Collective excitations of ultracold molecules on an optical lattice. Roman Krems University of British Columbia

Transcription

1 Collective excitations of ultracold molecules on an optical lattice Roman Krems University of British Columbia

2 Collective excitations of ultracold molecules trapped on an optical lattice Sergey Alyabyshev Chris Hemming Felipe Herrera Jie Cui Marina Li9nskaya Jesus Perez Rios Ping Xiang Alisdair Wallis Roman Krems Zhiying Li, now at Harvard University Timur Tscherbul, now at Harvard University Funding: Peter Wall Ins9tute for Advanced Studies

3 This talk 1. Ultracold chemistry a new exciting research field 2. New physics with ultracold molecules in an optical lattice

4 12 Nobel prizes to 27 scientists for research of low temperature phenomena since for the development of methods to cool and trap atoms with laser light for the achievement of Bose-Einstein condensation in dilute gases of alkali metal atoms, and for early fundamental studies of the properties of the condensates

5 12 Nobel prizes to 27 scientists for research of low temperature phenomena since for the development of methods to cool and trap atoms with laser light for the achievement of Bose-Einstein condensation in dilute gases of alkali metal atoms, and for early fundamental studies of the properties of the condensates 20XX - for Ultracold Chemistry

6 Temperature scale (Kelvin)

7 cold Temperature scale (Kelvin)

8 ultra-cold cold Temperature scale (Kelvin)

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

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

11 Magnetic trap Magnetic field middle of the trap

12 Evaporative cooling More delicate methods: evaporative cooling

13 & $ 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 ^ " % ) +*

14 !" #%$ & '( ) *+, $.-/ 0-213#4$3' 1 - &35

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

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

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

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

19 ' Typical cross section Collision energy (Kelvin)

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

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

22 ' 3 ~ # " " " " '#

23 2 2 #%$ & ' -* $.- / 0-21#%$' 1- & ) - / # ( - $

24 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)

25 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)

26 Collective excitations of molecules in an optical lattice

27 It has now become possible to create dense ensembles of diatomic molecules, both polar and non-polar, at nanokelvin temperatures

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29 Ultracold molecules on optical lattices = molecular crystals with unusual properties: Intermolecular interactions are very weak, much weaker than the energy of rotational splitting in molecules Molecules are held in the crystal by optical field forces, not intermolecular interactions

30 Is rotational excitation of a molecule a single-particle or collective excitation?

31 What can we do with molecules on a lattice that cannot be done with conventional crystals?

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33 Frenkel exciton φ n = n 00 n N ψ = n C n φ n

34 Frenkel exciton φ n = n 00 n N ψ k = n e ik r n N φ n

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

36 Negative effective mass =>! negative refraction of EM field!

37 Rotational excitons are controllable

38 E(k) (khz) E(k) (khz) γ β α E x k a E(k) (khz) E(k) (khz) E x α, β k a γ

39 Excitons are sensitive to impurities Exciton impurity interactions can be controlled!

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41 Pure Exciton Hamiltonian: Impurities!

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

43 E eg ( 10 4 MHz) E eg (khz) σ 2D (Å) LiCs LiRb ε (kv/cm) ε ε 0 (mv/cm)

44 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,

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

46 Applications! Time-domain quantum simulation of localization of quantum particles:! timescale of Anderson localization! dynamics of exciton localization as a function of effective mass, exciton! bandwidth, and exciton-impurity interaction strength! effect of disorder correlations on localization and delocalization! Negative refraction of MW fields! Controlled preparation of many-body entangled states of molecules! Effects of dimensionality and finite size on energy transfer in crystals!

