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Eugene Demler (Harvard) . Quantum magnetism of ultracold atoms. Theory collaborators: Robert Cherng, Adilet Imambekov, Vladimir Gritsev, Takuya Kitagawa, Mikhail Lukin, Susanne Pielawa, Joerg Schmiedmayer Experiments: Bloch et al., Schmiedmayer et al., Stamper-Kurn et al. Harvard-MIT.

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quantum magnetism of ultracold atoms

Eugene Demler(Harvard)

Quantum magnetism of ultracold atoms

Theory collaborators:

Robert Cherng, Adilet Imambekov,

Vladimir Gritsev, Takuya Kitagawa, Mikhail Lukin,

Susanne Pielawa, Joerg Schmiedmayer

Experiments:

Bloch et al.,Schmiedmayer et al., Stamper-Kurn et al.

Harvard-MIT

$$ NSF, AFOSR MURI, DARPA

ferromagnetism in itinerant systems

?

Ferromagnetismin itinerant systems

Magnetism in condensed matter systems

Stoner instability.

Double exchange

Frustrated magnetic

systems

Antiferromagnetism

slide3

Quantum magnetism of ultracold atoms

Familiar models, New questions

Spin dynamics in 1d systems

Luttinger model and nonequilibrium dynamics.

New characterization: full distribution functions

Ferromagnetic F=1 spinor condensates

Quantum Hall ferromagnets in disguise.

Skyrmion crystal phases

spin dynamics in 1d systems ramsey interference experiments
Spin dynamics in 1d systems:Ramsey interference experiments

arXiv:0912.4643

T. Kitagawa, S. Pielawa, A. Imambekov, J.Schmiedmayer,

V. Gritsev, E. Demler

slide5

1

Working with N atoms improves

the precision by .

t

0

Ramsey interference

Atomic clocks and Ramsey interference:

ramsey interference with bec

time

Ramsey Interference with BEC

Single mode

approximation

Interactions should

lead to collapse and

revival of Ramsey fringes

Amplitude of

Ramsey fringes

ramsey interference with 1d bec
Ramsey Interference with 1d BEC

1d systems in microchips

1d systems in optical

lattices

Two component BEC

in microchip

  • Ramsey interference in 1d tubes:
  • Widera et al.,
  • PRL 100:140401 (2008)

Treutlein et.al, PRL 2004,

also Schmiedmayer, Van Druten

ramsey interference in 1d condensates
Ramsey interference in 1d condensates

A. Widera, et al, PRL 2008

Collapse but no revivals

ramsey interference in 1d condensates1
Ramsey interference in 1d condensates

Spin echo experiments

A. Widera, et al, PRL 2008

Only partial revival

after spin echo!

Expect full revival of fringes

slide10

Spin echo experiments in 1d tubes

Single mode approximation does not apply.

Need to analyze the full model

ramsey interference in 1d time evolution
Ramsey interference in 1dTime evolution

Luttinger liquid provides good agreement with experiments.

A. Widera et al., PRL 2008. Theory: V. Gritsev

Technical noise could also

lead to the absence of echo

Need “smoking gun” signatures

of many-body decoherece

probing spin dynamics using distribution functions

Distribution

Probing spin dynamics using distribution functions

Distribution contains information

about all the moments

→ It can probe the system Hamiltonian

Joint distribution function can

also be obtained!

distribution function of fringe contrast as a probe of many body dynamics
Distribution function of fringe contrastas a probe of many-body dynamics

Short segments

Radius =

Amplitude

Angle =

Phase

Long segments

distribution function of fringe contrast as a probe of many body dynamics1
Distribution function of fringe contrastas a probe of many-body dynamics

Splitting one

condensate

into two.

