Alloptical BoseEinstein condensation and its application to spinor studies

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All-optical Bose-Einstein condensationand its
application to spinor studies
Prof. Michael Chapman Graduate Students Murray
Barrett, Ph.D. Jake Sauer Kevin Fortier Sally
Maddocks Meriam Mukai Undergrad Chris
Hamley Michael Allman

• Ming-Shien Chang

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Quantum Computing LabPostdoc position opening

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Chapman Lab

• All-Optical BEC
• Todays talk
• Magnetic guiding
• Storage ring
• Cavity QED with neutral trapped atoms
• Quantum information

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Storage Ring for Neutral Atoms

• Magnetic Guiding - Atom fiber optics
• delivery of ultracold atoms
• coherent state transport
• atom interferometry

1 cm
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Neutral Atom Storage Ring
Magnetic guiding and neutral atom storage ring
Limits vacuum, bumpy ring
J. A. Sauer et al, PRL 87, 270401(2001)
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Comparison
TeVatronFermiLabs
NeVatronChapmanLabs
1.6 km
10 mm
1 cm
1012 eV confinement 4 km Circumference Over 2500
Employees gt5 Billion building cost
10-9 eV confinement 6 cm Circumference Over 1
Employee lt5 Billion building cost
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Cavity QED with Trapped Atoms
Delivery of atoms to optical cavity
MOT
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Suspension system
Cavity QED with Trapped Atoms
w1
w2
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Suspension system
Cavity QED with Trapped Atoms
w1
w2
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All Optical Bose-Einstein Condensation a simple,
fast technique
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Quantum degeneracy in dilute gases

• Dilute gas
• Binary interactions
• Avoid molecule, liquid, or solid formation.

Classical regime
Quantum regime
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What is condensed in BEC?

• Simplest picture non-interacting bosons in a box
• quantized energy levels of motional degrees of
  freedom
• BEC macroscopic number of atoms in the ground
  state
• Condensed in momentum space
• Composite boson 7Li, 23Na, 85Rb, 87Rb, 133Cs,
  etc.
• BEC energy scale lt 10-10 eV
• electron ionization energy scale eV
• Real BEC experiments
• Harmonic potential well
• also condensed in real space
• Interaction between atoms
• Finite number of atoms

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Route to quantum degeneracy

• Pre-cooling and trapping schemes
• spontaneous scattering of photons is used to cool
  atoms to near the Doppler limit (100mK).
• sub-Doppler cooling
• magneto Optical Trap (MOT)
• Further cooling and trapping schemes
• Evaporative cooling
• Trapping schemes
• Optical trap
• Magnetic trap

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Evaporative cooling

• Remove hot atoms through collisions of particles
• Trade-off lose atoms during the cooling
• Requirements
• Elastic collisions dominate inelastic collisions
• thermalization time lt lifetime of the sample
• Simple
• Works for a wide range of temperatures and
  densities

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Optical Trap

• Far detuned lasers work as static field
• Focused laser beam form a 3D trap
• Importance of optical trap
• State-Independent Potential
• Trapping of Multiple Spin States
• Evaporative Cooling of Fermions

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If its so simple, why is it so hard?

• Evaporative cooling in an optical dipole trap
  first observed in 1994 (same year as in alkali
  magnetic traps)

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If its so simple, why is it so hard?

• Inefficient loading from MOT
• Capture small fraction of atoms
• Poor starting conditions for evaporative cooling

• Atoms prone to heating induced by spontaneous
  scattering and laser jitter

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Optical Dipole Trap
E- field maximum
Focused CO2 laser beam l 10.6 mm
trapped atoms
For power P 11 Watt, and beam focus, w0 70
mm,
Photon scattering rate couple/hour
U0100mK
Evaporation is too slow for our trap lifetime
(10 s)
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Cross trap

• Two intersecting traveling waves
• Large loading volume provided by the wings
• Tight confinement provided at the intersection
• Provided atoms are cold enough

600ms later
Loading from MOT
n gt 1014 cm-3 psd gt 0.001
106 atoms loaded
MOTn 1010cm-3 Psd 10-6
tight confinement ? high density ? fast
evaporation
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All Optical BEC2001
First cover illustration in 100 yr history of the
Physical Review

• We solved the loading problem
• gt 1014 atoms/cm3 spatial density
• gt 10-3 initial phase space density
• 106 atoms loaded
• All optical BEC is fast (and simple)
• Load CO2 laser trap from simple vapor cell MOT of
  87Rb
• ramp down CO2 laser trap beams in 2 sec
• BEC

