Interacting Ultra Cold Atomsa brief overview

Fei Zhou PITP, University of British Columbia

at Quantum Nanoscience conference, Noosa Blue, Australia, Jan 23, 2006

Collaborators: I. Affleck (UBC), E. Demler (Harvard), Z. C. Gu (TsingHua),M. Snoek (Utrecht), C. Wu (UCSB), H. Zhai (TsingHua)

$: Office of the Dean of Science, UBCNSERC, Canada

Sloan foundation, New York

Ultra Cold atoms

Many-body physics (condensed matter

physics)

Quantum information Storages and

quantum computers

Few body physics(Nuclear physics,Atomic physics)

Field theories(emergent gauge fields,color superconductivity,Neutron star physics)

Cosmology and gravity(Kimble mechanism,Unruh Radiation etc)

Topological quantum computer (Kitaev, 97)

2| g1| g

Bosons in optical lattices

• S=0 bosons

• S=1 bosons

S=0 bosons in lattices

In (a) and (b), one boson per site. t is the hopping and can be varied by tuning laser intensities of optical lattices; U is an intra-site interaction energy. In a Mott state, all bosons are localized.

M. P. A. Fisher et al., PRB 40, 546 (1989);On Mott states in a finite trap, seeJaksch et al., PRL. 81, 3108-3111(1998).

U

Mott states ( t << U)

Condensates (t >>U)

Phase diagrams

E(k,x)

n=3

n=2

n=1

x

n

x

2

1

Atomic Mott states in a trapt

n=1

SF or BEC

n=2

n=3

n=4

n

Small t

Large t

.

/

/

),π

R:(,,φB:(

.n|α

|Sn,n|)(n:|

|iφθe

θ||iφθe

φ)(θn|

21

0

21

02

0

1

0

0

01

12

012

)

sincos

sin,

Interacting S=1 bosons

.2,0,,4

)()(

02

,2121

FggM

ag

grrrrU

FF

FF

Stamper-Kurn et al., 98.Ho, 98; Ohmi & Machida, 98; Law,98.

Condensates of S=1 bosons (sodium type)

(d>1)N(Q)

Q

xy

z

(Zhou, 01)

Half vortices in BECs of sodium atoms

In a half vortex, each atom makes a spin rotation; a half vortex carries one half circulation of an integer vortex. A half vortex ring is also a hedgehog.

circulation

y

spin rotation

Z

x

y

x

The vortex is orientated along the z-direction; the spin rotation and circulating current occur in an x-y plane.

z

ring

Each site is characterized by two unit vectors, blue and red ones. a) nematic BECs (nBEC); b) Nematic mott insulators (NMI); c) Spin singlet mott insulators (SSMI).

Mott states of Spin-One Bosons

CCCCO3

12

Nematic-spin singlet transitions (Mott Insulators)

vs. (proportional to hopping) is plotted here. (Snoek and Zhou, 03; Demler, et al., 03; Demler and Zhou, 02)

SSMI NMI

Fermions

• S=1/2 fermions in Optical Lattices

• S=3/2 fermions, quintet pairing, exotic vortices studied (Wu, Hu and Zhang, 2003-2006).

• Feshbach resonances with population difference (Experiments: MIT group, the Rice University’s Group and JILA group; Theory effeorts: Son and Stephanov, 2005; Pao et al.,2005; Sheehy and

Radzihovsky; Gu, Warner and Zhou; …….)

• Lattice Feshbach resonances (Stability of Mott states and invasion of superfluidity, factorized superfluids in 1D; Wu, Gu and Zhou, 2005-2006)

And more…...

S=1/2 Fermions in optical lattices

(small band width)

Neel OrderedSpin liquids Neel ordered only at T=0

S=1/2 femions across Feshbach resonances

B

E (6Li)

F=3/2

F=1/2

Resonances between state 1 of |1/2,1/2> and state 2 of |1/2,-1/2>.

Only electron spins shown

Superfluids near Feshbach Resonances

1 )( Fskax

sa

Binding energy

B

The Chemical potential and Mol. Fraction at resonance

For y <<1, at FbR the many-body states are INDEPENDENT of both two body parameters such as the bg scattering length, the magnetic moments and the many-body parameter: the fermi momentum.

Wide resonance (Ho and Diener, 04)

Energy splitting and population imbalance

A conventional quantum statistical system

I

E(k)

k

E(k)

k

Cold atoms

Energy Landscape 1: Negative Scattering Length (N fixed) (Gu, Warner and Zhou, 05)

Energy Landscape 2: positive scattering length

Energy Landscape 3: Near resonance

Phase Separation in a Constrained Subspace(i.e. population imbalance is conserved)

M-H curve for a global ground state

Critical population imbalance

Phase separated states

I

M M

I

1

N

Gapless SFSF+N

Gapless SF + N

Negative scattering length Positive scattering length

Zwierlein et al., 2005 ; Also studied by the Rice group.

Superfluids of polarized fermi gases

Resonances take place along the blue dashed line (in the “universal regime”). ( Son et al., 2005; also see Sheehy and Radzihovsky, 2005)

LOFF

Partially polarizedF.L.

Fully polarizedF.L.

SF + Fermi sea

Splitting between two chemical potentials

inverse of scattering length

(p, -p+Q)

• many important and exciting new issues in many-body cold atomic matter (magnetic superfluids & Mott states, topological phases, superfluids with population imbalance etc).

• Cold atomic matter might also be applied to understand various fundamental concepts/issues in other fields.

• There are a lot we can learn about/from cold atoms.

Summary