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Rigorous Mean-Field Dynamics of Lattice Bosons: Quenches from the Mott Insulator

This study explores the out-of-equilibrium dynamics of lattice bosons, focusing on quenches from the Mott insulator phase. It utilizes the Gutzwiller mean-field theory and dynamics to investigate the emergence of superfluidity and the stability of the Mott insulator state. The results have implications for experimental studies with ultracold atoms in optical lattices.

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Rigorous Mean-Field Dynamics of Lattice Bosons: Quenches from the Mott Insulator

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  1. Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator Michiel Snoek September 21, 2011 FINESS 2011 Heidelberg

  2. Motivation Out-of-equilibrium many-body quantum mechanics: • Theoretically very challenging • Experimentally feasible with ultracold atoms: • Decoupled from the environment • Highly tunable • New questions: thermalization

  3. Gutzwiller Mean-Field Theory • Gutzwiller mean-field theory: decoupling of the hopping term • Mean-field eigenstates are product states over the lattice sites: Fisher et al., PRB 40, 546 (1989) Rokhsar and Kotliar, PRB 44, 10 328 (1991) Sheshadri et al., EPL 22, 257 (1993)

  4. Gutzwiller Mean-Field Theory • Decomposition in Fock basis: • Self-consistentsolution: • Mott insulator: • Superfluid: • Goodagreementwith 3D QMC calculations • Exactfor infinite dimensions/fullyconnectedlattice

  5. Gutzwiller Mean-Field Dynamics • Time-evolutiondrivenbymean-fieldHamiltonian: • Non-linear differential equationforthecn(t): • with

  6. Fullyconnectedlattice Sciolla & Biroli [PRL 105, 220401 (2010)]: • Hamiltonian is invariant under lattice site permutations • Ground states are invariant under permutations. • Dynamics driven by a classical Hamiltonian. • Gutzwiller dynamics is exact M. Snoek, EPL 95, 30006 (2011)

  7. Quenches from the Mott insulator

  8. Quenchesfrom the MottInsulator • Phase diagram for one particle per site: SF MI 0 U/J Uc /J

  9. Quenchesfrom the MottInsulator • We find a dynamical critical interaction Ud: • If Uf > Ud: superfluid order emerges SF MI 0 U/J Ud /J Uc /J

  10. Quenchesfrom the MottInsulator • We find a dynamical critical interaction Ud: • Uf > Ud: superfluid order emerges • Uf < Ud: the system remains insulating SF MI 0 U/J Ud /J Uc /J

  11. Quenches from the Mott insulator • Equationsofmotionforn=N/V=1, Nmax = 2: • Mott insulator: • Groundstatefor • Steadystate: • Stability?

  12. Quenches from the Mott insulator • Contourswith H=0 for different Uf: • Dynamicalcriticalinteraction: • Uf<Ud : disconnected branches, stableMottinsulator • Uf>Ud: connected branches, unstableMottinsulator

  13. Quenches from the Mott insulator • Numericalverification: • ExponentialincreaseforUf>Ud • InfinitesimaloscillationsforUf<Ud • Results independent of Nmax

  14. Quenches from the Mott insulator • Exponent: • Numerical fits (points) • Analyticalexpressionfromlinearizedequations of motion (line):

  15. Quenchesfrom the Mottinsulator • Observable using optical lattice systems. • U/J can be quenched by • Changing the optical lattice depth • Feshbach resonances • Ud expected to shift, but positive • Trapping potential obscures transition: • Particle transport after the quench • Wedding cake structure: external source of superfluid order.

  16. Conclusions • Gutzwiller mean-field dynamics is exact on the fully connected lattice and therefore a controlled mean-field method. • A dynamical critical interaction Ud separates stable and unstable Mott insulators after a quench. • Observable with ultracold atoms in optical lattices

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