47 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

48 Energy (MHz) γ Energy (cm -1 ) γ β α B(mT) B(mT) Energy (MHz) γ β B(mT)

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50 Coupling Energy (khz) E=1 kv/cm E=2 kv/cm E=5 kv/cm Exciton Bandwidth (khz) B (mt)

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53 3 (a) 4 (b) Ψ 2 (1/N mol ) Ψ 2 (1/N mol ) (c) (d) x (in units of a) x (in units of a)

54 Frenkel exciton φ n = n 00 n N ψ k = n e ik r n N φ n

55 Frenkel exciton φ n = n 00 n N ψ k = n e ik r n N φ n Ψ = 1 Nmol i C i Φ S i Φ S i = M S = 1/2 ri M S = 1/2 rj. j i

56 Frenkel exciton φ n = n 00 n N ψ k = n e ik r n N φ n Ψ = 1 Nmol i C i Φ S i Φ S i = M S = 1/2 ri M S = 1/2 rj. j i α + β

57 1 B = mt 1 B = mt A(t) B = mt t (ms) B = mt t (ms)

58 Applications! Crystal with tunable impurities:! Time-domain quantum simulation of localization of quantum particles:! timescale of Anderson localization! dynamics of exciton localization as a function of effective mass, exciton! bandwidth, and exciton-impurity interaction strength! effect of disorder correlations on localization and delocalization! Negative refraction of MW fields! Controlled preparation of many-body entangled states of molecules! Effects of dimensionality and finite size on energy transfer in crystals! Optical lattice of magnetic molecules:! Crystal with tunable magnetic properties, tunable spin waves! Preparation of many-body entangled states of spin up-down pairs!???!

59 Tunable exciton phonon interactions = Tunable Holstein Hamiltonian

60 Ĥ ex = i Ĥ = Ĥex + Ĥph + ĤI ( ɛeg + D ij ) ˆB i ˆB i + i,j i Ĥ ph = ω 0 (â q,λâq,λ ) q,λ J i,j ˆB i ˆB j Ĥ I = 1 2 i,j i ( â i + â i â ) j â j { g Dij [ ˆB i ˆB i + ˆB j ˆB j ] + g Jij [ ˆB i ˆB j + ˆB j ˆB i ]}

61 Energy (khz) One dimensional array of LiCs molecules g J g D Θ = Θ = g D g J Electric field (kv/cm) Electric field (kv/cm)

62 Probability Probability No phonons With phonons E (kv/cm) t (µs) Time (µs)

63 Quantum particles with tunable quantum statistics

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65 Kinematic Interaction Operators are neither bosonic, nor fermionic One-particle state: Two-particle state: Bose/Fermi other

66 What does this mean? The same molecule cannot be excited twice! The two excitations are coupled! k 1 and k 2 are not conserved, however the total wavevector K = k 1 + k 2 should be conserved

67 Two-Particle Schroedinger Equation In terms of K and k:

68 Bound state solutions? Notation: No solutions

69 However, Schroedinger equation has a simple solution Under this condition if the dispersion curve shape is such that for a specific value of the total wave vector K=K * (and specific branches ρ 1 and ρ 2 ) the sum does not depend on the relative wave vector k. This solution is (N-1)-time degenerate (ndegeneracy) and has the following wave function: n is the (fixed) distance between excitations in site representation!

70 Can happen for branches with high symmetry: K k =π/a k =3π/4a -2π/a 2π/a k =π/4a k =0

71 Can be realized with Frenkel rotational excitons in an optical lattice with oblique electric field: E θ E = 0 E = 10 kv/cm

72 What can we do with molecules on a lattice that cannot be done with conventional crystals? 1. Study rotational excitons: Rotational excitons are controllable * Electric field can be used to control exciton effective mass, exciton impurity interactions and exciton exciton interactions 2. Study quantum statistics of excitons * The role of kinematic interactions remains an open question 3. Study energy transfer in molecular ensembles * Could be used for quantum simulation of energy transfer in photosynthetic complexes and polaron physics

73 References Felipe Herrera, Marina Litinskaya, and RK, space holder space Phys. Rev. A 82, (2010). Jesus Perez-Rios, Felipe Herrera and RK, space holder space New J. Phys. 12, (2010). Felipe Herrera and RK, arxiv: T. V. Tscherbul and RK, PRL 97, (2006). Related 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). Book R. V. Krems, W. C. Stwalley, and B. Friedrich (eds.), Cold Molecules: Theory, Experiment, Applications, CRC Press (2009) pages.