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