Creating new states of matter:

Selim JochimMPI für Kernphysik andUniversität Heidelberg

Experiments with ultra-cold Fermi gases

Henning MoritzETH 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-TC 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

2

2dBB

h

mk T 3 1dBD n

Fermions and Bosons:

FermienergyEF=kBTF

Bose-Einstein condensation Degenerate Fermi gas

Bosons Fermions

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

JILABoulder

1995

MIT1995

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 BECAre normal BECsA 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

2nd day

3rd day

• BEC of molecules• BEC/BCS crossover• Gap, collective excitations/ Cooper pairs

superconductivity• Vortices• Imbalanced spin mixtures

4th 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:

kF

/hk photon momentum (recoil)

scattering rate

Lithium:

3419

9

6.63 10 Js6MHz 10 N

671 10 m

xF

x

acceleration:

175 2 5

26

6 10 N/ 6 10 / 10

10 kg

xa F m x m s g

Model: 2 level atom:

g

e

0 02

0 0

s( )

2 1 s [2( )/ ]

0ω

Line width

s0: saturation

Spontaneous scattering rate:

Optical molasses

• Doppler shift: Doppler k v

v

2 0g s 1 0e ( )( )kF k kvv

blue detunedred detuned

Doppler molasses:

20

20

8

[1 (2 ) ]tot

vk sF

s

( 0; )kv

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, whenkin,min/ 2 / 2E

T = /2kB

≈ a few MHz Tmin typically 0.1…0.25 mK

Prediction by Hänsch, Schawlow, Wineland, Dehmelt (1975)

Much lower temperatures observed!!!

Time-of flight measurement:

,n g1,n e

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:

2 2E

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

h

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!

h

Raman-couplingOptical 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 B kv E.g.: Li, Na

“Extend” MOT to obtain slow atomic beam

MOT ….

(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)

U B

21/ 2U E I p E

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

dd /Lt B

Ways around the zero:

Time Orbiting Potential (TOP) Trap:

• Rotate zero of magnetic field fast enough such that the atoms don’t 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 fieldand confine the atoms axially

Ioffe Pritchard-trap

Optical traps (dipole force)

• Electric field induces dipole:

E p

1/ 2U p E

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

Fdip = - Udip

optical dipole potential

optical dipole force

Fdip = - Udip

optical dipole potential

dipole potential

scattering rate

0

„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 d ln( )

d ln( )

D

N

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

pote

nti

al

• 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:

U

kT

loss

el

R

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)

• HeatingPhoton scatteringParametric heatingAnti-evaporation (e.g. Majorana spin flips)

• Trap geometry

Efficiency

• Graph: Typical efficiencies ….

truncation parameter

EV

coolin

g e

ffici

en

cy

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

( , , ) (0

, )( , ) absn x y z l x ytI I x y e

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:

C FF

~ exp2

T Tk a

Idea: Use Bosons to cool Fermions

• Bosons can be cooled with “established” technology

• Not the first degenerate Fermi gas, but a very instructive one:

• 6Li cooled by bosonic 7Li (Rice U., ENS Paris):

• Difference of just one neutron makes all the difference!

6Li+7Li 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”