Roman Krems University of British Columbia

Transcription

1 Rotational Frenkel excitons in optical lattices with polar molecules Roman Krems University of British Columbia felipe-manuscript-comments-nov9.pdf felipe-manuscript-comments-dec9.pdf

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3 Ultracold molecules on optical lattices = molecular crystals with unusual properties: Intermolecular interactions are very weak, yet significant enough to give rise to collective phenomena Molecules are held in the crystal by optical field forces, not intermolecular interactions

4 This talk I. Ultracold molecules on an op2cal la3ce as a crystal with tunable exciton impurity interac2ons. II. Ultracold molecules on an op2cal la3ce as a crystal with tunable magne2c proper2es. III. Ultracold molecules on an op2cal la3ce as a crystal with tunable exciton phonon interac2ons.

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6 Frenkel exciton φ n = n n+1... N ψ = n C n φ n

7 Frenkel exciton φ n = n n+1... N ψ k = n e ik r n N φ n

8 Dispersion Curves! 2 2 E(k) ( in units of 1-6 B) ", #! k a E(k) (khz) E(k) (khz) "! k a #

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

10 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

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12 Pure Exciton Hamiltonian: Impurities!

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

14 Tunable impurities! CsF LiCs LiRb!E eg LiCs LiRb!E eg (!1 4 MHz) E (kv/cm) " 2D (Å) 1 8 k=1-8 Å k=1-6 Å k=1-5 Å E (mv/cm)

15 Exciton impurity Hamiltonian matrix! Ĥ 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 N mol N i i n =1 e i(q k) i n,

16 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)

17 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!

18 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, 6

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

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

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24 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)

25 Frenkel exciton φ n = n n+1... N ψ k = n e ik r n N φ n

26 Frenkel exciton φ n = n n+1... 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

27 Frenkel exciton φ n = n n+1... 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

28 1 B = mt 1 B = mt A(t) B = mt t (ms) B = mt t (ms)

29 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!???!

30 Tunable exciton phonon interactions = Tunable Holstein Hamiltonian

31 Ĥ ex = i Ĥ = Ĥex + Ĥph + ĤI ( ɛeg + D ij ) ˆB i ˆB i + i,j i Ĥ ph = ω (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 ]}

32 Λ 12 (units of V dd ) Λ 12 (units of V dd ) λ θ (degrees)

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

34 This talk I. Ultracold molecules on an op2cal la3ce as a crystal with tunable exciton impurity interac2ons. II. Ultracold molecules on an op2cal la3ce as a crystal with tunable magne2c proper2es. III. Ultracold molecules on an op2cal la3ce as a crystal with tunable exciton phonon interac2ons.

35 References Felipe Herrera, Marina Litinskaya, and RK, space holder space Phys. Rev. A 82, (21). Jesus Perez-Rios, Felipe Herrera and RK, space holder space New J. Phys. 12, 137 (21). Felipe Herrera and RK, arxiv: T. V. Tscherbul and RK, PRL 97, 8321 (26). Related Reviews R. V. Krems, Perspective on Cold Controlled Chemistry, fill this space Phys. Chem. Chem. Phys. 1, 479 (28). R. V. Krems, Int. Rev. Phys. Chem. 24, 99 (25). Book R. V. Krems, W. C. Stwalley, and B. Friedrich (eds.), Cold Molecules: Theory, Experiment, Applications, CRC Press (29) - 75 pages.