Fundamental Physics with
Ultra-Cold Matter
From particle physics to condensed matter
Seth A. M. Aubin
University of Toronto, Canada
February 16, 2006
College of William and Mary
Outline
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 Fundamental Physics
 Constructing larger quantum systems.
 Exploring interactions inside atoms.
What’s Ultra-Cold Matter ?
mK
 Very Cold
μK
 Typically nanoKelvin – microKelvin
nK
 Atoms/particles have velocity ~ mm/s – cm/s
 Very Dense … in Phase Space
p
p
x
Different temperatures
Same phase space density
p
x
x
Higher
phase space density
Ultra-cold Quantum Mechanics
Quantum mechanics requires
p
Dx  Dp  /2
Dp
 fundamental unit of phase space volume
x
Dx  Dp  /2
Dx
 Quantum physics is important when
PSD ~ 1
Equivalent:
deBroglie wavelength ~ inter-particle separation
ndeBroglie ~ 1
Boltzmann
Quantum régime
régime
Quantum Statistics
Bosons
Fermions
 symmetric multi-particle
wavefunction.
 anti-symmetric multi-particle
wavefunction.
 Integer spin: photons, 87Rb.
 ½-integer spin: electrons,
protons, neutrons, 40K.
 probability of occupying a
state |i> with energy Ei.
P( Ei ) 
 probability of occupying a
state |i> with energy Ei.
1
e
( Ei   ) / kT
P( Ei ) 
1
NBEC
1
Ni
Ni
Ei
EF
1
e ( Ei   ) / kT  1
Ei
How do you make ULTRA-COLD matter?
Two step process:
1. Laser cooling
 Doppler cooling
 Magneto-Optical Trap (MOT)
2. Evaporative cooling
 Magnetic traps
 Evaporation
Doppler Cooling
Lab frame
excited

v
ground
Atom’s frame
 ' 
 ' 
Lab frame, after absorption
v-vrecoil
2
87Rb:  = -
m/s
Vrecoil
=
6
mm/s
Absorb a photon  atom gets k momentum kick.
I = Isat
 Repeat process at 107 kicks/s  large deceleration.
 Emitted photons are radiated symmetrically
Vdoppler ~10docm/s
not affect motion on average
m/s
Magneto-Optical Trap (MOT)
Problem:
Doppler cooling reduces momentum spread of atoms only.
 Similar to a damping or friction force.
 Does not reduce spatial spread.
 Does not confine the atoms.
Solution:
Spatially tune the laser-atom detuning with the Zeeman shift from a
spatially varying magnetic field.
B, 
z
~10 G/cm
~14 MHz/cm
Magneto-Optical Trap (MOT)
Magneto-Optical Trap (MOT)
10-13
10-6
1
thermal
atoms
Laser
cooling
quantum
behavior
~ 100 K
???
PSD
Magnetic Traps
Interaction between external magnetic field
and atomic magnetic moment:


U   B
B
For an atom in the hyperfine state F, mF
cos  mF / F
Energy = minimum


U  g F mF  B B
|B| = minimum
Micro-magnetic Traps
Advantages of “atom” chips:
 Very tight confinement.
 Fast evaporation time.
 photo-lithographic production.
 Integration of complex trapping
potentials.
 Integration of RF, microwave and
optical elements.
 Single vacuum chamber apparatus.
Iz
Evaporative Cooling
Remove most energetic
(hottest) atoms
Wait for atoms to
rethermalize among
themselves
Wait time is given by the elastic collision rate kelastic = n  v
Macro-trap: low initial density, evaporation time ~ 10-30 s.
Micro-trap: high initial density, evaporation time ~ 1-2 s.
Evaporative Cooling
Remove most energetic
(hottest) atoms
P(v)
Wait for atoms to
rethermalize among
themselves
Wait time is given by the elastic collision rate kelastic = n  v
Macro-trap: low initial density, evaporation time ~ 10-30 s.
Micro-trap: high initial density, evaporation time ~ 1-2 s.
v
RF Evaporation

