Ultracold Molecules and Cold Controlled Chemistry. Roman Krems University of British Columbia

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1 Ultracold Molecules and Cold Controlled Chemistry Roman Krems University of British Columbia

2 Sergey Alyabyshev Zhiying Li Timur Tscherbul

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

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

5 Temperature Scale (Kelvin) Coldest T in the universe

6 !" #%$ & '( ) *+, $.-/ 0-213#4$3' 1 - &35

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

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

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

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

11 ' Typical cross section Collision energy (Kelvin)

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

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

14 ' 3 ~ # " " " " '#

15 Ultracold chemistry new regime of chemistry Possibility to study controlled chemical reactions quantum effects in chemistry detailed mechanisms of chemical reactions role of individual ro-vibrational energy levels in determining chemical reactivity See Cold Controlled Chemistry : R. V. Krems, PCCP 10, 479 (2009)

16 Ultracold chemistry new regime of chemistry Possibility to study effects of quantum statistics and manybody physics on chemical reactions effects of tunable fine and hyperfine interactions on chemical reactions effects of external space symmetry on chemical reactions See Cold Controlled Chemistry : R. V. Krems, PCCP 10, 479 (2009)

17 200 0 Rb 2 + Cs 2 Energy (cm -1 ) RbCs + RbCs R (atomic units) T. V. Tscherbul, G. Barinovs, J. Klos, and RK, Phys Rev A 78, (2008)

18 Chemical reactions in magnetic traps

19 Magnetic trap Magnetic field middle of the trap

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

21 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

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

23 Enhancement of spin relaxation (a 3D view)

24 Polar molecules in a microwave cavity Molecular Hamiltonian: H mol = BN 2 Field Hamiltonian: H f = ω(ââ N) Molecule - Field Interaction: H mol,f = dɛ 0 2 N ( â + â ) cos χ Basis set: NM N N + n The matrix elements: N + n NM N H mol,f N M N N + n NM N cos χ N M N ( ) δ n,n +1 + δ n,n 1 NM N cos χ N M N δ M N,M N ( ) δ N,N +1 + δ N,N 1

25 Polar molecule in a microwave cavity

26 Polar molecule in a microwave cavity N = 1 N = 1 (b) #! R 2B e ) N = 0 N = 0 a 0 N =0, N + a 1 N =1, N 1 a 0 N =0, N 1 + a 1 N =1, N 2 no absolute ground state

27 0.2 Energy (in units of B e ) M S =-1/2 M S =1/2 M S =-1/2 M S =1/ Cross section (in units of Å 2 ) h _ ω = 1.9 B e ; Ω = 1 B e h _ ω = 1.9 B e ; Ω = 2 B e Magnetic field, T

28 Tuning molecular interac/ons with Feshbach resonances

34 Feshbach resonance

35 S-wave elastic scattering cross section (a.u.) Magnetic field (Gauss)

36 Resonances in molecule - molecule collisions Cross Section, Å Magnetic field, Gauss T. V. Tscherbul, Y. V. Suleimanov, V. Aquilanti, and RK, New J. Phys 11, (2009)

37 Microwave-laser-eld modication of molecular resonances

38 Polar molecule in a microwave cavity N = 1 N = 1 (b) #! R 2B e ) N = 0 N = 0 a 0 N =0, N + a 1 N =1, N 1 a 0 N =0, N 1 + a 1 N =1, N 2 no absolute ground state

39 Calculation by Sergey Alyabyshev 10 6 Cross section (in units of Å 2 ) ω = 0.7 B e Ω = 0.20 B e ω = 0.7 B e Ω = 0.02 B e ω = 1.9 B e Ω = 0.02 B e He + NH elastic scattering B (T)

40 Calculation by Sergey Alyabyshev Cross section (in units of Å 2 ) B = G ω = 0.70 B e B = G ω = 0.75 B e Ω (in units of B e )

41 Calculation by Sergey Alyabyshev Cross section (in units of Å 2 ) B = G Ω = 0.1 B e B = G Ω = 0.02 B e B = G Ω = 0.01 B e ω (in units of B e )

42 Reactions in conned geometries

44 THE JOURNAL OF CHEMICAL PHYSICS 129, Quantum theory of chemical reactions in the presence of electromagnetic fields T. V. Tscherbul a and R. V. Krems Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada Received 29 April 2008; accepted 12 June 2008; published online 21 July 2008

49 r e l 0 Elastic collisions D. S. Petrov and G. V. Shlyapnikov, PRA 64, (2001)

50 3D collision core r e l 0 Elastic collisions D. S. Petrov and G. V. Shlyapnikov, PRA 64, (2001)

