Marco Fattori Universal Quantum Simulator with cold atoms in optical lattices

1. Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi Marco Fattori Universal Quantum Simulator with cold atoms in optical lattices Conferenza e Mostra Centro Fermi 29-30 Novembre 2007, Roma

2. Universal Quantum Simulator • Our understanding of phenaomena in nature is based on our ability of • conjecturing some Hamiltonian H • see if it is able to successfully describe the properties of the system under exam • Simulating quantum systems on a classical computer can be very hard • For example, let’s consider N spin ½ . . . . 2N numbers are neededd to address the state of the system N a 2N 2N matrix is needed to describe the evolution of the system . . . . . . . . . . . . . . . . . . Solving this problem in general can be very hard!!

3. Universal Quantum Simulator The rule of simulation that I would like to have is that the number of computer elements required to simulate a large physical system is only to be proportional to the space-time volume of the physical system. I don’t want to have an explosion!! R. P. Feynman I would like to have an exact simulation, in other words, that the computer will do “exactly” the same as nature R. P. Feynman

4. for fermions for bosons • simplest model of interacting particles (electrons) in a lattice • generalization beyond the band theory description of solids • it incorporates the short range part of the Coulomb interaction, avoiding the high complexity of the long range Coulomb force. • Used to describe electronic properties of solids with narrow band. It predicts metal-Mott insulator transition in metal oxides and for 4He in porus material. • Resolved in 1D, in higher dimensions is not known for most of the space of parameters, coupling constants, electron concentration, temperature, etc.. Hubbard model Some Hamiltonians used to describe physical systems

5. t-J Model • Used to explain how magnetic order in antiferromagnetic insulator, if doped, gives way to superconductivity • Describes the motion of holes in an antiferromagnet • Describes High Tc superconductor containing copper oxides planes • Anisotropic Heisenberg model (XXZ) • It is used to describes quantum magnetism in condensed matter systems Some Hamiltonians used to describe physical systems

6. Ultracold atoms in optical lattices A periodic potential for an atomic system may be easily obtained from the interference of two counterpropagating off-resonant laser beams For sufficiently strong periodic potentials and low temperatures, the atoms will be confined to the lowest Bloch band and will evolve exactly according to the Hubbard model Atoms interacting with a “crystal of light” are a candidate to realize a UQS to simulate condensed matter systems. The two Feynman statement are satisfied.

7. UQS with ultracold atoms in optical lattices Designing the optical potential tuning potential strength time-dependent potentials tuning lattice spacing designing complex/disordered structures

8. UQS with ultracold atoms in optical lattices Designing the optical potential tuning potential strength time-dependent potentials tuning lattice spacing designing complex/disordered structures

9. UQS with ultracold atoms in optical lattices Designing the optical potential tuning potential strength time-dependent potentials tuning lattice spacing designing complex/disordered structures

10. UQS with ultracold atoms in optical lattices Designing the optical potential tuning potential strength time-dependent potentials tuning lattice spacing designing complex/disordered structures

11. UQS with ultracold atoms in optical lattices Designing the optical potential tuning potential strength time-dependent potentials tuning lattice spacing designing complex/disordered structures

12. UQS with ultracold atoms in optical lattices • Degrees of freedom can be frozen arbitrarily, so physical situations with reduced dimensionality are accessible 3D 2D 1D • Boson or fermions can be used • No crystal vibration, so long simulation times • Interaction strength can be tuned, tuning the atomic scattering length (Fano-Feshabch resonances)

13. K at Florence 41K (Boson): Giovanni Modugno, et al., Bose-Einstein condensation of potassium atoms by sympathetic cooling, Science, 294, 1320 (2001) 40K (Fermion): Giovanni Modugno, et al. Collapse of a Degenerate Fermi Gas, Science, Vol 297, pp 2240 (2002) …only recently we have achieved BEC of39K in the |F=1, mF=1> state time G. Roati, et al. 39K Bose Einstein Condensate with tunable interactionPhys. Rev. Lett. 99, 010403 (2007)

14. Tuning of the interaction in 39K via Fano-Feshbach resonances • At first glance 39K has unfavorable collisional properties: negative scattering length (aKK=-33 a0) Vc VS(R) Ec • Fano-Feshbach resonance Ms’≠ Ms + B field VS’(R) • The BEC can be stabilized against collapse • The interaction energy U in the Hubbard model can be tuned at will

15. Feshbach spectroscopy on 39K Resonance in the F=1 manifold Huge degree of tunability C. D’Errico, et al, New Journal of Physics 9 223 (2007) mF=1 Broad Feshbach resonance D=50 G Knowledge of the scattering length vs B for all the three sublevels mF=-1,0,1

16. z pz pz z z Bloch oscillations with a tunable 39K BEC • We can use a known quantum model to test our ability to control the scattering length • Quantum transport in a periodic potential in the presence of an external force Bloch Oscillations After a time T of Bloch Oscillations Interference contrast is destroyed by the interaction

17. Bloch oscillations with tunable 39K BEC Lattice parameters: l = 1032 nm, slattice= 6, nradial=40 Hz 100 a0 vs 1 a0 100 a0 1 a0 0 ms 0.4 ms 0.8 ms 1.2 ms 1.6 ms 2 ms 2.4 ms 2.8 ms 3.2 ms 3.6 ms 4 ms T =0 ms T =4 ms

18. Rate of decoherence vs scatteing length D. Witthaut et al., Phys. Rev. E 71, 036625 (2004) Good agreement exp vs theory M. Fattori et al. submitted to PRL arXiv:0710.5131v1 Bloch oscillations with tunable 39K BEC Peak width vs time

19. Bloch oscillations with tunable 39K BEC • Minimum of the decoherence coincide with the zero crossing predicted by our Feshbach spectroscopy analysis. • We have an optimum control of the scattering length • We are actually performing trapped atom interferometry with an almost ideal gas • We address lattice noise induced decoherence • We can simulate electron dynamics in periodic lattice. Note that B. O. have been nevere observed in a natural crystal because the scattering time is much shorter than the Bloch period. Only observed in semiconductor superlattices where tbloch is 600 fs.

20. Summary • Why a UQS could be a powerfull device for the study of condensed matter systems • Atoms in optical lattices are optimum candidate for realizing a UQS • BEC of 39K, Feshbach spectroscopy and Bloch oscillations with a 39K BEC Outlook • Study Bloch oscillations in disordered potentials • Study the effect of the interaction on Anderson localization of an atomic wave in a disordered potential • 3D lattice with a more stable laser • Single atom addressing • Production of cold molecules in the ground state to add long range interaction

21. UQS

22. After a time T of Bloch Oscillations z pz pz z z Interferometric scheme: Bloch Oscillations ___________________________________________________________________ • External force F (in our case gravity) • The condensate is loaded in an array of potential wells • The condensate y is put in a coherent superposition of Wannier Stark fi states parametrized with the lattice site index. with interaction Interference contrast is destroyed by the interaction.