Creating new states of matter:

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Creating new states of matter
Experiments with ultra-cold Fermi gases
Selim Jochim MPI für Kernphysik and Universität
Heidelberg
Henning Moritz ETH Zürich
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Introduction

• 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 .

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What is an ultracold quantum gas?

• Gas shows quantum effects when the wave packets
  start to overlap

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Fermions and Bosons
At zero temperature .
Bosons
Fermions
Fermi energy EFkBTF
Bose-Einstein condensation
Degenerate Fermi gas
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What makes ultracold gases special?

• Compare with superfluids, like He, or
  superconductors
• Density is way lower -gt 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!)

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First BEC experiments
JILA Boulder 1995
Rb
Na
MIT 1995
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Fermi degenerate gases
Two isotopes of Lithium in the same trap in
thermal equilibrium
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Superfluid Fermi Gases

• Molecular condensates

Look like a normal BEC Are normal BECs A little
bit of cheating?
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Observe superfluidity
A rotating superfluid cloud needs to exhibit
vortices
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What will the course be about?
Today

• How do we make/manipulate/detect ultracold gases
• Laser cooling
• Trapping
• Evaporative cooling in conservative potentials
• Detection and manipulation of ultracold atoms

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2nd day

• 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

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3rd day

• BEC of molecules
• BEC/BCS crossover
• Gap, collective excitations/ Cooper pairs ?
  superconductivity
• Vortices
• Imbalanced spin mixtures

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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

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Spontaneus light force
photon momentum (recoil)
scattering rate
Lithium
acceleration
Frisch 1933 Deflection of a sodium beam using a
Na-lamp
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Model 2 level atom
Spontaneous scattering rate
s0 saturation
G
Line width
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Optical molasses

• Doppler shift

red detuned
blue detuned
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Doppler molasses
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? Optical molasses!
Harold Metcalf (1986)
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How cold can we get?
Spontaneous emission causes heating, due to
randomly distributed emission. stationary state
when heating ratecooling rate minimal, when
T ??/2kB
? a few MHz ? Tmin typically 0.10.25 mK
Prediction by Hänsch, Schawlow, Wineland, Dehmelt
(1975)
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Much lower temperatures observed!!!
Time-of flight measurement
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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
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Sisyphus cooling

• Light shift on Zeeman level
• (Clebsch Gordan coefficients)

Counter propagating Laser beams with orthogonal
polarization create a polarization grating
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Sideband cooling
Quantization of trap potential
egt
Condition for sideband cooling Lamb-Dicke
regime Localize atoms better than Dxltlt l
ggt
Used in this way in ion traps!
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Raman-sideband cooling
Optical pumping
Raman-coupling
A little more complicated, but universal!
e.g. in optical lattice!
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Magneto-optical trap
Optical molasses magnetic field polarisation
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MOT in 3D
Quadrupole field through anti-Helmholtz
coils, Counterpropagating laser beams in x,y,z,
with proper polarization
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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!)

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Loading from and atomic beam
Atoms with a low vapor pressure ? need to be
evaporated from an oven.
(need to compensate Doppler shift!)
Slow an atomic beam?
? make use of spontaneous light scattering!
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Zeeman slower
Make use of Zeeman tuning
Extend MOT to obtain slow atomic beam
Apply magnetic field, such that
E.g. Li, Na
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MOT .
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(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
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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!!!

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Conservative potentials for atoms

• Spatially varying magnetic field (magnetic trap)
• ? trap polarized atoms
• Far detuned laser fields (?induce dipole)

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Magnetic trap

• Simplest configuration quadrupole field (MOT)
• ? There is a problem, when the atoms get colder

µB
Majorana spin flips at B0!
Orientation of the magnetic field should not
change faster than Larmor frequency
B
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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!

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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
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Optical traps (dipole force)

• Electric field induces dipole

E
p
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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 p
• Intensity minimum is trap (e.g. hollow beam)

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optical dipole interaction
red detuning (wltw0)
blue detuning (wgtw0)
optical dipole force Fdip - ?Udip optical
dipole potential
attraction
repulsion
For most applications Need to go for very large
detunings!
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Why an optical trap?

• Challenge
• Typically, very large intensities are required
  to create the desired potential
• Also, photon scattering has to be taken care of!

• Potential is independent of spin state, magnetic
  field
• Very flexible opportunities to shape potentials,
• ? e.g. optical lattice

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Evaporative cooling

• Idea Remove hottest atoms, while thermal
  equilibrium is maintained

Important figure of merit Gain in phase space
density per loss of particles
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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)

potential
position
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EV cooling techniques

• In optical traps, reduce trap depth by reducing
  laser power.

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Evaporative cooling

• Important quantities
• Truncation parameter
• Ratio of good to bad collisions

Bad collisions E.g. dipolar relaxation,
three-body recombination .
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Optimize EV cooling

• Efficiency limited by
• Collision rate
• LossesBackground 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

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Efficiency

• Graph Typical efficiencies .

EV cooling efficiency
truncation parameter h
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Optimize EV cooling

• Geometry matters when the gas becomes (close to)
  hydrodynamic, e.g. trap frequency lt collision
  rate
• Example for inefficient geometry
• Magnetic trap with gravitational sag

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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!)

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Absorption imaging

• resonant cross section of the atoms l2
• (depends on Clebsch-Gordan coefficients)
• Considerable absorption already at very low
  density

Image shadow on CCD!
Important advantage See ALL scattered photons
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Absorption imaging
This is the quantity we measure
In the same way, measure momentum
distribution Time of flight (TOF) measure
spatial distribution after a certain time of
flight
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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

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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!

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6Li7Li cooled together

• Two MOTs for the two isotopes (10GHz isotope
  shift)
• Magnetic trap traps both isotopes

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Challenges to achieve very low T

• Bosons condense to BEC -gt heat capacity drops to
  zero, no more cooling effect
• Interactions between Fermions are necessary to
  observe interesting physics -gt spin mixture is
  needed
• To study pairing effects, wish to tune pairing
  energy!
• All of this Tomorrow by Henning Moritz

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Literature

• Metcalf and van der StraatenLaser cooling and
  trapping
• Ketterle, Durfee and Stamper-KurnMaking,
  probing and understanding Bose-Einstein
  condensates