51 3D collision core r e The wave function is l 0 proportional to the regular 3D wave function Elastic collisions D. S. Petrov and G. V. Shlyapnikov, PRA 64, (2001)

52 3D collision core r e [ ] The wave function is l 0 proportional to the regular 3D wave function ψ α (r) = i πηϕ 0 (0) 1 k α r [ e ik α r S αα e ik αr ] φ α Y 00 (ˆr) Elastic collisions D. S. Petrov and G. V. Shlyapnikov, PRA 64, (2001)

53 3D collision core r e [ ] The wave function is l 0 Asymptotic region proportional to the regular 3D wave function ψ α (r) = i πηϕ 0 (0) 1 k α r [ e ik α r S αα e ik αr ] φ α Y 00 (ˆr) Elastic collisions D. S. Petrov and G. V. Shlyapnikov, PRA 64, (2001)

54 ψ( r) = [ ϕ 0 (z)e i q ρ f 00 (ɛ)ϕ 0 (z) ] i 8πqρ eiqρ φ α Y 00 (ˆr) 3D collision core r e [ ] The wave function is l 0 proportional to the regular 3D wave function Asymptotic region ψ α (r) = i πηϕ 0 (0) 1 k α r [ e ik α r S αα e ik αr ] φ α Y 00 (ˆr) Elastic collisions D. S. Petrov and G. V. Shlyapnikov, PRA 64, (2001)

55 Inelastic collisions r e Z. Li and RK, PRA 79, (2009)

56 Inelastic collisions Couplings occur in 3D collision core r e Z. Li and RK, PRA 79, (2009)

57 Inelastic collisions Couplings occur in 3D collision core r e The confined and unconfined channels can be treated separately. Z. Li and RK, PRA 79, (2009)

58 Inelastic collisions ψ α α sc = α α l m l ν 1 2 α r 1 S α l m l α00 χ i2π k α Y 00(ˆr i )e i(k α r l π/2) φ α Y l m l (ˆr) Couplings occur in 3D collision core r e The confined and unconfined channels can be treated separately. Z. Li and RK, PRA 79, (2009)

59 Inelastic collisions ψ α α sc = α α l m l ν 1 2 α r 1 S α l m l α00 χ i2π k α Y 00(ˆr i )e i(k α r l π/2) φ α Y l m l (ˆr) Couplings occur in 3D collision core r e The confined and unconfined channels can be treated separately. The asymptotic wave function for inelastic collisions: ψ α α sc = α α ν 1 2 α f α α e ik α r r φ α Z. Li and RK, PRA 79, (2009)

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

61 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).

62 l 0 Purely-3D Purely-2D Zhiying Li and RK, Phys. Rev. A 79, (R) (2009)

63 ! in /! el l 0 (in units of 10 4 Bohr) Z. Li and R.V. Krems, Phys. Rev. A 79,050701(R) (2009)

64 10-1! quasi-2d /! 3D (Bohr -1 ) l 0 (in units of 10 3 Bohr) Z. Li and R.V. Krems, Phys. Rev. A 79,050701(R) (2009)

65 Cold molecules and Ultracold Chemistry 1998: Magnetic trapping of CaH( 2 Σ) at 0.1 K. 1998: Photassociation of ultracold atoms 2005: Measurements of atom - molecule inelastic scattering at 10 6 K 2006: Experimental confirmation of Wigner s threshold law for inelastic collisions of molecules 2008: Precision measurements of collision cross sections using cold beams and trapped molecules 2008: Dense ensembles of ultracold KRb and Cs 2 in the ground ro-vibrational state created : Measurements of chemical reactions at ultracold T To come: : BEC of molecules in the ro-vibrationally ground state 2009: Ultracold controlled chemistry

66 References S. V. Alyabyshev and R. V. Krems, PRA 80, (2009). Z. Li and R. V. Krems, PRA 79, (R) (2009). Z. Li, S. V. Alyabyshev and R. V. Krems, PRL 100, (2008). 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 Phys. Chem. Chem. Phys. 10, 479 (2008). R. V. Krems, Int. Rev. Phys. Chem. 24, 99 (2005). Books R. V. Krems, W. C. Stwalley, and B. Friedrich (eds.), Cold Molecules: Theory, Experiment, Applications, CRC Press (2009) pages.

67 Cold Chemistry Group at UBC Sergey Alyabyshev Chris Hemming Felipe Herrera Zhiying Li Marina Li?nskaya Timur Tscherbul Erik Abrahamsson Harvard University UBC Physics Funding: Peter Wall Ins?tute for Advanced Studies

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