Title “New forms of quantum matter near absolute zero temperature” Wolfgang Ketterle Massachusetts Institute of Technology MIT-Harvard Center for Ultracold

“New forms of quantum matter near absolute zero temperature”

Wolfgang KetterleMassachusetts Institute of Technology

MIT-Harvard Center for Ultracold Atoms

5/23/06NASA workshop

Airlie Center

The ongoing revolution in atomic physics …

Enabling technology:Nanokelvin temperatures

The cooling methods

• Laser cooling• Evaporative cooling

Sodium BEC I experiment (2001)

How to measure temperatureHeight of the atmosphere

300 Kh=10 km

300 Kh=1 cm

e-(106)

Potential (gravitational) energy mgh = kBT/2(g: gravitational acceleration)

In thermal equilibrium: Potential energy ~ kinetic energy

1 nKh= 30 nm

1.05 nK

780 pK

450 pK

Trapping a sodium BECwith a single coil

Lowest temperature ever achieved: 450 picokelvin

Temperature measurement by imaging the size of the trapped cloud

A.E. Leanhardt, T.A. Pasquini, M. Saba, A. Schirotzek, Y. Shin, D. Kielpinski, D.E. Pritchard, and W. Ketterle, Science 301, 1513 (2003).

1 cm

Precision measurements withBose-Einstein condensates ...

We have to get rid of perturbing fields …

• Gravity• Magnetic fields

What distinguishes nanokelvin?

• Physics BEC Phase transition Quantum reflection Interactions• Ease of Manipulation

BEC @ JILA, June ‘95(Rubidium)

BEC @ MIT, Sept. ‘95 (Sodium)

T.A. Pasquini, Y. Shin, C. Sanner, M. Saba, A. Schirotzek, D.E. Pritchard, W.K.

Quantum Reflection of Ultracold Atoms

• Phys. Rev. Lett. 93, 223201 (2004)• Preprint (2006)

Silicon surface

Sodium BEC

Quantum Reflection from NanopillarsR

efle

ctio

n P

roba

bilit

y

Velocity (mm/s)

Solid Si surfaceReduced density Si surface

1 mm/s is 1.5 nK x kB kinetic energy



Loading sodium BECs into atom chipswith optical tweezers

BECproductionBEC

arrival

44 cm

T.L.Gustavson, A.P.Chikkatur, A.E.Leanhardt, A.Görlitz, S.Gupta, D.E.Pritchard, W. Ketterle, Phys. Rev. Lett. 88, 020401 (2002).

Atom chip with waveguides

Splitting of condensates

15ms Expansion

Two condensates

1mm

One trappedcondensate

Trapped 15ms expansion

1mm

Two condensates


Two condensates


Y. Shin, C. Sanner, G.-B. Jo, T. A. Pasquini, M. Saba, W. Ketterle, D. E. Pritchard, M. Vengalattore, and M. Prentiss: Phys. Rev. A 72, 021604(R) (2005).

Very recent progress:200 ms coherence time for an atom chip interferometer

Two condensates


The goal:Atom interferometry:Matter wave sensors

Use ultracold atoms to sense

Rotation NavigationGravitation Geological exploration



Two of the biggest questions in condensed matter physics:

The nature of high-temperature superconductors

Quantum magnetism, spin liquids

Strongly correlated, strongly interacting systems

Particle A Particle B

Pair A-B

How to get strong interactions?

Particle A Particle B

Pair A-B

Resonant interactionshave infinite strength

Unitarity limited interactions:• Pairing in ultracold fermions• Relevant to quark-gluon plasmas

E

Feshbach resonance

Magnetic field

Free atoms

Molecule

E

Feshbach resonance

Magnetic field

Free atoms

Molecule

Disclaimer: Drawing is schematic and does not distinguish nuclear

and electron spin.

E

Feshbach resonance

Magnetic field

Molecule

Two atoms ….

