1. Ultracold Polar Molecules in Gases and Lattices Paul S. Julienne Joint Quantum Institute, NIST and The University of Maryland Quantum Technologies Conference: Manipulating photons, atoms, and molecules August 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 to Zbigniew Idziaszek (Warsaw) Andrea Micheli, Guido Pupillo, Peter Zoller (Innsbruck) John Bohn, Goulven Quéméner (JILA) Svetlana Kotochigova (Temple), Robert Moszynski (Warsaw)

2. 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

3. 7 Li 6 Li Interactions: a = scattering length Truscott, Strecker, McAlexander, Partridge, Hulet, Science 291, 2570 (2001)

4. s-wave scattering phase shift Wavelength  2  / k Noninteracting atoms R  R = 0 Interacting atoms Phase shift

6. 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 (x10 5 ) Atom loss Change Mean field

7. From Greiner and Fölling, Nature 435, 736 (2008) Optical trap 1D Lattice (“pancakes”) 40 K 87 Rb

8. From I. Bloch, Nature Physics 1, 23 (2005) 2D Lattice (“tubes”) 3D Lattice (“dots”) 133 Cs 2

9. Dipoles: 1/R 3 interaction

10. Similar method had been proposed by Jaksch, Venturi, Cirac, Williams, and Zoller, Phys. Rev. Lett. 89, 040402(2002) for making non-polar Rb 2 in a lattice. Example with KRb molecule

11. 40000 40 K 87 Rb molecules v=0, J=0, single spin level 200 to 800 nK Density ≈ 10 12 cm -3 KRb 1. Prepare mixed atomic gas 1 2. Magneto-association to Feshbach molecule 2 3. Optically switch to v=0 ground state 3

12. Cs 2 1 2 3

13. 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)

14. Two kinds of collisions Elastic: bounce off each other Loss: go to different products Example: KRb + KRb  K 2 + Rb 2 Elastic cross section: Loss cross section: = S-matrix element for the entrance channel Rate constant:

15. 40 K 87 Rb v=0, N=0 I( 40 K) = 4 (9 levels) + I( 87 Rb) = 3/2 (4 levels) makes 36 levels total

16. Apply to 40 K 87 Rb collisions KRb + KRb’ 0.8x10 -10 cm 3 /s 1.9(4)x10 -10 cm 3 /s s-wave Measured Universal KRb + KRb 1.1(3)x10 -5 cm 3 /s/K0.8(1)x10 -5 cm 3 /s/K p-wave K + KRb 1.1x10 -10 cm 3 /s 1.7(3)x10 -10 cm 3 /s s-wave Universal rate limit, van der Waals potentials C 6 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)

18. Add an electric field Numerical coupled channels at large R QDT universal boundary conditions at small R Universal K for 40 K 87 Rb mass, C 6 Z. Idziaszek, G. Quéméner, J.L. Bohn, P.S. Julienne, Phys. Rev. A 82, 020703R (2010)

19. Scales of various interactions Energy Length Chemical van der Waals Dipolar Trap KRb at 50 kHz Kinetic KRb at 200 nK

20. 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 Quantum defect theory

21. 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.

22. 200 THz AB Chemistry: Reactions Inelastic events Short range R0R0 1 nm Long range -C 6 /R 6 Analytic long-range theory (B. Gao) a _ 20 GHz 6 nm Experimentally prepared separated species Properties of separated species 20 kHz (1  K) A+B dB > 500 nm Trap: a h ≈ 50 nm Dipole: a d Explosion happens

23. Long range Asymptotic Cold species prepared Chemistry Scatter off long-range potential “Universal” van der Waals rate constants Lost Reflect “Black hole” model A+B

24. QDT model Partial Absorption 0 ≤ y ≤ 1 s = a/a and y Parameterised by R0R0 1 nm a _ 6 nm Universal(vdW): Dipole: numerical (coupled channels) vdW: analytic

25. s-wave collision summary Complex scattering length a-ib If only a single s-wave channel,

26. 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 rate MQDT non-universal rate y=0.4

27. Add an electric field KRb has y =0.8 Hypothetical less reactive molecule

28. Reactive collisions in an electric field E/k B =250 nK

29. Elastic collisions in an electric field E/k B =250 nK

30. 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  A 2 + B 2 U = likely Universal, reactive loss NR = Non-Universal, non-reactive What about other species?

32. d=0.2 Debye d=0 Like fermions m=1

33. Quasi-2D KRb fermions 50 kHz trap dashed: unitarized Born dashed: semiclassical (instanton)

34. Physical dipole

35. Quasi-2D KRb E/k B = 240 nK

36. 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 Cs 2 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.