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Understanding Feshbach molecules with long range quantum defect theory Paul S. Julienne

EuroQUAM satellite meeting, University of Durham, April 18, 2009. Understanding Feshbach molecules with long range quantum defect theory Paul S. Julienne Joint Quantum Institute, NIST and The University of Maryland. Collaborators (theory) Tom Hanna, Eite Tiesinga (NIST)

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Understanding Feshbach molecules with long range quantum defect theory Paul S. Julienne

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  1. EuroQUAM satellite meeting, University of Durham, April 18, 2009 Understanding Feshbach molecules with long range quantum defect theory Paul S. Julienne Joint Quantum Institute, NIST and The University of Maryland Collaborators (theory) Tom Hanna, Eite Tiesinga (NIST) Thanks also to Bo Gao (U. of Toledo) and Cheng Chin (U. Chicago) J. K. Freericks (Georgetown U.), M. Maśka (U. Silesia), R. Lemański (Wroclaw)

  2. Outline • Sone general considerations 2. The significance of the long-range potential 0812.1486, Feshbach review 0902.1727, Book chapter 0903.0884, MQDT treatment LiK, KRb 3. Long-range potential + quantum defect theory for atom-atom collisions Can we get simple, practical models?

  3. E/kB 109 K Interior of sun 106 K E/h Surface of sun 1000 K Room temperature 1 THz 1 K Liquid He 1 GHz 1 mK Laser cooled atoms 1 MHz 1 K Optical lattice bands 1 kHz Quantum gases (Bosons or Fermions) 1 nK 1 Hz 1 pK

  4. 3. Population transfer STIRAP 2. Atom Association weakly bound pair Kohler et al, Rev. Mod. Phys. 78, 1311 (2006) Chin, et al, arXiv: 0812.1496 4. Polar molecules Dipolar gases, lattices Ultracold polar molecules are now with us 1. Atom preparation 100 kHz 100 THz

  5. Short range Separated atoms Long range A+B AB 10-10 eV (1 K) 10-4 eV 1 eV (E) scattering phase Y (E) bound state phase (Ei)=n at eigenvalue _ a -C6/R6 Analytic long-range theory (B. Gao) Properties of separated species “simple” “Core” independent of E ≈ 0

  6. where where QT = translational partition function T = thermal de Broglie wavelength of pair Replace for elastic collisions Phase Space density Time scale Dynamics Resonance scattering S-matrix theory of molecular collisions F. H. Mies, J. Chem. Phys. 51, 787, 798 (1969)

  7. Adapted from Gao, Phys. Rev. A 62, 050702 (2000); Figure from FB review Bound states from van der Waals theory

  8. Singlet Triplet Spectrum of van der Waals potential 40K87Rb Blue lines: a = ∞ Adapted from Fig. 8 Chin, Grimm, Julienne, Tiesinga, “Feshbach Resonances in Ultracold Gases”, submitted to Rev. Mod. Phys. arXiv:0813.1496

  9. -10.56 GHz -3.17 GHz -0.41 GHz

  10. -3.17 GHz -3.00 GHz

  11. vdW Energy scale Goal: Simple, reliable model for classification and calculation * Now: Full quantum dynamics with CC calculations All degrees of freedom with real potentials Exact, but not simple • * vdW-MQDT: Reduction to a simpler representation • Parameterized by • C6 van der Waals coefficient •  reduced mass • abg “background” scattering length • resonance width • B0 singularity in a(B) • magnetic moment difference

  12. Use vdW solutions for MQDT analysis • Analytic properties of (R,E) across thresholds (E) and between • short and long range (R) • Generalized Multichannel Quantum Defect Theory (MQDT): • F. H. Mies, J. Chem. Phys. 80, 2514 (1984) • F. H. Mies and P. S. Julienne, J. Chem. Phys. 80, 2526 (1984) • Ultracold: • Eindhoven (Verhaar group), JILA (Greene, Bohn) • P. S. Julienne and F. H. Mies, J. Opt. Soc. Am. B 6, 2257 (1989) • F. H. Mies and M. Raoult, Phys. Rev. A 62, 012708 (2000) • P. S. Julienne and B. Gao, in Atomic Physics 20, ed. by C. Roos, • H. Haffner, and R. Blatt (2006) (physics/0609013) • Analytic solutions for -C6/R6 van der Waals potential • B. Gao, Phys. Rev. A 58, 1728, 4222 (1998) • Also 1999, 2000, 2001, 2004, 2005 • Solely a function of C6, reduced mass , and scattering length a

  13. Bound states Scattering states For coupled channels case Given the reference the single-channel functions: for scattering (E>0) (E), C(E), tan (E) and bound states (E<0) (E) From vdW theory, given C6, , a MQDT theory (1984) gives coupled channels S-matrix and bound states. Assume a single isolated resonance weakly coupled to the continuum Yc,bg <<1, Ycc = -Ybg,bg = 0

  14. For magnetically tunable resonances: See Kohler et al, Rev. Mod. Phys. 78, 1311 (2006) Resonance strength Bound state E=0 shifts to Bound state norm Z as E → 0 Classification of resonances by strength, arXiv:0812.1496

  15. Closed channel dominated Entrance channel dominated “Broad” “Narrow”

  16. 6Li ab 7Li aa 1 2 E/kB (mK) 1 0 0 800 400 600 800 400 600 B (Gauss) B (Gauss) Closed channel dominated Entrance channel dominated Color: sin2(E)

  17. Corresponds to vdW MQDT when “box” width is chosen to be Bound state equation for level with binding energy Two-channel “box” model with

  18. Bound state E and Z for selected resonances Points: coupled channels Lines: box model Closed-channel character Energy

  19. 3 AND ONLY 3 free parameters arXiv: 0903.0884 Fit 9 s-wave measured resonances in 6Li40K from To about 2 per cent accuracy (3 G) E. Wille, F. M. Spiegelhalder, G. Kerner, D. Naik, A. Trenkwalder, G. Hendl, F. Schreck, R. Grimm, T. G. Tiecke, J. T. M. Walraven, et al., Phys. Rev. Lett. 100, 053201 (2008). Can we get simple models for bound and scattering states? Use vdW solutions for MQDT treatment Ingredients: Atomic hyperfine/Zeeman properties Atomic-molecule basis set frame transformation Van der Waals coefficient C6 S, T scattering lengths

  20. 40K87Rb aa resonances

  21. n=-2

  22. n = -3 A(-1) B(-2) D(-3)

  23. Ion-atom MQDT elastic and radiative charge transfer Na + Ca+ Model calculation only (no real Potentials) Ion-atom -C4/R4: Idziaszek, et al., Phys. Rev. A 79, 010702 (2009)

  24. Reflect Lost Transmit Reflect “Universal” van der Waals inelasticity Chemistry Long range Asymptotic A+B Cold species prepared Scatter off long-range potential Assume unit probability of inelastic event at small R

  25. “Universal” van der Waals model Applied to RbCs molecular quenching by Hudson, Gilfoy, Kotochigova, Sage, and De Mille, Phys. Rev. Lett. 100, 203201 (2008)

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