Dynamics of ferromagnetic spin1 BoseEinstein condensates in alloptical traps

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Dynamics of ferromagnetic spin-1 Bose-Einstein
condensates in all-optical traps
Qishu Qin Eva Bookjans Chris Hamley Kevin
Fortier Murray Barrett, Ph.D. Jacob Sauer,
Ph.D. Prof. Michael Chapman Wenxian Zhang,
Ph.D. Prof. Li You

• Ming-Shien Chang

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All Optical Bose-Einstein Condensation a simple,
fast technique
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Optical Trap
-

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

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A simple loading technique
CO2 trap loading
87Rb l 780 nm Natoms 200 x 106 T 30 mK

• - Sub-Doppler cooling
• Temporal dark MOT
• (Hänsch et al. PRA98)

Overlap of MOT and dipole trap
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Cross trap
Loading from MOT 106 atoms loaded

• Two intersecting traveling waves
• Large loading volume provided by the wings
• Tight confinement provided at the intersection

600 ms later n gt 1014 cm-3 psd gt 0.001
tight confinement ? high density ? fast
evaporation
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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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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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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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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
30,000 atoms
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Dynamical Trap Compression
P 70 w
w0
30 µm
70
2.5 mm
Time
0
0.6 s
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Crossing the BEC transition
300,000 atoms in final condensate 10-fold
improvement
lowering temperature
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• All-optical BEC
• 3 simple and fast techniques
• Cross trap
• Large period (5 µm) 1-D lattice
• Single beam, variable focus trap

Common features 87Rb CO2 trapping
laser Simple MOT lt 2 s evaporation time
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All Optical BEC2001

• Our experiment was first to provide
  simultaneously
• Good loading
• 106 atoms loaded
• gt 10-3 initial phase space density
• Fast evaporation
• gt 1014 atoms/cm3 spatial density
• Low heating rate in trap
• 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
• Voila, BEC

Chapman et al., 01
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Advantages of All-Optical Single-Focused Trap

• Really simple and robust
• 300,000 atom condensates from a modest MOT
• Evaporation in less than 2 seconds
• Requires only one CO2 laser beam

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Multi-Component Quantum Gases- Studies of Spinor
Bose Condensates
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Interacting Spin-1 BEC in an all-optical trap
Basic picture
F 0, 1, 2
Atomic Parameters
c2 ltlt c0
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Hamiltonian -- Spin 1
Short-range interaction, transforms as scalar
under spin rotations generically of form
Spin interaction
Density interaction
87Rb -- c2lt0,
23Na -- c2gt0,
Only true when B lt 20 mB
Tin-Lun Ho, PRL 81, 742 (1998)
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Spinor condensates in optical traps
Multi-component BEC with rotational symmetry
Hint
Ho, PRL98 Machida, JPS98
c2 ltlt c0
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Spinor condensates in optical traps
Interacting Hamiltonian
Spin mixing
Ho, PRL98 Machida, JPS98
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Coupled Gross-Pitaevskii Eqn. for Spin-1 Bose
Condensates
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When c2 0
3 Zeeman components are decoupled.
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Coherent spin mixing in a F 1 ferromagnetic
condensate
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0
-1
1
0
-1
1
0
-1
1
0
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Meta-stable spin configuration
At t0 (?1, ?0, ?-1) (0, 1, 0)
Spin mixing is noise driven.
GaTech (2002)
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Spinor oscillations from a metastable state
B0.014G/cm
B0.14 G B0.020 G/cm
Noise driven dynamics at early timedifficult to
compare with theory
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Spinors in a B field
quadratic Zeeman effect favors m0
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Ferromagnetic behavior
Anti-ferromagnetic spinor
Ferromagnetic spinor
You, 03
Chapman, 04
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Meta-stable spin configuration
At t0 (?1, ?0, ?-1) (0.5, 0, 0.5)
Spin mixing is noise driven.
Senstock et al. (2004)
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Deterministically initiate coherent spin mixing
At t0 (?1, ?0, ?-1) (0, 0.75, 0.25)
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Coherent Spin Mixing
Josephson dynamics driven only by spin-dependent
interactions A new macroscopic quantum system
Chapman, 05
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Coherent Spin Mixing
Oscillation Frequency
Bigelow, 99
Direct measurement of c (c2)
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First direct measuring the value of c2 (or a2 -
a0)
a2 - a0 -1.45(32) aB (this work) a2 - a0
-1.40(22) aB (spect. theory)
from oscillation frequency
rad/s.
from condensate expansion
cm3
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Coupled Gross-Pitaevskii Eqn. for Spin-1 Bose
Condensates
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Spin mixing is a nonlinear internal AC Josephson
effect
Under Single Mode Approximation (SMA) and define
You, 05
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Nonlinear Josephson oscillator energy contour
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AC Josephson Oscillations

• For high fields where d gtgt c, the system exhibits
  small oscillations analogous to AC-Josephson
  oscillations

Compare with weakly linked superconductors
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Controlling spinor dynamics
Quadratic Zeeman energy
when
? (rad)
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Controlling spinor dynamics
Change trajectories by applying phase shifts via
the quadratic zeeman effect
Ferromagnetic ground state
? (rad)
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Demonstrating coherence of ferromagnetic ground
state
Restarting the dynamics by phase-shifting out of
the ground state at a later time
Spin coherence time condensate lifetime
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Miscibility of spin-1 (3-component) superfluid
Goal minimize the total mean-field energy
1-fluid M-F
2-fluid M-F
3-fluid M-F
MIT, 98-99
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Miscibility of two-component superfluids

• Total Energy of two-component superfluid
• If they are spatially overlapped with equal
  mixture
• If they are phase separated
• The condensates will phase separated if

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Study miscibility m1 and m-1 states
At t0 (?1, ?0, ?-1) (0.5, 0, 0.5)
Apply 0.5 G to inhibit spin mixing (meta-stable
config).
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Study miscibility of m0 and m-1 (m-1) states
At t0 (?1, ?0, ?-1) (0, 0.5, 0.5)
Apply 0.5 G to suppress spin mixing population
osc. lt 1.
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Miscibility of two-component superfluid
After Stern-Gerlach Exp.
Ferromagnetic
MIT, 98-99
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Beyond SMA fragmentation of BEC and spin domain
formation
Single Mode Approx. (SMA)
Condensate size (2rc,2zc) (7, 70) ?m
condensate is unstable along the z (axial)
direction.
weak B gradient during TOF
z
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Validity of the SMA
Condensate should be physically smaller than spin
healing length
Spin healing length
1-D lattice
Cross trap
Single focus
cigar
disk
spherical
(2rc,2zc) (7, 70) ?m
(2rc,2zc) (1, 10) ?m
(2rc,2zc) (7, 7) ?m
Condensate size
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Summary

• Formation of spinor condensates in all-optical
  traps
• Coherent spinor dynamics
• Coherent spin mixing
• internal AC Josephson effects, atomic four-wave
  mixing
• Incoherent spinor dynamics
• miscibility of spin components
• spin wave formation during coherent spin mixing
• modulation instability (MI) or dynamical
  instability induced spin domain formation.

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Future directions and outlook for spinor
condensate researches

• Josephson oscillator
• SMA
• Shappiro levels (dynamics localization)
• Non-destructive imaging techniques to follow spin
  mixing.
• Spinor condensate of only 1000 atoms (in a mG
  environment)
• quantum noise
• complex ground state, SSS
• quantum atom optics
• Spin mixing of only two atoms
• two particles are inherently entangled after
  mixing.
• Optical Feshbach resonance
• to tune s-wave scattering length which
  subsequently tune the percentage of entanglement.

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