Interazioni e transizione superfluido-Mott

1. Interazioni e transizione superfluido-Mott

2. Interacting bosons in a lattice • SUPERFLUID • Long-range phase coherence • Poissonian number fluctuations • Gapless excitation spectrum • Compressible • MOTT INSULATOR • No phase coherence • No number fluctuations (Fock states) • Gap in the excitation spectrum • Not compressible Bose-Hubbard model for interacting bosons in a lattice:

3. Superfluid to Mott Insulator transition measuring coherence via matter-wave interference momentum distribution of the 87Rb atomic sample after expansion (LENS, 2006) first experimental demonstration in M. Greiner et al., Nature 415, 39 (2002)

4. Time-of-flight imaging P. Pedri et al., Phys. Rev. Lett.87, 220401 (2001)

5. Time-of-flight imaging M. Greiner et al., Nature 415, 39 (2002)

6. Superfluid-Mott transition M. Greiner et al., Nature 415, 39 (2002) measuring coherence after time-of-flight: superfluid-Mott transition

7. Superfluid-Mott transition M. Greiner et al., Nature 415, 39 (2002) reversible quantum phase transition Restoring phase coherence from a Mott insulator

8. Collapse & Revival M. Greiner et al., Nature 419, 51 (2002)

9. Excitation spectrum Example: weakly-interacting BEC Bogoliubov spectrum Small momentum k  collective excitations, phonons Large momentum k single particle spectrum

10. BEC Excitation spectrum Excitation spectrum of a weakly interacting BEC in harmonic trap J. Steinhauer et al., PRL 88, 120407 (2002)

11. Excitation spectrum --- 2U U measurement of excitation spectrum via lattice modulation (T. Stöferle et al., PRL 92, 130403 (2004)) Mott Insulator spectrum

12. Excitation spectrum M. Greiner et al., Nature 415, 39 (2002) application of a magnetic field gradient

13. In-situ density measurement N. Gemelke et al., Nature 460, 995 (2009). in-situ imaging of the density distribution incompressible central region with 1 atom/site

14. Quantum information

15. Qubits Quantum bit (qubit) coherent superposition

16. Entanglement Entangled states

17. Quantum gates via ultracold collisions Quantum Logic via the Exchange Blockade in Ultracold Collisions D. Hayes, P. Julienne, I. Deutsch, PRL 98, 070501 (2007) Example of implementation of a quantum gate for identical fermionic particles: Symmetrization of the wavefunction:  collisional phase-shift no collisional phase-shift Implementation of the gate with fidelity ~ 1

18. Quantum gates via ultracold collisions Controlled exchange interactions between pairs of neutral atoms in OL M. Anderlini et al., Nature448, 452 (2007) Experimental realization of the exchange phase-shift in a lattice of double wells:

19. Detecting correlations

20. Hanbury-Brown & Twiss effect correlations between joint probability at detector positions 2 interference between quantum-mechanical paths of identical particles U. Fano, Am. J. Phys. 29, 539 (1961)

21. HBT interferometry in quantum gases absorption image of a Mott Insulator state d approx. 50000 detectors in a single image!

22. Noise correlations

23. Noise interferometry: bunching for bosons (Mott) S. Foelling et al., Nature 434, 481 (2005)

24. Noise interferometry: antibunching for fermions T. Rom et al., Nature 444, 733 (2006)

25. Detecting correlations M. Schellekens et al., Science 310, 648 (2005) Time-resolved time-of-flight detection of metastable He atoms

26. Bunching for bosons (thermal) M. Schellekens et al., Science 310, 648 (2005)

27. Antibunching for fermions T. Jeltes et al., Nature 445, 402 (2007) He-4 He-3