1. Optical Lattices 1 Greiner Lab Winter School 2010 Florian Huber 02/01/2010

2. Outline Solid State Physics How to make optical lattices How to diagnose optical lattices

3. Solid State Physics Phonons Lattice vibrations Thermal properties (isolators) Mediating electron-electron interaction in type 1 (=BCS) superconductors Acoustic and optical phonons Electrons Electrical and thermal properties Semiconductors Magnetism Quantum Simulation

4. Lattice Atoms in solids arranged in regular pattern In general: 3D = 14 Bravais lattices… … but we usually only have to deal with simple cubic (s.c.) lattices x y

5. Free Electrons High School Physics: Metal Reduction of energy by delocalizing outer electrons (more or less) free electron gas

6. Bloch’s Theorem Delocalized electrons “feel” periodic potential, thus their wave function has to inherit periodicity a Free ElectronsElectrons in Per. Pot. Wave function Dispersion

7. Band Gap 1 st Brillouin Zone Restrict to 1 st BZ x Standing wave 2 has higher probability near the ion cores  higher energy than 1  band gap

8. From free to tightly bound Lattice Depth Harmonic oscillator energies (Solid state systems: Atomic energy levels)

9. Bloch VS. Wannier Bloch waves: – Delocalized – Plane-wave-like Deeper lattices better described by Wannier functions: – Localized on each lattice site – Closer to QHO Eigenstates – Intuitive picture for J in Bose-Hubbard

10. Bloch Oscillations

11. Optical Dipole Force

12. One Dimension Intensity Here: red detuned

13. More dimensions 1D2D3D “Pancakes” “Tubes” D>1: Typically orthogonal beams are not interfering.  different frequency or orthogonal polarizations Otherwise: Relative phase matters! Simple-cubic

14. Harmonic Confinement In D>1 configuration: – Additional (anti-) confinement due to Gaussian profile of orthogonal laser beams. Red detuned: Blue detuned: Potential

15. Realization

16. Recycling Recycle a beam to make lattice along another axis – Beams are interfering!  Different lattice pattern

17. Adiabatic loading of superfluid (slower than what? Tunneling?) Sudden release and TOF: Matter wave point sources on each lattice site BEC in Lattice 1/ext. confinement 1/lattice spacing 1/f(Tunneling)

18. Lattice Pulsing Depth measurement Cycle: – BEC (superfluid) – Lattice suddenly pulsed on – Lattice suddenly switched of again – Image diffraction pattern in TOF – Repeat and vary intensity

19. Lattice Pulsing: Grating Picture Position dependent AC Stark shift of lattice imprints a phase pattern into BEC depending of the intensity/duration of the pulse (thin-grating)

20. Lattice Pulsing: Band Picture Projection Time evolution TOF Lattice On Lattice Off

21. Lattice Pulsing: Raman Picture S P

22. Bragg Scattering

23. Lattice Pulsing: Math Bessel Proportional to lattice depth

24. Lattice Pulsing: Pictures

25. Parametric Heating

26. Band Mapping Adiabatic Ramp Down of Lattice Depth preserves the quasi-momentum 1 st BZ

27. Band Mapping Increase lattice depth

28. Band Mapping: Higher Bands Why only every other band?