Presentation on theme: "Creating new states of matter: Selim Jochim MPI für Kernphysik and Universität Heidelberg Experiments with ultra-cold Fermi gases Henning Moritz ETH Zürich."— Presentation transcript:
Creating new states of matter: Selim Jochim MPI für Kernphysik and Universität Heidelberg Experiments with ultra-cold Fermi gases Henning Moritz ETH Zürich
Major breakthroughs in this field have made this field an exciting one in the past decade Fermi Superfluidity, Crossover to a gas of Bosons (weakly bound molecules) With tunable interactions: Model system for High-T C superconductors, Neutron stars, Quark-Gluon Plasma and more …. Introduction
What is an ultracold quantum gas? Gas shows quantum effects when the wave packets start to overlap
Fermions and Bosons: Fermi energy E F =k B T F Bose-Einstein condensation Degenerate Fermi gas BosonsFermions At zero temperature ….
What makes ultracold gases special? Compare with superfluids, like He, or superconductors: Density is way lower -> dilute gas makes description very simple Lab-in-a-trap type of systems with many easy-to-use knobs, such as temperature confinement (single well, periodic …), Interactions (even do controlled chemistry!)
First BEC experiments JILA Boulder 1995 MIT 1995 Rb Na
Fermi degenerate gases Two isotopes of Lithium in the same trap in thermal equilibrium
Superfluid Fermi Gases: Molecular condensates Look like a normal BEC Are normal BECs A little bit of cheating?
Observe superfluidity A rotating superfluid cloud needs to exhibit vortices
What will the course be about? How do we make/manipulate/detect ultracold gases –Laser cooling –Trapping –Evaporative cooling in conservative potentials –Detection and manipulation of ultracold atoms Today:
How to cool a Fermi gas - special challenges, - like forbidden collisions - Pauli blocking, etc. Scattering length Concept of Feshbach resonance to tune interactions make things interesting! Making ultracold molecules, BEC of molecules 2 nd day
3 rd day BEC of molecules BEC/BCS crossover Gap, collective excitations/ Cooper pairs superconductivity Vortices Imbalanced spin mixtures
4 th day Condensed Matter Physics with atoms? Periodic potentials, bosonic Case: Mott isolator Fermions: The Fermi Surface Interactions of Fermions in optical lattices Low dimensional systems Future directions with optical lattices Final discussion
Spontaneus light force: Frisch 1933: Deflection of a sodium beam using a Na-lamp: photon momentum (recoil) scattering rate Lithium: acceleration:
Model: 2 level atom: Line width s 0 : saturation Spontaneous scattering rate:
Optical molasses Doppler shift: blue detuned red detuned
Harold Metcalf (1986) Optical molasses!
How cold can we get? Spontaneous emission causes heating, due to randomly distributed emission. stationary state when heating rate=cooling rate minimal, when T = /2k B a few MHz T min typically 0.1…0.25 mK Prediction by Hänsch, Schawlow, Wineland, Dehmelt (1975)
Much lower temperatures observed!!! Time-of flight measurement:
Sub Doppler and sub recoil cooling So far we only considered a 2-level atom, typically, there are several Zeeman-sublevels. different Zeeman-sublevel experience different light shifts, dressed atom picture: Rabi frequency
Sisyphus cooling Light shift on Zeeman level (Clebsch Gordan coefficients) Counter propagating Laser beams with orthogonal polarization create a polarization grating:
Sideband cooling Condition for sideband cooling: Lamb-Dicke regime: Localize atoms better than x<< |g> |e> Quantization of trap potential Used in this way in ion traps!
Raman-sideband cooling e.g. in optical lattice! Raman-coupling Optical pumping A little more complicated, but universal!
Magneto-optical trap Optical molasses + magnetic field + polarisation:
MOT in 3D Quadrupole field through anti-Helmholtz coils, Counterpropagating laser beams in x,y,z, with proper polarization
How to load a MOT? Most simple technique: Load atoms from vapor! but: trapping velocity is limited to v a few 10 m/s, e.g. Rb., Cs. only a small fraction of the Boltzmann distribution can be trapped! also: atomic vapor limits the vacuum and causes trap loss (Especially critical for subsequent experiments!)
Loading from and atomic beam Atoms with a low vapor pressure: need to be evaporated from an oven. Slow an atomic beam? make use of spontaneous light scattering! (need to compensate Doppler shift!)