Preliminary results

by J. Schmiedmayer’s group

slide15

Long segments

Short segments

l =110 mm

l =20 mm

Expt

Theory

Data: Schmiedmayer et al.,

unpublished

slide16

Skyrmion crystals in ferromagnetic F=1

spinor condensates

R. Cherng, Ph.D. Thesis

slide17

Spinor condensates. F=1

Three component order parameter: mF=-1,0,+1

Contact interaction depends on relative spin orientation

When g2>0 interaction is antiferromagnetic. Example 23Na

Favors condensation into mF=0 state (or its rotation)

When g2<0 interaction is ferromagnetic. Example 87Rb

Favors condensation into mF=1 state (or its rotation)

spin textures in ferromagnetic rb condensates
Spin textures in ferromagnetic Rb condensates

mF=-1

Imbalanced

(non-equilibrium)

Initial populations

mF=-1

Equal

(equilibrium)

Initial populations

mF=0

mF=0

mF=+1

mF=+1

Vengalattore et al., PRL (2008)

spin textures checkerboard pattern
Spin textures: checkerboard pattern

Equal populations

Spectrum in

Momentum

Space

Transverse

Longitudinal

Vengalattore et al.,

PRL (2008)

slide20

q

Magnetic dipolar interactions in spinor condensates

Comparison of contact and dipolar interactions.

Typical value a=100aB

For 87Rb m=mB and e=0.007

Interaction of F=1 atoms

Spin dependent interactions in 87Rb are small

A. Widera, I. Bloch et al.,

New J. Phys. 8:152 (2006)

a2-a0= -1.07 aB

energy scales
Energy scales

B

F

High energy scales

Precession (115 kHz)

  • Spin independent S-wave scattering (gsn=215 Hz)

Quasi-2D geometry

Low energy scales

Spin dependent

S-wave scattering (gsn=8 Hz)

Quadratic Zeeman (1 Hz)

Dipolar interaction

(gdn = 1 Hz)

slide22

Dipolar interactions

Fast Larmor precession strongly modifies effective dipolar interactions

Fourier components of effective interaction (in-plane field)

slide23

Instabilities of ferromagnetic F=1 Rb condensate due to dipolar interactions

Theory: unstable modes in the regime

corresponding to Berkeley experiments.

Cherng, Demler, PRL (2009)

Experiments.

Vengalattore et al. PRL (2008)

from microscopic hamiltonian to effective low energy theory
From microscopic Hamiltonian to effective low energy theory

Dipolar and quadratic Zeeman

Fixed density

Maximally polarized

  • Lamacraft, PRA (2008)

Low energy manifold

Magnetization

Condensate phase

Superfluid velocity

mermin ho relation
Mermin-Ho relation

Magnetization

Skyrmion density

Superfluid velocity

Superfluid velocity

Divergence flow

Mermin-Ho

Skyrmion density

non linear sigma model
Non-linear sigma model

Low-energy Lagrangian

Superfluid flow related

to skyrmion density

Superfluid kinetic energy

Spin Stiffness

Skyrmion interaction (Log)

effective hamiltonian
Effective Hamiltonian

Spin dependent interactions

Skyrmion interaction

Interaction strengths

find all spin groups consistent with constraints
Find all spin groups consistent with constraints
  • Intrinsic constraints
    • Zero net skyrmion charge
    • Maximally polarized magnetization
    • Explicit symmetry breaking via external field
  • D2 point group
    • SG = p2mm, p2mg, p2gg
  • Phenomenological constraints
    • Rectangular lattice
    • No easy-axis or easy plane
    • Zero net magnetization
skyrmions in ferromagnets
Skyrmions in ferromagnets

Spin space

Real space

Radial coordinate

Azimuthal coordinate

~

Ordinary ferromagnets. Equations of motion

Single skyrmion solution

Spinor ferromagnets. Equations of motion

exact solutions for spinor condensates
Exact solutions for spinor condensates

Spin space

Real space

Stereographic coordinates

Holomorphic coordinates

Separation of variables

static solution ansatz

single skyrmion solutions
Single skyrmion solutions

Ordinary ferromagnet

Spinor condensate ferromagnet

lattice of skyrmions
Lattice of skyrmions

Ordinary ferromagnet

Spinor condensate ferromagnet

spin textures skyrmion lattice
Spin textures: skyrmion lattice

Skyrmion lattice solution

without dipolar interactions

Equal populations

Transverse

Longitudinal

spin textures
Spin textures

Skyrmion lattice solution

with dipolar interactions

Equal populations

Transverse

Longitudinal

slide39

Quantum magnetism of ultracold atoms

New questions, interesting physics

Harvard-MIT

Spin dynamics in 1d systems

Luttinger model and nonequilibrium dynamics.

New characterization: full distribution functions

Ferromagnetic F=1 spinor condensates

Quantum Hall ferromagnets in disguise.

Skyrmion crystal phases