Quantum Physics
&
Ultra-Cold Matter
Seth A. M. Aubin
Dept. of Physics
College of William and Mary
December 16, 2009
Washington, DC
Outline
 Quantum Physics: Particles and Waves
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 What can you do with ultra-cold matter
Quantum Physics
Summary or “take home message”:
1. It’s weird
 defies everyday common sense.
Quantum Physics
Summary or “take home message”:
1. It’s weird
 defies everyday common sense.
2. LIGHT behaves as both a PARTICLE and a WAVE.
Quantum Physics
Summary or “take home message”:
1. It’s weird
 defies everyday common sense.
2. LIGHT behaves as both a PARTICLE and a WAVE.
3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE.
Quantum Physics
Summary or “take home message”:
1. It’s weird
 defies everyday common sense.
2. LIGHT behaves as both a PARTICLE and a WAVE.
3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE.
4. If something is in 2 PLACES AT ONCE, then it will INTERFERE.
Quantum Physics
Summary or “take home message”:
1. It’s weird
 defies everyday common sense.
2. LIGHT behaves as both a PARTICLE and a WAVE.
3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE.
4. If something is in 2 PLACES AT ONCE, then it will INTERFERE.
5. Quantum physics is science’s most accurate theory.
Quantum Physics
Summary or “take home message”:
1. It’s weird
 defies everyday common sense.
2. LIGHT behaves as both a PARTICLE and a WAVE.
3. Matter (i.e. atoms) behaves as both a PARTICLE and a WAVE.
4. If something is in 2 PLACES AT ONCE, then it will INTERFERE.
5. Quantum physics is science’s most accurate theory.
Quantum Accuracy
Electron’s g-factor: ge = 2.002 319 304 362
12-digits
Theory and experiment agree to 9 digits.
[Wikipedia, 2009]
Light as a wave
LASER
source
Screen
Light as a wave
LASER
source
Screen
Light as a wave
LASER
source
Screen
Light as a wave
LASER
source

Light as a wave
Intensity
hA
Pat
th
Pa
LASER
source
B

angle
screen

Also works for single photons !!!
[A. L. Weiss and T. L. Dimitrova, Swiss Physics Society, 2009.]
Experiment uses a CCD camera (i.e. sensor in your digital camera).
Photons follow 2 paths
simultaneously
Intensity
hA
Pat
path A
LASER
source
th
Pa
B

path B
angle
screen

… but, Matter is a
Outline
 Quantum Physics: Particles and Waves
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 What can you do with ultra-cold matter
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
How cold is Ultra-Cold?
1000 K
room temperature, 293 K
Antarctica, ~ 200 K
K
mK
Dilution refrigerator, ~ 2 mK
[priceofoil.org, 2008]
μK
Ultra-cold quantum temperatures
nK
Ultra-cold Quantum Mechanics
Room temperature:
 Matter waves have very short wavelengths.
 Matter behaves as a particle.
Ultra-Cold Quantum temperatures:
 Matter waves have long wavelengths.
 Matter behaves as a wave.
Room
temperature
Quantum
régime
Quantum Statistics
Bosons
Integer spin: photons, 87Rb.
Fermions
½-integer spin: electrons,
protons, neutrons, 40K.
Bose-Einstein Condensate (BEC)
Degenerate Fermi Gas (DFG)
All the atoms go to the absolute bottom of trap.
Atoms fill up energy “ladder”.
How do you make ULTRA-COLD matter?
Two step process:
1. Laser cooling
 Doppler cooling
 Magneto-Optical Trap (MOT)
2. Evaporative cooling
 Micro-magnetic traps
 Evaporation
Magneto-Optical Trap (MOT)
~ 100 K
Micro-magnetic Traps
Advantages of “atom” chips:
Iz
 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.
[Figure by M. Extavour, U. of Toronto]
Evaporative Cooling
Remove most energetic
(hottest) atoms
Wait for atoms to
rethermalize among
themselves
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
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
BEC History
1925:
1924:
S. N. Bose
describes the statistics
of identical boson
particles.
A. Einstein
predicts a low
temperature phase
transition, in which
particles condense
into a single
quantum state.
1995:
E. Cornell, C. Wieman, and
W. Ketterle observe BoseEinstein condensation in
87Rb and 23Na.
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 can cool fermionic 40K atoms
sympathetically with an 87Rb BEC.
“Iceberg”
BEC
Fermi
Sea
Sympathetic Cooling
Low
temperature
“High”
temperature
Quantum
Behavior
Outline
 Quantum Physics: Particles and Waves
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 What can you do with ultra-cold matter
Atom Interferometry
Spatial interferometry
 Precision measurements of forces.
Time-domain interferometry
 atomic clock.
BEC Interferometry
Spatial Atom Interferometry
IDEA: replace photon waves with atom waves.
 atom  photon
Example: 87Rb atom @ v=1 m/s  atom  5 nm.
green photon  photon  500 nm.
2 orders of magnitude increase in resolution
at v=1 m/s !!!
Mach-Zender atom Interferometer:
Path A
D1
Path B
D2
Atomic Clocks
 Special type of atom interferometer.
 Temporal interference, instead of spatial.
 Most accurate time keeping devices that exist.
 State-of-the-art: accuracy of 1 part in 1016 … 16 digits !!!
Applications:
 Keeping time.
 GPS Navigation.
 Deep space navigation.
Summary
 Quantum Physics.
 Ultra-cold atom technology.
 Matter-wave interferometry.
Ultra-cold atoms group
Francesca Fornasini
Brian Richards
Prof. Seth Aubin
Lab: room 15
Office: room 333
saaubi@wm.edu
Megan Ivory
Austin Ziltz
Jim Field
Yudistira Virgus
Thywissen Group
D. McKay
B. Cieslak
S. Myrskog
A. Stummer
Colors:
Staff/Faculty
Postdoc
Grad Student
Undergraduate
M. H. T. Extavour
L. J. LeBlanc
T. Schumm
J. H. Thywissen