Tunable crystals of ultracold polar molecules!

Transcription

1 Tunable crystals of ultracold polar molecules! Sergey Alyabyshev Chris Hemming Felipe Herrera Jie Cui Marina Li9nskaya Jesus Perez Rios Ping Xiang Roman Krems! University of British Columbia! Zhiying Li, now at UBC Physics Timur Tscherbul, now at Harvard University Funding: Peter Wall Ins9tute for Advanced Studies

2 Solid-state crystals are very complex

3 Hreal = Hmodel + Hcomplicating

4 Quantum Simulation! Design simple controllable systems with some of the same properties as complex quantum systems, such as solid-state crystals!

5 Cold Controlled Chemistry PCCP 1, 479 (28) Ultracold Molecules: Science, Technology, Applica>ons New J Phys 11, 5549 (29) Ultracold Controlled Chemistry Physics 3, 1 (21)

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

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8 This talk! I. Ultracold molecules on an optical lattice as a crystal with tunable exciton impurity interactions! II. Ultracold molecules on an optical lattice as a crystal with tunable magnetic properties!

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

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

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

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

14 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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16 Pure Exciton Hamiltonian: Impurities!

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

18 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)

19 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,

20 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)

21 5. 3. No diagonal disorder Ψ(x) 2 (1/N mol ) Diagonal disorder ~ off-diagonal disorder Large diagonal disorder x (a)

22 5. 4. f (t) t (µs).25 Ψ(x) 2 (1/N mol ) C(k) x (a) ka

23 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!

24 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

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

26 Enhancement of spin relaxation First-order Stark effect T. V. Tscherbul and R.V. Krems, PRL 97, 8321 (26)

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

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31 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)

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

33 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

34 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

35 1 B = mt 1 B = mt A(t) B = mt t (ms) B = mt t (ms)

36 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!???!

37 Future work: including controlled dissipation Felipe Herrera, Ping Xiang

38 2 1 N = 2 Energy N = 1-1 N = Electric field (kv/cm)

39 2 1 N = 2 Energy N = 1-1 N = Electric field (kv/cm)

40 Couple to an electronically excited state 2 1 N = 2 Energy N = 1-1 N = Electric field (kv/cm)

41 References Felipe Herrera, Marina Litinskaya and RK, arxiv: Jesus Perez-Rios, Felipe Herrera and RK, arxiv:17.458