Ultra-Cold Matter Technology
for
Many-Body Physics and Interferometry
Seth A. M. Aubin
Dept. of Physics, College of William and Mary
April 19, 2007
AMO Seminar
Old Dominion University
Outline
 Ultra-cold Matter Apparatus
 Apparatus review
 High efficiency evaporation
 Bose-Fermi Degeneracy
 Physics
 Past: 40K-87Rb cross-section.
 Present: BEC interferometry.
Path A
Path A
 Future: Fermion interferometry.
Polar molecules for many-body physics.
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
 Magneto-Optical Trap (MOT)
 Optical Molasses
2. Evaporative cooling
 Magnetic traps
 Evaporation
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
ERF  

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.
Light-Induced Atom Desorption (LIAD)
Conflicting pressure requirements:
• Large Alkali partial pressure  large MOT.
• UHV vacuum  long magnetic trap lifetime.
Solution: Use LIAD to control pressure dynamically !
 405nm LEDs (power=600 mW) in a pyrex cell.
Micro-Magnetic Trap Difficulties
Technology:
 Electroplated gold wires on a silicon substrate.
 Manufactured by J. Estève (Aspect/Orsay).
Z-trap current
Trap Potential: Z-wire trap
Iz
defects
Evaporated Ag and Au (B. Cieslak and S. Myrskog)
RF for evaporation
Magnetic Dimple Trap: Extra Compression
T=19 K
n(r )  13 exp  U (r ) kT 
T=7 K
faxial boosted by
two (to 26 Hz)
Outline
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 Physics
 Past: 40K-87Rb cross-section.
Path A
 Present: BEC interferometry
Path A
 Future: Fermion interferometry.
Polar molecules for many-body physics.
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 !
S. Aubin et al.
Nature Physics 2, 384 (2006).
Outline
 Intro to Ultra-cold Matter
 What is it ?
 How do you make it ?
 Bose-Einstein Condensates
 Degenerate Fermi Gases
 Physics
 Past: 40K-87Rb cross-section.
Path A
 Present: BEC interferometry
Path A
 Future: Fermion interferometry.
Polar molecules for many-body physics.
Past:
Surprises with Rb-K
cold collisions
Naïve Scattering Theory
Collision Rates
Rb-Rb
Rb-K
 RbRb  nRb RbRb vRbRb
 RbK  nRb RbK vRbK
2
8aRbRb
2
4a RbK
aRbRb  5.238 nm
aRbK  10.8 nm
 RbK
 2 .7
 RbRb
Sympathetic cooling
should work really well !!!
Sympathetic cooling 1st try:
 “Should just work !” -- Anonymous
 Add 40K to 87Rb BEC  No sympathetic cooling observed !
Solution: Work Harder !!!
 Slow down evaporative ramp 2s  6s !!!
 Decrease amount of 87Rb loaded !
 Added Tapered Amplifier to boost 767 nm 40K MOT
power.
 Direct absorption imaging of 40K.
 Optical pumping of 40K.
 More LIAD lights.
 Alternate MOTs: 25s 40K + 3s 87Rb.
 Dichroic waveplates for MOT power balance.
 Decompress micro B-Trap.
 Increase B-Trap Ioffe B-field.
 Clean up micro B-trap turn-off.
Experiment:
Sympathetic cooling only works
for slow evaporation
10
Evaporation 3 times slower
than for BEC
4
Phase Space Density
102
100
105
106
10-2
10-4
10-6
10-8
Atom Number
107
Cross-Section Measurement
TK40 (K)
Thermalization of 40K with 87Rb
What’s happening?
Rb-K Effective range theory
Rb-K Naïve theory
Rb-Rb cross-section
Present:
BEC Interferometry
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:
Measure a phase difference
(D) between paths A and B.
Path A
D1
Path B
D2
DAB can be caused by a difference in length, force, energy, etc …
RF beamsplitter
How do you beamsplit ultra-cold atoms ?
Energy
h
x
RF beamsplitter
How do you beamsplit ultra-cold atoms ?
Energy
h
x
RF beamsplitter
How do you beamsplit ultra-cold atoms ?
Energy
h
x
RF beamsplitter
How do you beamsplit ultra-cold atoms ?
Energy
Position of well is
determined by 
hrabi =
Atom-RF coupling
h
x
Implementation
figure from Schumm et al., Nature Physics 1, 57 (2005).
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a final value
BRF ~ 1 Gauss
Interferometry Experiment
Fringe spacing = (h  TOF)/(mass  splitting)
Species-dependent Potentials
K40 probe (Rb87 present but unseen):
Rb87 probe (K40 present but unseen):
K40 +Rb87 probes (both species visible but apparent O.D.
about 50% smaller than actual):
Atomic Physics 20, 241-249 (2006).
Future:
Fermion Interferometry
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:
Measure a phase difference
(D) between paths A and B.
Path A
D1
Path B
D2
DAB can be caused by a difference in length, force, energy, etc …
Bosons and Fermions … again
1st Idea: use a Bose-Einstein condensate
Photons (bosons)  87Rb (bosons)
 Laser has all photons in same “spatial mode”/state.
 BEC has all atoms in the same trap ground state.
Identical bosonic atoms interact through collisions.
PROBLEM
 Good for evaporative cooling.
 Bad for phase stability: interaction potential
energy depends on density -- DAB is unstable.
Better Idea: Use a gas of degenerate fermions
 Ultra-cold identical fermions don’t interact.
 DAB is independent of density !!!
 Small/minor reduction in energy resolution
since DE ~ EF .
EF
Spatial Atom Interferometry
External force sensing:
 Gravitational fields, via
their mass.
 Magnetic fields, via the
Zeeman effect.
 Electric fields, via the
Stark effect.
Measure inertial forces and gradients  navigation.
Example: Rotation sensitivity for 1 cm2 Sagnac (40K)
 noise ~ 108 (rads / s)  cycle
Measuring Sub-mm Gravity
Interferometers:
 Mach-Zender
 Bloch oscillations:
 optical lattice.
 double well potential.
BEC proposal: S. Dimopoulos et al., Phys. Rev. D 68, 124021 (2003).
Example: 106 40K atoms at 100 m from a 100 m thick iridium test mass (100 m
arm separation) will feel an acceleration of 10-9 m/s2.
 Signal  to  Noise  0.6 for 10 s of phase accumulati on.
Systematic errors -- i.e. what’s the membrane for?
 Look for gravity effect by varying atom-test mass distance.
 Surface forces (Casimir-Polder/Van der Wall) are much larger than gravity.
 use a stationary membrane to “pin” and minimize the surface force.
(see for example, J. E. Sipe, JOSA B 4, 481 (1987) )
Future:
Novel Many-Body Physics
with Polar Molecules
Odd-wave Cooper Pairing
BCS superconductors/superfluids
The Cooper pair consists of S-wave pairing of spin 
and spin  particles (S=0, L=0).
High-Tc superconductors
The pairing mechanism is D-wave in nature.
Superfluid 3He
Cooper pair has P-wave orbital angular momentum.
[Figure from K. Madison, UBC]
Superfluid ultra-cold degenerate Fermi Gas
The pairing mechanism is S-wave in nature.
M. Zwierlein et al.,
Nature 435, 1047 (2005)
Ultra-cold Polar Molecular Gases
Prediction: Superfluidity with odd-wave Cooper pairing.
[ M. A. Baranov et al., PRA 66, 013606 (2002) ]
Fermionic Superfluid KRb
Electric dipole moment of the ground state of KRb is
d  0.3 ea 0
[Kotochigova et al. PRA 68, 022501 (2003)]
Following the treatment of M. A. Baranov et al., PRA 66, 013606 (2002)
o
2md 2
ad   2 2  2250 A
 

