NNew measurements and new physics withand new physics with
spinor BEC
Lincoln TurnerYi i Li St M ll S b ti JYingmei Liu, Steven Maxwell, Sebastian Jung
Eduardo Gomez, Adam BlackPaul LettPaul Lett
Optical trapping
First suggested by Lekhotov (1978)Demonstrated by Chu (1986)y ( 9 )Applied to BEC (Stamper-Kurn 1998)All-optical BEC (Chapman 2001)
Some initial experiments on spinor BEC: domain formation and i i (MIT 8 )interactions (MIT group 1998-9)
Feshbach resonancesTunable interactionsMolecule formationDegenerate Fermi gasesDegenerate Fermi gasesBEC/BCS crossover
What is a spinor BEC?
Magnetic traps hold onlyMagnetic traps hold only one sign of spin projection.
( )( ) ( ) in e θψ = rr r
O ti l t h ld ll i j ti
( ) ( )ψ
Optical traps hold all spin projections
⎛ ⎞( )( ) ( ) ...
( )
F
nξ
ψξ
−⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟⎝ ⎠
rr r ( ) ( ) 1T =ξ r ξ r
( )Fξ+⎜ ⎟⎝ ⎠r
Stern-Gerlach imaging
Put the BEC in a magnetic gradient
Spin components separate
I ith b ti i iBarrett, Sauer,ChImage with absorption imaging ChapmanPRL 87 010404(2001)
Symmetry and interactions
Interactions
For experimentalists For theorists
C i l b i h F
2 2
1 2 1 24( ) ( )
F
f fV a Pπδ− = − ∑r r r r
Contact potential but with F+1 scattering lengths
1 2 1 20,2,...
( ) ( ) f ff
V a Pm
δ=∑r r r r
Odd f forbidden by Bose symmetry.MDDI small but measurable for F=1MDDI small but measurable for F 1
Projection ontototal spin
Spin-mixing oscillations23Na c>0NIST
0 4
0.6
0.2
0.4
Black, Gomez, LDT, Jung, LettPRL 99 070403 (2007)
0
20 400 60
80
87Rb c
F=1 interactionsOnly one spin-changing interaction allowed is
|+1> |-1> ⇔ |0> |0>
⇔( )( ) ( )V δ + F F
Order parameter has three components
⇔( )1 2 1 2 0 2 1 2( ) ( )V c cδ− = − + ⋅r r r r F F
O de pa a ete as t ee co po e ts
1
0
( , )( , ) ( ) ( , )
tt n t
ξψ ξ
−⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟
rr r r
Three coupled Gross-Pitaevski equations:
1 ( , )tξ +⎜ ⎟⎝ ⎠r
Topological defects galore
Spin textures
Spin knots
Spin knotsSpin vortex lattices
Nematic disclinationsSpin solitons
Coreless vortices
Single mode approximation
Assume that the spatial wavefunction is:– constant – identical for all three spin components
1 ( )( ) ( ) ( )
tt n t
ξψ ξ
−⎛ ⎞⎜ ⎟= ⎜ ⎟r r 0
1
( , ) ( ) ( )( )
t n tt
ψ ξξ +
= ⎜ ⎟⎜ ⎟⎝ ⎠
r r
Further break up into populations ρ and phases θ
1 ( )1 ( )
i tt e θρ −⎛ ⎞⎜ ⎟
0
1
1
( )0
( )1
( )
( , ) ( ) ( )
( )
i t
i t
t e
t n t e
t e
θ
θ
ρ
ψ ρ
ρ +
−
+
⎜ ⎟= ⎜ ⎟
⎜ ⎟⎜ ⎟⎝ ⎠
r r
⎝ ⎠
Magnetisation and the linear Zeeman effect
Magnetisation is m=ρ+ − ρ−Constant of the motion
E
Constant of the motion
Populations normalised
ρ+ + ρ0 + ρ− = 1
Whole system described by:One population, say ρ0(t)Overall phase θ = θ + θ – 2θ0
BOverall phase θ θ+ + θ− 2θ0
( )2 20 0 0 01 (1 ) cos (1 )E c mρ ρ ρ θ δ ρ= − + − − + −( )QuadraticZeemanSpin interaction
c>0 for antiferromagnetic 23Na
Effective Hamiltonian for F=1 in SMA
( )2 20 0 0 01 (1 ) cos (1 )E cn n n m nθ δ= − + − − + −E0.6
0 4
0 2
0.4
ρ0
( )2 20 0 0 01 (1 ) cos (1 )E cn n n m nθ δ= − + − − + −
0
0.2
0 π 2π-2π -π0
θ
( )2 20 0 0 01 (1 ) cos (1 )E c mρ ρ ρ θ δ ρ= − + − − + −QuadraticZeemanSpin interaction
Destructive Stern-Gerlach measurementsd
/ m
sti
on p
erio
dO
scill
at
Magnetic field / μTMagnetic field / μT
Faraday measurement of transverse magnetisation
Spin precesses around bias field
Polarization alternately rotatedleft and right.
-+
Faraday signal
F
No rotation when spin is perpendicular to beam.
B
F
Put cube at 45° to input polarization, get bright field signal that is nulled for no rotation.
B
mF
that is nulled for no rotation.
Net effect is a signal oscillating at the Larmor frequency.the Larmor frequency.
Faraday measurement, details
Experimentalist here Theorists here
2 mm
0 μm
Calibrated apertureon xy stage
2 2
Image of BEC~0.5mm
Compound lens:1.8x relay, achromatic pair11x telescope rot x
F dxθ ∝ ∫11x telescope20x total magnification
∫
Faraday measurement: spin oscillations
Spin oscillations: period divergence/
ms
on p
erio
d O
scill
ati
Magnetic field / μT
Decoherence in the F=1 SMA system
Single-mode ground state
Non-linear Landau-Zener tunneling
γ γ
Lucas Rutten, Monash
Summary: single-mode spin-1 system
We now understand:
Free evolution
Ground state …
… and how it gets there (decoherence)
Adiabatic(ish) evolution
Anything else?
Shapiro steps
Phenomenology in Josephson systemsgy p y
Add a magnetic field dither
Macroscopic Quantum State Trapping (MQST)
Spin echoes of magnetic dipole-dipole interaction (MDDI)
Beyond mean-field: Spinor squeezing
Chang et al, PRL 99 080402 (2007)
Beyond single mode
87Rb Ferromagnetichas lower energy
23Na Antiferromagnetichas lower energy has lower energyhas lower energy
Won’t form domains:Robins et al PRA 64 021601R (2001)Robins et al. PRA 64 021601R (2001)
Zhang et al. PRL 95 180403 (2005)
Can form domains:Al d l A 8 6 ( 8)Alexander et al. PRA 78 023632 (2008)
Application: micromagnetometry
Conclusions
Optical trapping ⇒ spinor order parameter
Single-mode F=1 model
F d tFaraday measurement– Well adapted to measuring a single spatial mode
“NMR” extensions spinor squeezing– NMR extensions, spinor squeezing …
Microscale atomic magnetometers
