Ultracold Polar Molecules in Gases and Lattices Paul S. Julienne

1. 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)

2. 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)

3. 7Li 6Li Truscott, Strecker, McAlexander, Partridge, Hulet, Science291, 2570 (2001) Interactions: a = scattering length

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

6. Atom loss Number of Atoms (x105) Change Mean field Change Scattering length (relative sale) 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).

7. 1D Lattice (“pancakes”) Optical trap 40K87Rb From Greiner and Fölling, Nature 435, 736 (2008)

8. 2D Lattice (“tubes”) 133Cs2 3D Lattice (“dots”) From I. Bloch, Nature Physics 1, 23 (2005)

9. Dipoles: 1/R3 interaction

10. 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.

11. 40000 40K87Rb molecules v=0, J=0, single spin level 200 to 800 nK Density ≈ 1012 cm-3 1. Prepare mixed atomic gas 2 1 3 2. Magneto-association to Feshbach molecule KRb 3. Optically switch to v=0 ground state

12. Cs2 2 3 1

13. 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.

14. 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:

15. 40K87Rb v=0, N=0 I(40K) = 4 (9 levels) + I(87Rb) = 3/2 (4 levels) makes 36 levels total

16. Universal Measured s-wave 1.9(4)x10-10 cm3/s 0.8x10-10 cm3/s KRb + KRb’ p-wave 1.1(3)x10-5 cm3/s/K 0.8(1)x10-5 cm3/s/K KRb + KRb 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): 1.7(3)x10-10 cm3/s 1.1x10-10 cm3/s s-wave K + KRb 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 40K87Rb mass, C6 Z. Idziaszek, G. Quéméner, J.L. Bohn, P.S. Julienne, Phys. Rev. A 82, 020703R (2010)

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

20. 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

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. Short range Long range AB 20 GHz 200 THz _ a -C6/R6 Analytic long-range theory (B. Gao) Chemistry: Reactions Inelastic events Experimentally prepared separated species A+B 20 kHz (1 K) 1 nm 6 nm ldB > 500 nm R0 Trap: ah ≈ 50 nm Dipole: ad Properties of separated species Explosion happens

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

24. Partial Absorption 0 ≤ y ≤ 1 QDT model Parameterised by vdW: analytic s = a/a and y 6 nm 1 nm _ a R0 Dipole: numerical (coupled channels) Universal(vdW):

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

26. JILA Experiment MQDT non-universal rate y=0.4 MQDT universal rate 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).

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

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

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

30. 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

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

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

34. Physical dipole

35. Quasi-2D KRb E/kB = 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 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.