Tc


 1.44 exp  
TF
 2 p F ad




Tc = critical temperature for superfluidity
For 104 fermionic 40K87Rb molecules in a trap with fr = 500 Hz and fz = 30 Hz,
we get
n = 3 x 1013 molecules/cm3
TF = 0.6 K
Tc/TF = 0.8  Tc = 0.5 K
How do you get
Ultra-Cold KRb?
Feshbach Resonance
 weakly bound KRb
+
Photo-association
 stimulated transition
to the ground state
Recent news !!!
Weakly bound KRb produced in a 3D optical lattice..
C. Ospelkaus et al., Phys. Rev. Lett. 97, 120402 (2006).
S. Kotochigova et al.,
Eur. Phys. J. D 31, 189–194 (2004).
Summary
EF
 Degenerate Bose-Fermi mixture on a chip.

40K-87Rb
cross-section measurement.
 BEC Interferometry.
 Future: Fermion Interferometry
 Future: Ultra-cold polar molecules.
Thywissen Group
S. Aubin
D. McKay
B. Cieslak
S. Myrskog
M. H. T. Extavour
A. Stummer
T. Schumm
Colors:
Staff/Faculty
Postdoc
Grad Student
Undergraduate
L. J. LeBlanc
J. H. Thywissen
Ultra-cold atoms group
Aiyana Garcia
Prof. Seth Aubin
Apparatus
Design
Apparatus
Atom
Chip
MOT
Chamber
Turbo
Pump
RGA
Transport Path
Bellows
and
shutter
Ion
Pumps
Apparatus … continued
Atom
Chip
MOT
Chamber
Transport Path
[photo from Thywissen group]
[figure from M. Greiner et al., Phys. Rev. A 63, 031401(2001)]
The Problem with Fermions
Identical ultra-cold fermions do not interact
At very low temperatures,
  
l rp 0
If l  0 , then two atoms must scatter as an s-wave:

ik r
  
e
ikz
ikz
s  wave (r  r1  r2 )  e  e  2as 
r


s-wave is symmetric under exchange of particles: r  r
as = 0 for fermions