Zeeman slower Make use of Zeeman tuning: Apply magnetic field, such that E.g.: Li, Na Extend MOT to obtain slow atomic beam
(Density) limitation of the MOT What limits the (phase space) density in a MOT? Collisions with background gas ( vapor cell!) Light assisted collisions: e.g.: photo association! max. phase space density: 10 -5
How to obtain a quantum gas? So far: No success with exclusively optical cooling, but it provides excellent starting conditions Also: No success without optical cooling!!!
Conservative potentials for atoms Spatially varying magnetic field (magnetic trap): trap polarized atoms Far detuned laser fields ( induce dipole)
Magnetic trap Simplest configuration: quadrupole field (MOT) There is a problem, when the atoms get colder: B µB Majorana spin flips at B=0! Orientation of the magnetic field should not change faster than Larmor frequency
Ways around the zero: Time Orbiting Potential (TOP) Trap: Rotate zero of magnetic field fast enough such that the atoms dont take notice … …but slower than the Larmor frequency Time averaged potential!
Trap with offset field Ioffe-Bars with minimum (0G) in the center Pinch-coils produce an offset field and confine the atoms axially Ioffe Pritchard-trap
Optical traps (dipole force) Electric field induces dipole: E p
oscillating E-Feld E-field oscillates slower than resonance (red detuned light) dipole oscillates in phase Intensity maximum is trap (e.g. focus) E-field oscillates faster than resonance (blue detuned) Dipole phase is shifted by Intensity minimum is trap (e.g. hollow beam)
optical dipole interaction optical dipole force F dip = - U dip optical dipole potential optical dipole force F dip = - U dip optical dipole potential dipole potential scattering rate redred detuning 0 blueblue detuning 0 attraction repulsion For most applications: Need to go for very large detunings!
Why an optical trap? Potential is independent of spin state, magnetic field Very flexible opportunities to shape potentials, e.g. optical lattice Challenge: Typically, very large intensities are required to create the desired potential Also, photon scattering has to be taken care of!
Evaporative cooling Idea: Remove hottest atoms, while thermal equilibrium is maintained Important figure of merit: Gain in phase space density per loss of particles
EV cooling techniques In magnetic traps, use RF fields to convert atoms to a high-field seeking state at distinct magnetic field (i.e. position) position potential
In optical traps, reduce trap depth by reducing laser power. EV cooling techniques
Evaporative cooling Important quantities: Truncation parameter: Ratio of good to bad collisions: Bad collisions: E.g. dipolar relaxation, three-body recombination ….
Optimize EV cooling Efficiency limited by Collision rate Losses Background gas (increase collision rate) Binary collisions (scales just as EV cooling) Three body collisions (go for low density) Heating Photon scattering Parametric heating Anti-evaporation (e.g. Majorana spin flips) Trap geometry
Optimize EV cooling Geometry matters when the gas becomes (close to) hydrodynamic, e.g. trap frequency < collision rate: Example for inefficient geometry: Magnetic trap with gravitational sag
Which trap to use? Magnetic trap: Easy evaporation, Well defined potential Constant trap frequency Optical trap More freedom with trap potentials Can trap atoms in absolute (magnetic) ground state Have to take care of photon scattering (use far off- resonant traps!)
Absorption imaging resonant cross section of the atoms ~ 2 (depends on Clebsch-Gordan coefficients) Considerable absorption already at very low density: Image shadow on CCD! Important advantage: See ALL scattered photons
Absorption imaging In the same way, measure momentum distribution: Time of flight (TOF): measure spatial distribution after a certain time of flight This is the quantity we measure
Challenges when cooling Fermions Identical ultracold particles do not collide (s-waves). Pauli blocking makes cooling of a degenerate Fermi gas very inefficient. Also: Very low temperatures required to observe superfluidity:
Idea: Use Bosons to cool Fermions Bosons can be cooled with established technology Not the first degenerate Fermi gas, but a very instructive one: 6 Li cooled by bosonic 7 Li (Rice U., ENS Paris): Difference of just one neutron makes all the difference!
6 Li+ 7 Li cooled together Two MOTs for the two isotopes (10GHz isotope shift) Magnetic trap traps both isotopes …
Challenges to achieve very low T Bosons condense to BEC -> heat capacity drops to zero, no more cooling effect Interactions between Fermions are necessary to observe interesting physics -> spin mixture is needed To study pairing effects, wish to tune pairing energy! All of this: Tomorrow by Henning Moritz
Literature Metcalf and van der Straaten: Laser cooling and trapping Ketterle, Durfee and Stamper-Kurn Making, probing and understanding Bose-Einstein condensates