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Roman Krems University of British Columbia Frenkel exciton physics with ultracold molecules Sergey Alyabyshev Felipe Herrera Jie Cui Marina Litinskaya Jesus Perez Rios Chris Hemming Ping Xiang Alisdair Wallis Funding: Peter Wall Institute for Advanced Studies Roman Krems University of British Columbia Zhiying Li, now at Harvard University Timur Tscherbul, now at Harvard University Quantum simulation of condensedmatter physics with ultracold molecules Condensed-matter systems are modeled by simple Hamiltonians For example: Bose-Hubbard Hamiltonian – describes an esnemble of interacting bosons on a lattice 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) It’s hard to diagonalize these simple Hamiltonians! Quantum simulation Create a system that is described exactly by a model Hamiltonian Interrogate the system to learn its properties Condensed-matter systems are modeled by simple Hamiltonians For example: Bose-Hubbard Hamiltonian – describes an esnemble of interacting bosons on a lattice Heuristic derivation: g = 4πa/m scattering length 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) One can also use hyperfine interactions and realize spin-lattice Hamiltonians using 1Σ molecules with hyperfine interactions Holstein Hamiltonian – describes a particle (e.g. electron) in a bath of bosons (e.g. phonons) Holstein Polaron spectrum: Weak coupling regime Strong coupling regime 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) Holstein Hamiltonian – describes a particle (e.g. electron) in a bath of bosons (e.g. phonons) Electronic excitation of molecules in a molecular crystal Electronic excitation of molecules in a molecular crystal Holstein polaron energy in an optical lattice with LiCs molecules J ~ 7 kHz Holstein Hamiltonian One-dimensional array of 5 LiCs molecules on an optical lattice Beyond quantum simulation Can molecules on an optical lattice be used to realize dynamical systems that can not be realized in solid-state crystals? Electronic excitation of molecules in a molecular crystal Frenkel biexciton: Can two Frenkel excitons form a bound state? Never observed in sold-state molecular crystals … In solid-state molecular crystals: states of different parity states of the same parity In solid-state molecular crystals: D << J In order for two excitons to form a bound state, we must have |D|>2|J| G. Vektaris, JCP 101, 3031 (1994) In solid-state molecular crystals: states of different parity states of the same parity LiCs molecules in an optical lattice with lattice separation a = 400 nm Frenkel biexciton in a one-dimensional system of LiCs molecules on an optical lattice A molecular crystal with tunable impurities Impurities One impurity: H E0 Bn Bn Eimp Bn=0 Bn=0 J mn Bm Bn † † n 0 † n Scatterer with the strength = difference in transition energies: † † † H E0 Bn Bn J mn Bm Bn ( Eimp E0 )Bn=0 Bn=0 n n Breaks translational symmetry Mixes states with different k V0 † H E ( k ) B ( k ) B ( k ) B ( k ) B( q ) N k,q k † 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 Phys. Rev A 82, 033428 (2010) Spin excitations in a crystal of magnetic molecules 2 molecules J SrF(2Σ) New J. Phys. 12, 103007 (2010) Ultracold molecucules may allow for the study of novel Frenkel exciton physics Study the formation and properties of Frenkel biexcitons Controlled exciton – phonon interactions -> bipolarons, possibly other interesting quasi-particles. Creation of excitons with negative effective mass => negative refraction of EM field A crystal with tunable exciton – impurity interactions => controlled Anderson localization of excitons Quantum simulation of the Holstein model Energy transfer in mesoscopic molecular aggregates Controllable open systems, potentially with both Markovian and non-Markovian baths