vdW):
vdW: analytic
6 nm
_
a
Dipole: numerical
(coupled channels)
s-wave collision summary
If only a single s-wave channel,
Complex scattering length a-ib
JILA Experiment
MQDT
MQDTnon-universal
universal raterate
y=0.4
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).
Add an electric field
Hypothetical
less reactive
molecule
KRb has
y =0.8
Reactive collisions in an electric field
E/kB=250 nK
Elastic collisions in an electric field
E/kB=250 nK
What about other species?
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
From Piotr S. Zuchowski and Jeremy M. Hutson, arXiv:1003.1418
Like fermions m=1
d=0
d=0.2 Debye
Quasi-2D KRb fermions
50 kHz trap
dashed:
unitarized
Born
dashed:
semiclassical
(instanton)
Physical
dipole
Quasi-2D KRb E/kB = 240 nK
Some ultracold reactions can be understood simply
QDT = versatile and powerful theory for molecular collisions:
Takes advantage of scale separation of long and short range
Analytic or numerical implementations
More 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: KRb
Non-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.