In a harmonic trap:
B
RF

B
 RF frequency determines energy at which
spin flip occurs.
 Sweep RF between 1 MHz and 30 MHz.
 Chip wire serves as RF B-field source.
Outline
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 Fundamental Physics
 Constructing larger quantum systems.
 Exploring interactions inside atoms.
Bose-Einstein Condensation of 87Rb
10-13
thermal
atoms
10-6
MOT
magnetic
trapping
105
1
evap.
cooling
PSD
BEC
Evaporation Efficiency
d ln(PSD)
 3.95  0.1
d ln(N)
87Rb
BEC
RF@1.740 MHz:
RF@1.725 MHz:
RF@1.660 MHz:
N = 7.3x105, T>Tc
N = 6.4x105, T~Tc
N=1.4x105, T<Tc
87Rb
BEC
RF@1.740 MHz:
RF@1.725 MHz:
RF@1.660 MHz:
N = 7.3x105, T>Tc
N = 6.4x105, T~Tc
N=1.4x105, T<Tc
Surprise! Reach Tc with
only a 30x loss in number.
(trap loaded with 2x107 atoms)
 Experimental cycle = 5 - 15 seconds
Fermions: Sympathetic Cooling
Problem:
Cold identical fermions do not interact due
to Pauli Exclusion Principle.
 No rethermalization.
 No evaporative cooling.
Solution: add non-identical particles
 Pauli exclusion principle
does not apply.
We cool our fermionic 40K atoms
sympathetically with an 87Rb BEC.
“Iceberg”
BEC
Fermi
Sea
Sympathetic Cooling
104
102
100
105
106
107
Cooling Efficiency
2
10
4
10
106
108
D ln(PSD)
8
D ln(N)
Below TF
0.9 TF
0.35 TF
 For Boltzmann statistics and a harmonic trap,
 For ultra-cold fermions, even at T=0,
1
2
1
2
mv2  12 kT  v  T
mv  EF
2
EF
 vF  2
m
Pauli Pressure
Fermi
Boltzmann
Gaussian Fit
First time on a chip !
arXiv: cond-mat/0512518
Outline
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 Fundamental Physics
 Constructing larger quantum systems.
 Exploring interactions inside atoms.
So What ?
What can you do with ultra-cold atoms ?
Larger ultra-cold quantum systems:
 Condensed matter physics
 Ultra-cold chemistry
Probe fundamental forces inside the atom:
 Parity violation in atoms and molecules
 Electron-dipole moment measurements
Applied Physics:
 Atomic clocks
 Matter-wave interferometry
What’s Special about
Ultra-cold Atom ?
Extreme Control:
 Perfect knowledge (T=0).
 Precision external and internal control with magnetic, electric, and
electromagnetic fields.
Interactions:
 Tunable interactions between atoms with a Feshbach resonance.
 Slow dynamics for imaging.
Narrow internal energy levels:
 Energy resolution of internal levels at the 1 part per 109 – 1014.
 100+ years of spectroscopy.
 Frequency measurements at 103-1014 Hz.
 Ab initio calculable internal structure.
Condensed Matter Simulations
IDEA: use ultra-cold atoms to simulate electrons in a crystal.
 useful if condensed matter experiment is difficult or theory is
intractable.
Advantages:
 Atoms are more easily
controlled and probed than
electrons.
 An optical lattice can
simulate a defect-free crystal
lattice.
 All crystal and interaction
parameters are easily tuned.
The Hubbard Model
 Model of particles moving on a lattice.
 Simulates electrons moving in a crystal.
H  t
 a
{i , j },

i ,

a j ,  ai , a j ,  U  ai, ai , ai, ai ,
Hopping term, kinetic energy
i
Particle-particle interaction
Optical Lattice
Laser standing wave creates
an optical lattice potential for
atoms.
Hopping term, t
 control with laser intensity
Use a Feshbach resonance to
control atom-atom interaction, U.
 tune with a magnetic field.
Bose-Hubbard Model
IDEA: Put a BEC in a 3D optical lattice.
 Look for Mott-Insulator transition by varying ratio
U/t.
 Gas undergoes a quantum phase transition from a
superfluid to an insulating state at U/t ~ 36 (cubic lattice).
Excellent agreement with theory !!!
Fischer et al., Phys. Rev. B 40, 546 (1989).
U/t~0
U/t < 36 U/t ~ 36 U/t > 36
Greiner et al., Nature 415, 39-44 (2002).
Jaksch et al., Phys. Rev. Lett. 3108 (1998).
Fermi-Hubbard Model
IDEA: do the same thing with fermions !!!
 Put a degenerate Fermi gas in an optical lattice.
 See what happens.
Theory:
 Very hard  not yet solved analytically.
 Numerical simulations are difficult due to Fermi Sign Problem.
 Computation is “NP hard”.
d-wave
superconductor !
Possible model for
high-Tc materials
n=filling fraction
Hofstetter, Cirac, Zoller, Demler, Lukin
Phys. Rev. Lett. 89, 220407 (2002).
Figure from K. Madison, UBC.
Fundamental Interactions
in atoms and molecules
Fundamental Interactions:
 Weak Interaction  Parity Violation.
 Nuclear anapole moment.
?
 Electron-neutrino correlations in
-decay.
 Time-reversal symmetry breaking
 Searching for Super-symmetric
extensions of the Standard Model.
Use a big accelerator
… or Exotic atoms and molecular states:
 Rare or artificial isotopes (Francium, Potassium isomer, etc…).
 Polar molecules … larger molecules.
Cold and ultra-cold atoms are very useful.
What’s Parity Violation ?





d2r
d 2 ( r)
F  ma  m 2  m
 F
2
dt
dt
Parity transformation:
x  x
 Force is parity odd
y  y
z  z
2
P
e
H
 
