Effects of electric static and laser fields on cold collisions of polar molecules. Roman Krems University of British Columbia

Transcription

1 Effects of electric static and laser fields on cold collisions of polar molecules Roman Krems University of British Columbia

2 UBC group: Zhiying Li Timur Tscherbul Erik Abrahamsson Sergey Alyabishev Chris Hemming Collaborations: Alexei Buchachenko - Moscow Grzegorz Chalasinski - Warsaw Alex Dalgarno - Harvard John Doyle - Harvard Gerrit Groenenboom - Nijmegen Sture Nordholm - Sweden Maria Szczesniak - Michigan

3 Outline Introduction What's interesting about cold molecules? Methods to produce cold molecules Electric-eld-control of molecular collisions How electric elds can help cool molecules Collisions of molecules in a microwave cavity Threshold laws for collisions in 2D Outlook: Collision physics and ultra-cold molecules

4 Applications of cold molecules Tunable interactions Quantum computation High-precision spectroscopy Controlled chemistry The dipole-dipole interaction A. Micheli, G. K. Brennen, and P. Zoller, Nature Phys. 2, 341 (2006)

5 Tunable interactions Cold molecules Orientation and alignment Controlled chemistry

6

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8 Experimental methods for cooling molecules

9 Magnetic trap

10 ) ) r A r B R $ #$% % %! "! & & & '(*),+ + +

11 Trap loss...

12 How do electric fields affect spin relaxation? Induce couplings between the rotational levels ( N = 1) Increase the energy gap between the rotational levels R. V. Krems, A.Dalgarno, N.Balakrishnan, and G.C. Groenenboom, PRA 67, (R) (2003)

13 Theory of collisions in external fields Coupled equations

14 Spin relaxation is suppressed

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

16 Enhancement of spin relaxation (a 3D view)

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

18 Trap loss...

19 Microwave traps for polar molecules D. DeMille et al.: Microwave traps for cold polar molecules 379 Fig. 2. Energies of dressed states vs. applied microwave electric field strength. State labels are zero-field basis states ψ Jmn, DeMille, Glenn, and Petricka, Eur. J. Phys. D 31, 375 (2004)

20 Energy levels of a diatomic molecule in a microwave field 60 Energy (in units of rotational constant) µ ε 0 ( in units of rotational constant)

21 Energy levels of a diatomic molecules in a microwave field Energy (in units of rotational constant) µ ε 0 (in units of rotational constant)

22 Energy levels of a diatomic molecules in a microwave field Energy (in units of rotational constant) (N=0, n=q) (N=0, n=q-1) µ ε 0 (in units of rotational constant)

23 Collisions of molecules in a microwave cavity Molecular Hamiltonian: H mol = BN 2 Field Hamiltonian: H f = ω(aa n) Molecule - Field Hamiltonian: H mol,f = µ ω 2ɛ 0 V cos θ ( a + a ) Basis set: NM N n The matrix elements of of the molecule - eld Hamiltonian: n NM N H mol,f N M N n NM N cos θ N M N ( ) δ n,n +1 + δ n,n 1 NM N cos θ N M N δ M N,M N ( ) δ N,N +1 + δ N,N 1

24 Energy levels of a diatomic molecules in a microwave field Energy (in units of rotational constant) a(n=0, n=q) + b(n=1,n=q-1) + c(n=1,n=q+1) a(n=0, n=q-1) + b(n=1, n=q) + c(n=1,n=q-2) µ ε 0 (in units of rotational constant)

25 Superposition states of molecules in a microwave eld Ψ ground = a N = 0, n = N +b N = 1, n = N 1 + c N = 1, n = N + 1 +d N = 0, n = N 2 + e N = 0, n = N + 2 N is the average number of photons O-resonant light: w = 0.01B. µɛ 0 = 0.1B µɛ 0 = 0.3B µɛ 0 = 0.5B a = a = a = b = a = a = c = c = c = d = a = a = e = a = a = 0.448

26 Collisionally induced transitions between field-dressed states elastic scattering 10 3 ω = 1.9 B Cross section (Å 2 ) ω = 1.1 B ω = 0.01 B Collision energy: 0.3 cm µε 0 (in units of rotational constant)

