1. Experiments with Fermi e Bose atomic gases in optical lattices Giovanni Modugno LENS, Università di Firenze, and INFM XXVII Convegno di Fisica Teorica, Cortona, May 2005

2. Outline of the talk Production and properties of atomic quantum gases; optical lattices Experiments with Bose-Einstein condensates: superfluid transport, instabilities and localization driven by interactions Experiments with Fermi gases: fundamental transport phenomena and applications Future directions Motivations Ultracold atomic gases in optical lattices are potentially a powerful model system to study condensed-matter problems (almost everything can be easily tuned) Interesting applications beyond condensed matter are arising Introduction

3. Roati et al. Phys.Rev. Lett. 89, 150403 (2002). 145 nK 110 nK 80 nK 40 K 87 Rb fermions bosons Laser cooling in magneto-optical traps: T =10  K Evaporative/sympathetic cooling in magnetic traps: T =10nK Typical parameters: N = 10 5 -10 7 n =10 12 -10 14 cm -3 l = 10-1000  m T min =0.1 T F, 0.1 T c Production methods Detection of momentum distribution by absorption imaging with resonant light

4. Molecular interaction between neutral atoms: contact interaction -Even waves for identical bosons, odd waves for identical fermions - All waves with l  0 are thermally suppressed as E 2l No interactions between identical fermions below 100  K De Marco and Jin, Phys. Rev. Lett. 1999 Ultracold collisions

5. Magnetically tunable resonances tunable interaction in s, p, and other waves observed or expected for all alkali species (both homo- and hetero-nuclear) Fano-Feshbach resonances

6. Molecules formation at Fano- Feshbach resonances Bose-Einstein condensation of molecules JILA, Innsbruck, ENS, MIT, Rice University Molecules formation and Cooper pairing in Fermi gases F. Chevy and C. Salomon, Physics World, March 2005 Condensation of Cooper pairs

7. Optical dipole potential: 1D optical lattice: z Optical lattices Natural energy and momentum scales: = 1  m, q B = 5 mm s -1, E R = 100 nK, U = 1-100 E R Cubic lattices with various dimensionalities 1D, 2D, 3D, other geometries, lattices with large spacing 1-10  m, … x x ER0ER0 ER0ER0 q q -q B +q B

8. Bose gases in optical lattices Superfluidity and interactions in periodic potentials macroscopic transport at low interaction strengths insulating phases due to interactions

9. Gas di Bose in reticoli ottici: trasporto superfluido ___________________________________________________________________ 0 ms 20 ms 40 ms 60 ms 80 ms BEC Thermal cloud Transport of a superfluid Collective dipole oscillations F. Cataliotti, et al. Science 293, 843 (2001).

10. L. Fallani, et al. Phys. Rev. Lett. 93, 140406 (2004). Band spectroscopy and dynamical instabilities Optical lattices can be put in motion: Spectroscopy of the lattice band dispersion with a BEC What is the role of atomic interactions?

11. Band spectroscopy and dynamical instabilities What is the role of atomic interactions? L. Fallani, et al. Phys. Rev. Lett. 93, 140406 (2004).

12. SUPERFLUID PHASE 1.Long-range phase coherence 2.High number fluctuations 3.No gap in the excitation spectrum MOTT INSULATOR PHASE 1.No phase coherence 2.Zero number fluctuations 3.Gap in the excitation spectrum 4.Vanishing superfluid fraction 5.Vanishing compressibility (M. Greiner et al., Nature 415, 39 (2002)) Bose-Hubbard Hamiltonian Localization in a Mott insulator

13. Fermi gases in optical lattices Identical fermions: an ideal gas in a perfect periodic potential transport properties of a perfect crystal of atoms applications

14. Gas di Bose in reticoli ottici: trasporto superfluido ___________________________________________________________________ Transport of a non interacting Fermi gas Collective dipole oscillations s=7 s=0 Fermions remain trapped on the side of the harmonic potential

15. s=5 x E Ott, et al. Phys. Rev. Lett. 93, 120407 (2004), Rigol and Muramatsu, Phys.Rev. A 63, (2004), Hooley and Quintanilla, Phys. Rev. Lett. 93,080404, (2004). An ideal crystal is an insulator. EFEF Transport of a non-interacting Fermi gas

16. 0100200300400500600 100 1000 10000  BO decay time (ms) collisional rate (s ) Pezzè et al., Phys. Rev. Lett. 93, (2004); Ott et al., Phys. Rev. Lett. 92, 160601 (2004). ideal conductorreal conductor Tuning collisions in a boson-fermion mixture: crossover from an ideal conductor (that behaves like an insulator) to a real conductor Esaki-Tsu model for electrons in superlattices Collision-induced transport

17. s=5 RF sweep x E Atoms in delocalized states can be selectively removed with a RF knife Ott, et al., Phys. Rev. Lett. 93, 120407 (2004). Spectroscopy of localized states

18. Applications quantum computing atom interferometry for force sensing

19. Fermi Fermi: potential-induced localization Two localized particle per lattice site Loading procedure confines defects to the outer shell Tunable interactions between two states via F-F resonances Quantum registers: Bose vs Fermi What is needed: Macroscopic array of indidually addressable qubits Lowest possible number of defects Controllable, coherent interactions to perform operations Bose Bose: interaction-induced localization One localized particle per lattice site Controllable interactions between neighbouring sites via spin-selective lattices

20. q -q B +q B Bloch oscillations Semiclassical picture: Bloch oscillations Wannier-Stark states in a lattice tilted by gravity: interference Their interference oscillates: Wannier-Stark states and Bloch oscillations

21. Time-resolved Bloch oscillations of trapped, non-interacting fermions G. Roati, et al., Phys. Rev. Lett. 92, 230402 (2004). Bloch oscillations

22. a force sensorhigh spatial resolution Fermions trapped in lattices: a force sensor with high spatial resolution ( presently 50  m, but no fundamental limitations down to a few lattice sites) Bloch oscillations

23. Casimir-Polder potential in proximity of a dielectric surface I. Carusotto, L. Pitaevskii, S. Stringari, G. Modugno, M. Inguscio, cond-mat/0503141. Features: high resolution in presence of gravity direct measurement of forces low sensitivity to gradients high sensitivity (10 -7 g) Applications: atom-surface interactions out of thermal equilibrium possible deviations from Newton’s gravitational law at short distances Force sensing at the micrometer lengthscale

24. S. Dimopulos and A. A. Geraci, Phys. Rev. D 68, 124021 (2003) 10 -10 g 10 -7 g Search for non newtonian forces

25. Bose and Fermi gases in 1D optical lattices phenomenology of the band transport, transport of bosonic and fermionic superfluids fermionic Bloch oscillator: application to high precision study of fundamental phenomena Bose, Fermi and Fermi-Bose gases in 2D and 3D optical lattices condensed matter physics: Mott insulators, high Tc superfluidity, … low dimensionality systems: Luttinger liquids, BEC-BCS, … applications to quantum computing Optical lattice and random potentials Anderson localization, Bose and Fermi glasses, … BEC-BCS in presence of disorder Future directions Fermi surface in a 2D lattice

26. Estefania De Mirandes, Leonardo Fallani, Francesca Ferlaino, Vera Guarrera, Iacopo Catani, Luigi De Sarlo, Jessica Lye, Giacomo Roati, Herwig Ott Chiara Fort, Francesco Minardi, Michele Modugno Giovanni Modugno, Massimo Inguscio The quantum gas team at LENS