Free atoms

E

Feshbach resonance

Magnetic field

Molecule

… form an unstable molecule

Free atoms

E

Feshbach resonance

Magnetic field

Molecule

… form a stable molecule

Free atoms

E

Feshbach resonance

Magnetic field

Molecule

Atoms attract each other

Free atoms

E

Feshbach resonance

Magnetic field

Molecule

Atoms attract each otherAtoms repel each other

Free atoms

For

ce b

etw

een

atom

sS

catt

erin

g le

ngth

Feshbach resonance

Magnetic field

Atoms attract each otherAtoms repel each other

Observation of High-Temperature Superfluidity in

Ultracold Fermi Gases

BosonsParticles with an even number of protons, neutrons and electrons

FermionsParticles with an odd number of protons, neutrons and electrons

Bose-Einstein condensation atoms as waves superfluidity

At absolute zero temperature …

Fermi sea: Atoms are not coherent No superfluidity

Two kinds of fermions


Pairs of fermionsParticles with an even number of protons, neutrons and electrons

At absolute zero temperature …

Pairs of fermionsParticles with an even number of protons, neutrons and electrons

Bose-Einstein condensation atoms as waves superfluidity

Two kinds of fermionsParticles with an odd number of protons, neutrons and electrons


Two kinds of fermionsParticles with an odd number of protons, neutrons and electrons


Weak attractive interactions

Cooper pairslarger than interatomic distancemomentum correlations BCS superfluidity

Bose Einstein condensate of molecules

BCS Superconductor

Atom pairs Electron pairs

Molecules

Atoms

Energy

Magnetic field

Molecules are unstableAtoms form stable molecules

Atoms repel each othera>0

Atoms attract each othera<0

BEC of Molecules:Condensation of

tightly bound fermion pairs

BCS-limit:Condensation of

long-range Cooper pairs

Bose Einstein condensate of molecules

Atom pairs

BCS superfluid

Molecular BEC BCS superfluid

Molecular BEC BCS superfluid

Magnetic field

Molecular BEC BCS superfluidCrossover superfluid

High-temperature superfluidity at 100 nK?

Binding energy of pairsTransition temperature

10-5 … 10-4 normal superconductors10-3 superfluid 3He10-2 high Tc superconductors

0.3 high Tc superfluid

Fermi energyFermi temperature

(density)2/3

Scaled to the density of electrons in a solid:Superconductivity far above room temperature!

Optical trapping @ 1064 nm

axial = 10-20 Hzradial= 50–200 HzEtrap = 0.5 - 5 K

States |1> and |2> correspond to|> and |>

Preparation of an interacting Fermi system in Lithium-6

How to show that these gases are superfluid?

Quantization: Integer number of matter waves on a circle

Spinning a strongly interacting Fermi gas

Makes life hard …..

Container is an optical trapat high bias field!

• Imperfections of the beam• Anisotropy• Anharmonicity• Stray magnetic field gradients• Gravity• etc…

Have to fight against:

Vortex lattices in the BEC-BCS crossover

M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle,Nature 435, 1047-1051 (2005)

This establishes phase coherence and superfluidityin gases of molecules and of fermionic atoms

Astrophysical significance:• Superfluidity of neutron in neutron stars• Pulsar glitches

Atomic Bose-Einsteincondensate (sodium)

Molecular Bose-Einsteincondensate (lithium 6Li2)

Pairs of fermionicatoms (lithium-6)

Gallery of superfluid gases

Fermionic Superfluidity withImbalanced Spin Populations

Astrophysical significance:• Superfluidity of quarks in neutron stars

BCS Pairing of Fermions

Ene

rgy

21

Pairing costs kinetic energy, but there is gain in potentialenergy (attractive interaction between fermions)


Ene

rgy

21 Pairing energy

Unequal Fermi energies (non-interacting)(example: Apply magnetic field to a normal conductor)


Ene

rgy 2

1

Ene

rgy


2

1

Interacting case, fixed particle number:Phase separation! (Bedaque, Caldas, Rupak 2003)