27 Cross section for elastic scattering (Å 2 ) Change of a shape resonance in the presence of microwave radiation no field ω=1.9 B; µε 0 =0.5 B Collision energy (cm -1 )

28 Threshold laws for collisions in 2D

29 Threshold laws for collisions in 2D In 3D, we have Wigner's threshold laws for elastic scattering: collision cross section v 2l+2l In 2D, there is no l. The Hamiltonian is H = 1 d 2µρdρ ρ d dρ + l2 z 2µρ 2 + H as + V (ρ), The role of l is played by m, the projection quantum number. How are the Wigner's threshold laws modied, if we conne the system in 2D?

30 Let's look at low-energy scattering: In 3D, the Schrödinger's equation is [ 1 2µR 2 d dr R2 d dr ] l(l + 1) + 2µV (R) ψ(k, R) = k 2 ψ(k, R) 2µR2 Consider rst the solution to this equation with V = 0 and k = 0: [ 1 2µR 2 d dr R2 d dr ] l(l + 1) + 2µR 2 ψ(k, R) = 0 Let's look for the solution in the form ψ(r, k = 0) = constr s The derivative: 1 2µR 2 d dr R2 d dr Rs = s(s + 1)R s Hence, s(s + 1) = l(l + 1) or s = l and s = (l + 1).

31 A general solution at k = 0 is therefore ψ(k = 0, R) = A 1 R l + A 2 R (l+1) Now, for k 0, we have a Bessel equation and the general solution ψ(k, R) = Aj l (kr) + Bη l (kr) which can be re-written at small k as ψ(k, R) = (kr) l + tan δ l (kr) (l+1) For smooth and continuous matching to k = 0, we must require tan δ l k 2l+1 which gives after some manipulation: elastic scattering cross section k 4l

32 Repeating this derivation for 2D, we get cross secion 1 k ln 2 k, when m = 0 Using the formalism of Wigner, it is also possible to get the odiagonal cross sections: and cross secion for m = 0 m transitions k 2 m 1 1 ln 2 k cross secion for m > 0 m > 0 transitions k 2 m +2 m 1

33 Threshold collision laws Transition 3D 2D s-wave elastic σ = const σ 1 k ln 2 k s-wave to non-s-wave σ k 2l σ k 2 m 1 1 ln 2 k non-s-wave to non-s-wave σ k 2l+2l σ k 2 m +2 m 1 Why is this interesting?

34 Consider ultracold collisions of molecules in 2D. Angular momentum transfer of molecules - such as spin relaxation - must be accompanied by changes of m, if the magnetic eld axis is directed perpendicularly to the plane of connement If the magnetic eld axis is tilted, collisions do not have to conserve the total angular momentum projection Inelastic angular momentum transfer - such as spin relaxation - will then be much more ecient if the axis of the external eld is not perpendicular to the plane of connement.

35 B Suppressed collisional spin relaxation B Enhanced collisional spin relaxation

36 Conclusions Electric elds may suppress collisional loss from a magnetic trap Evaporative cooling in a microwave trap might be dicult (??) Microwave elds modify interactions of cold molecules Elastic and Inelastic Two-Body Collisions are modied in 2D

37 Outlook: Collision Physics and Ultracold Molecules Experiments with cold molecules may conrm or disprove Wigner's threshold laws more insight into long-range interactions elucidate rates for chemical reactions at ultracold Ts ultracold chemistry lots of applications demonstrate the possibility of controlling chemical reactions controlled chemistry lots of applications make coherent control of bimolecular reactions possible controlled chemistry provide new testground for statistical theories of molecules new reaction rate theories

38 References 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). R. V. Krems, PRL 93, (2004). Reviews R. V. Krems, Nature Physics 3, 77 (2007). R. V. Krems, Int. Rev. Phys. Chem. 24, 99 (2005). J. Doyle, B. Friedrich, R. V. Krems, and F. Masnou-Seeuws, Eur. Phys. J. D 31, 149 (2004).