Roman Krems University of British Columbia

1. Roman Krems University of British Columbia

2. Frenkelexciton physics with ultracold molecules Roman Krems University of British Columbia Sergey Alyabyshev Felipe Herrera Jie Cui Marina Litinskaya Jesus Perez Rios Chris Hemming Ping Xiang Alisdair Wallis Zhiying Li, now at Harvard University TimurTscherbul, now at Harvard University Funding: Peter Wall Institute for Advanced Studies

3. Quantum simulation of condensed-matter physics with ultracold molecules

5. Condensed-matter systems are modeled by simple Hamiltonians For example: Bose-Hubbard Hamiltonian – describes an esnemble of interacting bosons on a lattice

6. Condensed-matter systems are modeled by simple Hamiltonians For example: Holstein Hamiltonian – describes a particle (e.g. electron) in a bath of bosons (e.g. phonons)

7. It’s hard to diagonalize these simple Hamiltonians!

8. Quantum simulation Create a system that is described exactly by a model Hamiltonian Interrogate the system to learn its properties

9. Condensed-matter systems are modeled by simple Hamiltonians For example: Bose-Hubbard Hamiltonian – describes an esnemble of interacting bosons on a lattice

10. Heuristic derivation:

11. g = 4πa/m scattering length

13. Polar molecules on an optical lattices are great for quantum simulation Why? The dipole – dipole interactions are long-range (strengths of up to ~ 10 kHz) Molecules possess rotational structure (in addition to fine and hyperfine structure)

16. One can also use hyperfine interactions and realize spin-lattice Hamiltonians using 1Σ molecules with hyperfine interactions

17. Holstein Hamiltonian – describes a particle (e.g. electron) in a bath of bosons (e.g. phonons)

18. Holstein Polaronspectrum: Weak coupling regime Strong coupling regime

19. Holstein model Describes energy transfer in molecular aggregates, such as photosynthetic complexes M. Sarovar, A. Ishizaki, G. R. Fleming, and B. K. Whaley, Nature Physics 6, 462–467 (2010)

20. Holstein Hamiltonian – describes a particle (e.g. electron) in a bath of bosons (e.g. phonons)

21. Electronic excitation of molecules in a molecular crystal

22. Electronic excitation of molecules in a molecular crystal

29. Holstein polaron energy in an optical lattice with LiCs molecules J ~ 7 kHz

30. Holstein Hamiltonian

31. One-dimensional array of 5 LiCs molecules on an optical lattice

32. Beyond quantum simulation Can molecules on an optical lattice be used to realize dynamical systems that can not be realized in solid-state crystals?

33. Electronic excitation of molecules in a molecular crystal

39. Frenkelbiexciton: • Can two Frenkelexcitons form a bound state? • Never observed in sold-state molecular crystals …

41. In solid-state molecular crystals: states of different parity states of the same parity

44. In solid-state molecular crystals: D << J

45. In order for two excitons to form a bound state, we must have | D | > 2 | J | G. Vektaris, JCP 101, 3031 (1994)

46. In solid-state molecular crystals: states of different parity states of the same parity

47. LiCs molecules in an optical lattice with lattice separation a = 400 nm

48. Frenkelbiexciton in a one-dimensional system of LiCs molecules on an optical lattice

49. A molecular crystal with tunable impurities

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