Cold Controlled Chemistry. Roman Krems University of British Columbia

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1 Cold Controlled Chemistry Roman Krems University of British Columbia

2 Cold Chemistry Group at UBC Sergey Alyabyshev Chris Hemming Felipe Herrera Zhiying Li Timur Tscherbul Erik Abrahamsson UBC Physics Funding:

3 Outline Cold and ultracold molecules - denitions Chemistry at ultracold temperatures External eld control of molecular collisions at low Ts Reactions in magnetic traps Chemistry in conned geometries Electric eld modication of chemical reactions Possible applications of cold controlled chemistry

4 $ Centrifugal barrier o p yk j~ o v Œ t %Wjlkny j +j mwv]x jy yv kt r t r v %Wjlkny t j &+j mwv x jy yv kt r ~

5 Temperature scale (Kelvin)

6 cold Temperature scale (Kelvin)

7 ultra-cold cold Temperature scale (Kelvin)

8 ultra-cold cold warm hot Temperature scale (Kelvin)

9 Coldest T in the Universe ultra-cold cold warm hot Temperature scale (Kelvin)

10 & $ Ž Q w E! " #%$& (' ) +* ^ n " )Š & () +* z ^ 8 * " 8 rux!ÿ jlr y$# " " " " ^ z ^ )Š (' ^ Ev ( t x!ykn{ t r y EvŠ hj~rwy ( k v wt (Ov M xnv v r hj~ru v o6 Ev(Ot x!yk { rwyk v o ( v 8 jkzoƒ{ƒrhj( t x " % n ()Š ^ " % ) +*

11 !" #%$ & '( ) *+, $.-/ 0-213#4$3' 1 - &35

12 ' Typical Rate Coefficient room temperature Temperature (K) "!#%$'&)(*,+-#.0/,/ ,7,*09

13 ' Typical Rate Coefficient room temperature Temperature (K) "!#%$'&)(*,+-#.0/,/ ,7,*09

14 ' Typical Rate Coefficient room temperature Temperature (K) "!#%$'&)(*,+-#.0/,/ ,7,*09

15 ' Typical Rate Coefficient room temperature Temperature (K) "!#%$'&)(*,+-#.0/,/ ,7,*09

16 ' Typical cross section Collision energy (Kelvin)

17 ' Typical cross section Wigner s laws: elastic cross section ~ constant reaction cross section ~ 1/velocity Collision energy (Kelvin)

18 ' Wigner s laws: elastic cross section ~ constant reaction cross section ~ 1/velocity rate ~ velocity x cross section elastic rate ~ 0 reaction rate ~ constant

19 ' 3 ~ # " " " " '#

20 2 2 #%$ & ' -* $.- / 0-21#%$' 1- & ) - / # ( - $

21 External eld control of molecular collisions

23 Experimental and theoretical studies of the Coherent Control of unimolecular processes have seen spectacular growth over the last two decades. By contrast, Coherent Control of collisional processes remains a significant challenge. Paul Brumer, DAMOP Meeting abstract, 2007

24 Controlled dynamics Coherent control (Shapiro,...) External field control Controlled chemistry

25 External electric or magnetic elds may Close or open reaction channels Break the spherical symmetry of the problem Mitigate the role of centrifugal barriers in the reaction Induce Feshbach resonances that enhance reactivity Suppress or enhance the role of spin-orbit interactions Align or orient molecules Induce anisotropic interactions Conne translational motion in lower dimensions and thereby allow for control of molecular collisions works at low temperatures!

26 Chemical reactions in magnetic traps

27 q q p q p q triplet state A + BC singlet state B + AC

28 How do electric fields affect spin rel Induce couplings between the rotational levels (!N Energy diagram of a Increase 2 Σ diatomic the energy molecule gap between the rotational lev R. V. Krems, A.Dalgarno, N.Balakrishnan, and G.C. Groenenboom, PRA 67, 06

29 Enhancement of spin relaxation First-order Stark effect T. V. Tscherbul and R.V. Krems, PRL 97, (2006)

30 Enhancement of spin relaxation (a 3D view)

31 Reactions in conned geometries

33 ' Wigner s laws: elastic cross section ~ constant reaction cross section ~ 1/velocity rate ~ velocity x cross section elastic rate ~ 0 reaction rate ~ constant

34 Threshold collision laws Collision 3D 2D s-wave elastic σ = const σ 1 v ln 2 v s-wave reaction σ = 1/v σ 1 v ln 2 v s-wave to non-s-wave σ v 2l non-s-wave to non-s-wave σ v 2l+2l H. R. Sadeghpour et al, J. Phys. B 33, R93 (2000)

38 Z. Li, S. V. Alyabyshev, and RK, PRL 100, (2008).

39 Threshold collision laws Collision 3D quasi-2d s-wave elastic σ = const σ 1 v ln 2 v s-wave reaction σ = 1/v σ 1 v ln 2 v s-wave to non-s-wave σ v 2l σ v 2 m 1 1 ln 2 v non-s-wave to non-s-wave σ v 2l+2l σ v 2 m +2 m 1 Z. Li, S. V. Alyabyshev, and RK, PRL 100, (2008).