Breakdown of the BCS statewhen 1 –2

Superfluid gapis now smaller

N NS

Clogston 1962

FFLO/LOFF-State

BreachedPair State

Distorted FermiSurface

PhaseSeparation

Recent theory (>=2005): Carlson, Reddy, Cohen, Sedriakan,Mur-Petit, Polls, Müther, Castorina, Grasso, Oertel, Urban, Zappalà,Pao, Wu, Yip, Sheehy, Radzihovsky, Son, Stephanov, Yang,Sachdev, Pieri, Strinati, Yi, Duan, He, Jin, Zhuang, Caldas, Chevy

94%90%56%30%22%12%6%

Fermionic Superfluidity with Imbalanced Spin Populations

Population Imbalance: = (N2-N1)/(N2+N1)

|2>

0%

|1>

BEC-Side 1/kFa = 0.2

-100%-74%0% -2% -32%-16% -58%-48%

|2>

|1>BCS-Side 1/kFa = -0.15

Increase population imbalance

Momentum distribution after magnetic field sweep to the BEC side

|1>

|2>

Superfluidity is robust in the strongly interacting regime!

M.W. Zwierlein, A. Schirotzek, C.H. Schunck, W. Ketterle,Science 311, 492 (2006), published online on Science Express 21 December 2005

The Window of Superfluidity

De

crea

sin

g In

tera

ctio

n

1/kFa

0.11

0

– 0.27

– 0.44

BEC

BCSCon

dens

ate

Fra

ctio

n

Population Imbalance

Phase Diagram for Unequal Mixtures

Breakdown: Critical mismatch in Fermi energies EF Gap

EKin = 310 nK

350 nK

400 nK

430 nK Superfluid

Normal

BCSBEC

Critical P

opulation Imbalance

Ene

rgy

What is the nature of the superfluid state?

2

1

N NS

Phase Contrast Imaging

|1>

|2>

|3>

n2

n1

80 MHz

• Imaging beam red-detuned for |1>, blue-detuned for |2>

• Optical signal of phase-contrast imaging directly measures density difference n=n2-n1

Li linewidth: = 6 MHz

|1> |2>Equalmixture

In-trap images

The shell structure is a hint of the phase separation.

Direct imaging of the density difference

-50% -37% 20%0%-24%-30% 30% 40% 50%

Population imbalance

Reconstruction of 3D density profile

Only assumption: cylindrical symmetry

Phase Separation !!

=0.6

Atomic physics “knobs” to control many-body physics

Density 1011 to 1015 cm-3

Temperature 500 pK to 1 mKInteractions: scattering length a - to +

Choice of hyperfine state(s): |, |; spinors

Optical traps and lattices: 1D, 2D systems

Optical lattices with different symmetries

Spin dependent lattices

RotationDisorder

B

a

Use the tools and precision of atomic physicsto realize new phenomena (Hamiltonians)

of many-body physics Condensed-matter physics at ultra-low densities

(100,000 times thinner than air)

BEC I

Ultracold fermions

Martin ZwierleinChristian SchunckAndre SchirotzekPeter ZarthYe-ryoung LeeYong-Il Shin

BEC II

Na2 moleculesNa-Li mixtureOptical Lattices

Kaiwen XuJit Kee ChinDaniel MillerYingmei LiuWidagdo SetiawanChristian Sanner

BEC III

Atom chips, surface atomoptics

Tom PasquiniGyu-Boong JoMichele SabaCaleb ChristensenSebastian WillD.E. Pritchard

BEC IV

Atom opticsand optical lattices

Micah BoydErik StreedGretchen CampbellJongchul MunPatrick MedleyD.E. Pritchard

$$NSFONRNASADARPA Opening for postdoc

Documents

Title “New forms of quantum matter near absolute zero temperature” Wolfgang Ketterle Massachusetts Institute of Technology MIT-Harvard Center for Ultracold