2m R

 2
( P)
e
  H
2m
R
 Energy or Hamiltonian is parity even.
z
x
x
y
Right-handed
coordinate system
y
z
Left-handed
coordinate system
Physics does not change,
except for  sign
“I'll bet you only fifty to one
you don't find anything.”
-- Richard Feynman to Norman Ramsey,
on a proposed experiment to search for Parity Violation (1956).
A Brief History of Parity Violation
Early 1956: Feynman bets against Parity Violation.
October 1956: T.-D. Lee and C. N. Yang propose that
Parity may be violated.
January 1957: C.-S. Wu, E. Ambler, R. Hudson, R. Hayward,
and D. Hoppes observe parity violation in the -decay
of spin polarized Cobalt-60.
1957: T.-D. Lee and C. N. Yang win the Nobel Prize in
Physics for the discovery of Parity Violation.
-decay through W-- charged electroweak current
Weak Neutral Currents in Atoms
1974: M.-A. Bouchiat and C. Bouchiat
note that in heavy atoms:
3
S 
S


P
,
with


Z
PV
Spin independent effect!
Z = # of protons
Nuclear Anapole Moment:
  Z2.7
 
H anapole  I  P  parity odd
Spin dependent effect!
 ~ 10-10
in Francium (really small !)
Use a parity-forbidden transition!
“If it were really impossible,
they wouldn’t have bothered
to forbid it.”
-- Eric Cornell, paraphrasing Joseph Heller.
nS  nS  E1 transitio n
Parity forbidden
transition
Parity
Violation
Slightly allowed
transition
Atomic Physics Contribution
P.L. Anthony et al. (SLAC E158 collaboration),
Phys. Rev. Lett. 95, 081601 (2005).
Intro to Francium
Properties:
 Z = 87, heaviest alkali.
 Least stable of first 103
elements.
Fr
 Half-life ~ 1-20 minutes.
Artificially produced by
nuclear fusion reaction
18
O
+
@ 100 MeV
Au
Fr
215
neutrons
Francium MOT
PROBLEM: Accelerator produces only 106 Fr atoms/s.
 Very difficult to work with.
SOLUTION: Attach a Francium Magneto-Optical Trap to the accelerator.
 Cold Francium is concentrated in ~1 mm3 volume.
 With T < 100 K, Doppler broadening is negligible.
 Long integration times.
 Minimally perturbative environment (substrate free).
Francium MOT
PROBLEM: Accelerator produces only 106 Fr atoms/s.
 Very difficult to work with.
SOLUTION: Attach a Francium Magneto-Optical Trap to the accelerator.
 Cold Francium is concentrated in ~1 mm3 volume.
 With T < 100 K, Doppler broadening is negligible.
 Long integration times.
 Minimally perturbative environment (substrate free).
MOT collection efficiency ~ 1 %
MOT with ~105 210Fr atoms
S. A. et al., Rev. Sci. Instrum. 74, 4342 (2003).
Nuclear Anapole Moment
Nuclear anapole moment via parity violation  Unique probe of neutral current
electroweak interactions
inside
nucleus.
Anapole was first measured in
Cesium by the Wieman group
Wood et al.
Science 275, 1759 (1997).
Proton Anapole ?
Hasty et al., Science
290, 2117 (2000).
Meson-nucleon
couplings
[Figure from G. Gwinner, U. of Manitoba.]
Parity Violation
Atoms vs. Molecules
Atoms
Molecules
 Measure a “forbidden” parityviolating transition rate.
 Can also measure parity
violating energy splitting.
 114 (?) elements available.
 Chiral molecules are common.
 Easy to cool to ultra-cold
temperatures.
 Possible to cool to ultra-cold
temperatures.
 Easy to interpret parity violating
signals.
 Larger signals parity violating
signals.
Ultra-cold Chiral Molecules
 Chiral Molecules: need at least 4 atoms (example: H2O2).
 Parity violating energy splitting DE ~ 0.001–100 Hz.
 Favorable scaling: DE  Z5.
 Extremely high energy resolution required  ultra-cold molecules.
Right-handed H2O2
Left-handed H2O2
Summary
 Ultra-cold Matter
 BEC, Degenerate Fermions.
 Cooling and Trapping
 MOT, B-trap, evaporative cooling.
 Fermi-Hubbard model
 Parity violation and anapole moment
TRIUMF
FrPNC collaboration
TRIUMF – Vancouver, Canada
Professor G. Gwinner, Spokesperson, University of Manitoba
Professor G. D. Sprouse, SUNY Stony Brook
Dr. J. A. Behr, Research Scientist, TRIUMF
Dr. K. P. Jackson, Research Scientist, TRIUMF
Dr. M. R. Pearson, Research Scientist, TRIUMF
Professor L. A. Orozco, University of Maryland
Professor V. V. Flambaum, University of New South Wales
Dr. S. Aubin, Post-Doctoral Fellow, University of Toronto
Thywissen Group
S. Aubin
D. McKay
B. Cieslak
M. H. T. Extavour
S. Myrskog
A. Stummer
Colors:
Staff/Faculty
Postdoc
Grad Student
Undergraduate
L. J. LeBlanc
J. H. Thywissen
Thank You