Ultra-Cold Matter Technology

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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
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Outline

• Ultra-cold Matter Apparatus
• ? Apparatus review
• ? High efficiency evaporation
• ? Bose-Fermi Degeneracy
• Physics
• ? Past 40K-87Rb cross-section.
• ? Present BEC interferometry.
• ? Future Fermion interferometry.
• Polar molecules for many-body physics.

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Whats Ultra-Cold Matter ?

• Very Cold

? Typically nanoKelvin microKelvin ?
Atoms/particles have velocity mm/s cm/s

• Very Dense in Phase Space

Different temperatures Same phase space density
Higher phase space density
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Ultra-cold Quantum Mechanics
? Quantum physics is important when
Equivalent deBroglie wavelength inter-particle
separation
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Quantum Statistics
Bosons
Fermions

• anti-symmetric multi-particle wavefunction.
• ½-integer spin electrons, protons, neutrons,
  40K.
• probability of occupying a state igt with
  energy Ei.

• symmetric multi-particle wavefunction.
• Integer spin photons, 87Rb.
• probability of occupying a state igt with
  energy Ei.

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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
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Magneto-Optical Trap (MOT)
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Magneto-Optical Trap (MOT)
100 ?K
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Magnetic Traps
Interaction between external magnetic field and
atomic magnetic moment
For an atom in the hyperfine state

Energy minimum
B minimum
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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.

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Evaporative Cooling
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.
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Evaporative Cooling
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.
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RF Evaporation
In a harmonic trap

• 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.

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Light-Induced Atom Desorption (LIAD)

• Conflicting pressure requirements
• Large Alkali partial pressure ? large MOT.
• UHV vacuum ? long magnetic trap lifetime.

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Micro-Magnetic Trap Difficulties

• Technology
• Electroplated gold wires on a silicon
  substrate.
• Manufactured by J. Estève (Aspect/Orsay).

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Magnetic Dimple Trap Extra Compression
T19 ?K
T7 ?K
faxial boosted by two (to 26 Hz)
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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.
• ? Present BEC interferometry
• ? Future Fermion interferometry.
• Polar molecules for many-body physics.

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Bose-Einstein Condensation of 87Rb
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87Rb BEC
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87Rb BEC
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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.
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Sympathetic Cooling
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Below TF
0.9 TF
0.35 TF

• For Boltzmann statistics and a harmonic trap,
• For ultra-cold fermions, even at T0,

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Pauli Pressure
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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.
• ? Present BEC interferometry
• ? Future Fermion interferometry.
• Polar molecules for many-body physics.

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Past Surprises with Rb-K cold collisions
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Naïve Scattering Theory

• Sympathetic cooling 1st try
• Should just work ! -- Anonymous
• Add 40K to 87Rb BEC ? No sympathetic cooling
  observed !

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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.

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Experiment Sympathetic cooling only works for
slow evaporation
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Cross-Section Measurement
Thermalization of 40K with 87Rb
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Whats happening?
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Present BEC Interferometry
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Atom Interferometry
IDEA replace photon waves with atom waves. ?
?atom ?? ?photon
Example 87Rb atom _at_ v1 m/s ? ?atom ? 5 nm.
green photon ? ?photon ? 500 nm.
2 orders of magnitude increase in resolution at
v1 m/s !!!
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RF beamsplitter
How do you beamsplit ultra-cold atoms ?
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RF beamsplitter
How do you beamsplit ultra-cold atoms ?
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RF beamsplitter
How do you beamsplit ultra-cold atoms ?
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RF beamsplitter
How do you beamsplit ultra-cold atoms ?
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Implementation
figure from Schumm et al., Nature Physics 1, 57
(2005).
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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RF splitting of ultra-cold 87Rb
Scan the RF magnetic field from 1.6 MHz to a
final value BRF 1 Gauss
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Interferometry Experiment
Fringe spacing (h ? TOF)/(mass ? splitting)
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Species-dependent Potentials
Atomic Physics 20, 241-249 (2006).
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Future Fermion Interferometry
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Atom Interferometry
IDEA replace photon waves with atom waves. ?
?atom ?? ?photon
Example 87Rb atom _at_ v1 m/s ? ?atom ? 5 nm.
green photon ? ?photon ? 500 nm.
2 orders of magnitude increase in resolution at
v1 m/s !!!
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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.

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Spatial Atom Interferometry

• External force sensing
• Gravitational fields, via their mass.
• Magnetic fields, via the Zeeman effect.
• Electric fields, via the Stark effect.

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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).

• Systematic errors -- i.e. whats 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) )

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Future Novel Many-Body Physics with Polar
Molecules
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Odd-wave Cooper Pairing
BCS superconductors/superfluids The Cooper pair
consists of S-wave pairing of spin ? and spin ?
particles (S0, L0). High-Tc superconductors The
pairing mechanism is D-wave in
nature. Superfluid 3He Cooper pair has P-wave
orbital angular momentum. Superfluid ultra-cold
degenerate Fermi Gas The pairing mechanism is
S-wave in nature.
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Fermionic Superfluid KRb
Tc critical temperature for superfluidity
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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,
189194 (2004).
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Summary

• Degenerate Bose-Fermi mixture on a chip.
• 40K-87Rb cross-section measurement.
• BEC Interferometry.
• Future Fermion Interferometry
• Future Ultra-cold polar molecules.

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Thywissen Group
T. Schumm
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Ultra-cold atoms group
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Apparatus Design
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Apparatus
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Apparatus continued
photo from Thywissen group
figure from M. Greiner et al., Phys. Rev. A 63,
031401(2001)
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The Problem with Fermions
Identical ultra-cold fermions do not interact