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)

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

7Li 6Li

Interactions: a = scattering length

Truscott, Strecker, McAlexander, Partridge, Hulet, Science 291, 2570 (2001)

s-wave scattering phase shift

Wavelength 2/k

Noninteractingatoms

R

R = 0

Interactingatoms

Phaseshift

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

From Greiner and Fölling, Nature 435, 736 (2008)

Optical trap 1D Lattice (“pancakes”)

40K87Rb

From I. Bloch, Nature Physics 1, 23 (2005)

2D Lattice (“tubes”)

3D Lattice (“dots”)

133Cs2

Dipoles: 1/R3 interaction

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

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

Cs2

1

23

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)

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

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)

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)

Scales of various interactions

Energy Length

Chemical

van der Waals

Dipolar

TrapKRb at 50 kHz

Kinetic

KRb at 200 nK

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

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.

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

Long range Asymptotic

Cold speciesprepared

Chemistry

Scatter offlong-rangepotential

“Universal” van der Waals rate constants

Lost

Reflect

“Black hole”model

A+B

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

s-wave collision summary

Complex scattering length a-ib

If only a single s-wave channel,

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

Add an electric field

KRb hasy =0.8

Hypotheticalless reactive

molecule

Reactive collisions in an electric field

E/kB=250 nK

Elastic collisions in an electric field

E/kB=250 nK

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?

d=0.2 Debyed=0

Like fermions m=1

Quasi-2D KRb fermions

50 kHz trap

dashed:unitarized

Borndashed:

semiclassical(instanton)

Physicaldipole

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 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.