Collision dynamics of molecules and rotational excitons! in an ultracold gas confined by an optical lattice!

Transcription

1 Collision dynamics of molecules and rotational excitons! in an ultracold gas confined by an optical lattice! Sergey Alyabyshev Chris Hemming Felipe Herrera Zhiying Li UBC Physics Marina Litinskaya Timur Tscherbul Harvard University Erik Abrahamsson UBC Physics Roman Krems! University of British Columbia! Funding: Peter Wall Institute for Advanced Studies

2 Outline! I. Inelastic collisions of molecules confined by an optical lattice in quasi-2d geometry Effects of laser forces on reactive collisions! II. Controlled dynamics of rotational excitons in an array of molecules on an optical lattice! System with tunable exciton-impurity interactions! Scattering resonances in exciton-impurity collisions! Controlled localization/delocalization of excitons! III. Tuning ultracold molecules by microwave fields! Collision-induced absorption of non-resonant microwave photons near Feshbach resonances!

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8 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)

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

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

11 Zhiying Li, PRA 81, (2010)

12 Rotational Excitons in Optical Lattices with Polar Molecules! Scattering of molecular excitons by tunable impurities! Felipe Herrera, Marina Li.nskaya and RK, arxiv:

13 Optical lattice with polar molecules Ground: Excited: LiCs molecules

14 Dispersion Curves! E(k) ( in units of 10-6 B) ", #! k a E(k) (khz) E(k) (khz) "! k a #

15 Impurities! One impurity: Scatterer with the strength = difference in transition energies: Breaks translational symmetry Mixes states with different k

16 Tunable impurities! CsF LiCs LiRb!E eg LiCs LiRb!E eg (!10 4 MHz) E (kv/cm) " 2D (Å) 10 8 k=10-8 Å k=10-6 Å k=10-5 Å E (mv/cm)

17 Tunable impurities! CsF LiCs LiRb!E eg LiCs LiRb!E eg (!10 4 MHz) " 2D (Å) 10 8 k=10-8 Å k=10-6 Å k=10-5 Å E (kv/cm) E (mv/cm) Quantum simulations:! Tune exciton-impurity interactions! by an external electric field! Vary impurity distributions and concentrations!

18 Exciton impurity Hamiltonian matrix! Ĥ0 q,k = E(k)δ k,q, Ŵ q,k = 2 J(a) N mol (cos q a + cos k a) Off-diagonal disorder! N i i n =1 e i(q k) i n Diagonal disorder! ˆV q,k = V 0 N mol N i i n =1 e i(q k) i n,

19 No diagonal disorder Ψ(x) 2 (1/N mol ) Diagonal disorder ~ off-diagonal disorder Large diagonal disorder x (a)

20 , Dynamical Multiple Impurity Problem! Wave packet formation and dynamics, k-space distribution...

21 Ψ(x) 2 (1/N mol ) t = 0 t = 0.4 ms t = 0.8 ms x (a)

22 f (t) t (µs) 0.25 Ψ(x) 2 (1/N mol ) C(k) x (a) ka

23 Tuning ultracold molecules with microwave fields! S. V. Alyabyshev, T. V. Tscherbul and RK, PRA 79, (R) (2009)! S. V. Alyabyshev and RK, PRA 80, (2009). S. V. Alyabyshev and RK, submitted.!

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 (a) 0 α K = 0 Energy (in units of B e ) β γ α K = -1 δ ξ K = Ω R = ε 0 d (in units of B e )

26 Polar molecule in a microwave cavity

27 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

28 Cross section (Å 2 ) no mw field _ h ω/be = 0.7; Ω/B e = 0.02 (a) B (G) Cross section (Å 2 ) (b) B (G)

29 10 4 _ hω/b e = 0.7 Ω/B e = 0.02 Cross section (Å 2 ) h _ ω/b e = 0.7 Ω/B e = 0.2 _ hω/b e = 1.9 Ω/B e = B (G)

30 10 6 _ h ω/be = 0.7 _ h ω/be = 0.1 Cross section (Å 2 ) Ω (in units of B e )

31 Summary! Inelastic/Reactive collisions in quasi-2d geometry are suppressed! σreactive 3D σelastic 3D γ = = γ σquasi 2D reactive σ quasi 2D elastic 2E π ω 0 ; E ω 0 1 Z. Li and RK, PRA 79, (R) (2009).

32 Summary! Mixture of polar molecules on an optical lattice => rotational excitons with tunable impurities! Tunable scattering resonances for exciton impurity interactions! Tunable disorder => quantum simulation of localization! Localization/delocalization of excitons can be tuned by an electric field! Possibility to study finite-size and geometry effects on dynamics of excitons! F. Herrera, M. Li,nskaya and RK, arxiv

33 Summary! Collisions of ultracold molecules lead to absorption of far-detuned, non-resonant microwave photons! Non-resonant field absorption is dramatically enhanced near a Feshbach resonance! This can be used for detecting Feshbach resonances and tuning scattering properties of ultracold molecules! S. V. Alyabyshev and RK, to be published