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All Optical BEC
All Optical BEC
10 ms TOF images as temperature is lowered
through BEC 400 micron field of view
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All-optical atomic BEC in a (large period) lattice
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All-optical atomic BEC in a (large period) lattice
CO2 laser standing wave
With P 4 W, and w0 70 mm
4000 atoms / site loaded, not enough to make BEC
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Filling a few lattice sites

• To load large number of atoms into lattice site
• Add traveling wave to funnel atoms into a few
  sites
• 106 atoms over a few sites

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Pancake condensate
BEC in a lattice
Image after 10 ms expansion
10 ms TOF images as temperature is lowered
through BEC 400 micron field of view
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Pancake condensate
Image after 10 ms expansion as final temperature
is lowered
Fast expansion
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How many lattice sites are occupied?
Transfer to traveling wave for variable time and
releaseposition converted to momentum
Cool in lattice
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Measure the sites occupied

• visually measure
• number of sites occupied
• (transverse) trap frequencies

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Controlling the site loading
Vary funnel powers and lattice position during
transfer
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Interference of condensates
If two condensates overlap during expansion,
they will interfere
Analogous to interference of two coherent
independent lasers
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Macroscopic quantum interference
Relative velocity
Fringe spacing
Quantum interference of 30,000 atoms
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Studies of F1 and F2 Spinor BEC in an optical
trap
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F 1 Spinor
Weak magnetic field gradient applied during
TOF Population mF -1,0,1 3 1 1 (assuming
equal coupling to probe)
Much theoretical work on spinor condensates Ho,
Machida et al., Bigelow et al., Meystre et al.,
You et al. (anti)ferromagnetism, spin mixture,
spin squeezing
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We can control the spin population by applying
B-field gradients during evaporation
mf 1 0 -1
mf 1 0 -1
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Hamiltonian -- Spin 1
Short-range interaction, transforms as scalar
under spin rotations generically of form
Spin interaction
Density interaction
87Rb -- c2ltltc0, c2lt0
23Na -- c2ltltc0,c2gt0
Tin-Lun Ho, PRL 81, 742 (1998)
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Spinor condensates in optical traps
Multi-species BEC with rotational symmetry
Ho, PRL98 Machida, JPS98
Spin relaxation
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Spin mixing - theory

• Spin mixing (relaxation)
• Initial state m0 (lt100mG)
• Ferromagnetic convert to m1,0 You et al.
• Anti-ferromagnetic ( ideal gas) remain
  m0 Ketterle (1998)
• Normalization
• Magnization is conserved

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m0 spinor condensates
System is characterized by two parameters Normal
ization Magnetization
Initial condition m0 BEC simplifies the spinor
studies
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Spinors In the B field
quadratic Zeeman effect favors m0
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Ground state of spinor condensates

• Ground state is obtained by minimizing the energy
  functional

23Na F 1, c gt 0, is anti-ferromagnetic
Studied by MIT group
87Rb F 1, c lt 0, is ferromagnetic
experimentally unexplored
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Spinor phase diagram
(Ketterle et al, 1998)
Anti-ferromagnetic
Ideal gas
Ferromagnetic
23Na, Ketterle
87Rb, our work
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Spin mixing - experiment
Initial spinor mF0
For no interactions, m0 is lowest energy (2nd
order Zeeman shift)
B
2m0 ?? m-1 m1
At 2 sec
As a check initial mF -1 spinor remains pure
mF -1
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Ferromagnetic behavior
Anti-ferromagnetic spinor
Ferromagnetic spinor
You et al, 2003.
Chang, et al, PRL, 2004
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Suppressed noise of magnetization
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Spinor phase

• Single-mode approximation
• Definite phase relationship between components
• Ferromagnetic ?(?1, ?0, ?-1)(0, 0, 0)
• Antiferromagnetic (?1, ?0, ?-1)(??/2, 0, -?/2)
• For B? 0, Larmor precession is important
• How to measure phase
• Two-site interference

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Phases and dephasing of spinor BEC
SMA, ferromagnetic? f1 f0 f-1
Machida et al., PRA99
occassionally
mostly
Gradient is important 10mG/cm causes
(2p3.7/sec) phase change between components
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Pure M -1 interference
1 sec in a B 1.4G/cm
Fringe contrast much higher compared to mixed
spinor
fringe is clearly seen
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Manipulating Spinors

• Microwave spectroscopy
• Measure B field
• Pump spinor BEC F1?F2
• Create mixture of spinor BECs

0
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F2 spin-mixing
F2 spinor lifetime
50ms in the optical trap
mF -2 -1 0 1 2
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Summary

• Spinor condensates in optical traps
• F1 spinor
• Magnetization control
• Spin-mixing vs. B field
• Spin population oscillation, reduced number
  fluctuation
• Ferromagnetism study
• Spinor interference
• F2 spinor
• Spin-mixing