40 ' ' ' ' Energy (cm -1 ) Initial state Final state B, Tesla

41 hv o ' ' ' '

42 Effects of symmetry on ultra-cold collisions B Suppressed collisional spin relaxation

43 Effects of symmetry on ultra-cold collisions llisional spin relaxation B Enhanced collisional spin relaxation

44 Li + HF LiF + H

45 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds Quantum reactive scattering calculations in external elds I Arrangement Channel Hypersherical Coordinates (ACHC) y α=2 (AC+B) C z α A γ α R α α=3 (BC+A) r α α=1 (AB+C) B Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

46 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds Quantum reactive scattering calculations in external elds Denition of the Fock-Delves coordinates I Hyperradius (overall size) = I Hyperangles (triangle shape) q R 2 + r 2 ; = tan 1 r R ~ = cos 1 R ~r R r ; A y α=2 (AC+B) R α γ α r α α=1 (AB+C) C z α α=3 (BC+A) B Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

47 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds Hamiltonian of the system in an electric eld H = 2 @ V (; ; ) + H ef ( ) I Generalized Angular Momentum = sin 2 sin 2 2 I Interaction with electric + H ef ( ) = d E cos I Hyperne interactions (not included) I Dipole moment of the triatomic molecule as a whole (ignored since Ed triatom V ) 2 + j 2 cos 2 sin 2 Electric field (E) d χ Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

48 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds How is it dierent from eld-free reactive scattering? I Electric elds couple dierent rotational states H ef () = de cos = de X I Example: A space-xed coupled basis set jjmj `i = X M j ;M` q Y 1q (^d)y 1q (^E )! j = 1 hjm j `M`jJMijjM j i j`m`i I Matrix element of the interaction with electric elds hjmj `j de cos jj 0 Mj 0`0i J 1 J 0 ll 0 M 0 M I Conclusion: Electric elds couple dierent J-states j 1 j Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

49 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds Basis sets I Arrangement-dependent, space-xed, uncoupled basis jjm j ij`m`i vj( ; ) I Stark matrix elements within each arrangement hjm j `M`jH ef jj 0 Mj 0 `0M 0`i j 1 j 0 = Ed M j 0 Mj 0 j 1 j Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

50 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds Coordinate transformations I What about interaction and overlap matrix elements? R ~ 0 cos 0 = 1 sin 0 1 ~ R ~r 0 sin 0 1 cos 0 1 ~r 4D overlap integrals hjm j `M`jj 0 M 0 j `0M 0`i = Z Z d ^R d^r Y jmj (^r )Y`M`(^R ) Y j 0 M 0 j (^r 0)Y`0M 0`(^R 0) Too expensive! Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

51 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds Solution I Transformation to the body-xed coupled basis j+` X jjm j `M`i = ( 1) j `+M (2` + 1) 1=2 X K J=jj 4D integrals! 2D integrals j (2J+1) 1=2 ` J M j M` M jjmkijjki `j ( 1) K j ` J K 0 K hjm j `M`jj 0 M 0 j `0M 0`i! hjmk ; jkjjmk 0 ; j 0 K 0 i Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

52 Cold controlled chemistry Theory of reactive scattering in external elds Li + HF! LiF + H Molecular collisions in elds Energy diagram of the reaction Li + HF(v=0, j=0) v=1 HF(v=0) j ΔE = ev LiF(v=0) Electric field ev ev Timur V. Tscherbul and Roman V. Krems: Eects of electromagnetic elds on cold chemical reactions Department of Chemistry, University of British Columbia, Vancouver BC, Canada

53 10-15 T = 0.05 K Rate constant (cm 3 /s) T = 0.75 K Electric field (kv/cm)

54 Possible applications of cold controlled chemistry

55 Inelastic collisions and chemical reactions at ultra-cold temperatures are extremely state selective Inelastic collisions of H 2 with H Cross section for inelastic relaxation (A) H 2 (v=1, j=2) + H 2 (v=0, j=0) H 2 (v=1, j=0) + H 2 (v=0, j=0) H 2 (v=1, j=0) + H 2 (v=0, j=2) Collision energy (cm -1 ) can be used to produce molecules with inverted populations chemical lasers based on ultra-cold collisions

56 Controlled photodissociation of ultra-cold molecules M. G. Moore and A. Vardi, PRL 88, (2002): entangled pairs of molecules coherent control of bi-molecular collisions

57 Chemical reactions in magnetic traps Enhancement of spin relaxation (a 3D view) reactions near tunable avoided crossings geometric phase effects chemical reactions induced by fine interactions

58 Chemistry in confined geometries B Suppressed collisional spin relaxation B Enhanced collisional spin relaxation stereodynamics of ultra-cold collisions effects of symmetry breaking effects of long-range interactions

59 Collisions of molecules with tunable velocities resonances in chemical dynamics of molecule new systems to test reaction rate theories

60 References Z. Li, S. V. Alyabyshev and R. V. Krems, PRL 100, (2008). Z. Li and R. V. Krems, PRA 75, (2007). R. V. Krems, PRL 96, (2006). T. V. Tscherbul and R. V. Krems, PRL 97, (2006). T. V. Tscherbul, and R. V. Krems, JCP 125, (2006). Reviews R. V. Krems, Perspective on Cold Controlled Chemistry, fill this space to appear in PCCP (2008). R. V. Krems, Int. Rev. Phys. Chem. 24, 99 (2005).

Cold Controlled Chemistry. Roman Krems University of British Columbia

Cold Controlled Chemistry. Roman Krems University of British Columbia Cold Controlled Chemistry Roman Krems University of British Columbia Sergey Alyabyshev Zhiying Li Timur Tscherbul Outline Cold and ultracold molecules - denitions Chemistry at ultracold temperatures External