Transcript New forms of quantum matter near absolute zero temperature

“New forms of quantum matter
near absolute zero temperature”
Wolfgang Ketterle
Massachusetts Institute of Technology
MIT-Harvard Center for Ultracold Atoms
5/23/06
NASA 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 temperature
Height of the atmosphere
e-(106)
1 nK
h= 30 nm
300 K
h=10 km
300 mK
h=1 cm
Potential (gravitational) energy mgh = kBT/2
(g: gravitational acceleration)
In thermal equilibrium: Potential energy ~ kinetic energy
Lowest temperature ever
achieved: 450 picokelvin
1.05 nK
1 cm
Trapping a sodium BEC
with a single coil
780 pK
450 pK
A.E. Leanhardt, T.A. Pasquini,
M. Saba, A. Schirotzek, Y. Shin,
D. Kielpinski, D.E. Pritchard,
and W. Ketterle, Science 301,
1513 (2003).
Temperature measurement by
imaging the size of the trapped cloud
Precision measurements with
Bose-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)
Quantum Reflection of Ultracold Atoms
T.A. Pasquini, Y. Shin, C. Sanner, M. Saba, A. Schirotzek,
D.E. Pritchard, W.K.
• Phys. Rev. Lett. 93, 223201 (2004)
• Preprint (2006)
Sodium BEC
Silicon surface
Reflection Probability
Quantum Reflection from Nanopillars
Solid Si surface
Reduced density Si surface
Velocity (mm/s)
1 mm/s is 1.5 nK x kB kinetic energy
What distinguishes
nanokelvin?
• Physics
BEC Phase transition
Quantum reflection
Interactions
• Ease of Manipulation
Loading sodium BECs into atom chips
with optical tweezers
44 cm
BEC
arrival
BEC
production
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
1mm
One trapped 15ms
condensate Expansion
Two condensates
Splitting of condensates
1mm
Trapped
15ms
expansion
Two condensates
Splitting of condensates
Two condensates
Very recent progress:
200 ms coherence time for an atom chip interferometer
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).
Splitting of condensates
Two condensates
Atom interferometry:
The goal:
Matter wave sensors
Use ultracold atoms to sense
Rotation
 Navigation
Gravitation  Geological exploration
What distinguishes
nanokelvin?
• Physics
BEC Phase transition
Quantum reflection
Interactions
• Ease of Manipulation
Two of the biggest questions in condensed matter physics:
The nature of high-temperature superconductors
Quantum magnetism, spin liquids
Strongly correlated, strongly interacting systems
How to get strong interactions?
Pair A-B
Particle A
Particle B
Resonant interactions
have infinite strength
Pair A-B
Particle A
Particle B
Unitarity limited interactions:
• Pairing in ultracold fermions
• Relevant to quark-gluon plasmas
E
Free atoms
Molecule
Magnetic field
Feshbach resonance
Disclaimer: Drawing is schematic
and does not distinguish nuclear
and electron spin.
E
Free atoms
Molecule
Magnetic field
Feshbach resonance
Two atoms ….
E
Free atoms
Molecule
Magnetic field
Feshbach resonance
… form an unstable molecule
E
Free atoms
Molecule
Magnetic field
Feshbach resonance
… form a stable molecule
E
Free atoms
Molecule
Magnetic field
Feshbach resonance
Atoms attract each other
E
Free atoms
Molecule
Magnetic field
Feshbach resonance
Atoms repel each other
Atoms attract each other
E
Free atoms
Molecule
Magnetic field
Feshbach resonance
Atoms attract each other
Force between atoms
Scattering length
Atoms repel each other
Magnetic field
Feshbach resonance
Observation of HighTemperature Superfluidity in
Ultracold Fermi Gases
At absolute zero temperature …
Bosons
Particles with an even number of
protons, neutrons and electrons
Bose-Einstein condensation
 atoms as waves
 superfluidity
Fermions
Particles with an odd number of
protons, neutrons and electrons
Fermi sea:
 Atoms are not coherent
 No superfluidity
Pairs of fermions
Particles with an even number of
protons, neutrons and electrons
Two kinds of fermions
Fermi sea:
 Atoms are not coherent
 No superfluidity
At absolute zero temperature …
Pairs of fermions
Particles with an even number of
protons, neutrons and electrons
Bose-Einstein condensation
 atoms as waves
 superfluidity
Two kinds of fermions
Particles with an odd number of
protons, neutrons and electrons
Fermi sea:
 Atoms are not coherent
 No superfluidity
Weak attractive interactions
Cooper pairs
larger than interatomic distance
momentum correlations
 BCS superfluidity
Two kinds of fermions
Particles with an odd number of
protons, neutrons and electrons
Fermi sea:
 Atoms are not coherent
 No superfluidity
Atom pairs
Bose Einstein condensate
of molecules
Electron pairs
BCS Superconductor
Energy
Atoms
Molecules
Magnetic field
Molecules are unstable
Atoms form stable molecules
Atoms attract each other
Atoms repel each other
a<0
a>0
BEC of Molecules:
Condensation of
tightly bound fermion pairs
BCS-limit:
Condensation of
long-range Cooper pairs
Atom pairs
Bose Einstein condensate
of molecules
BCS superfluid
BEC
BCS supe
BEC
Magnetic field
BCS supe
BEC
Crossover superfluid
BCS supe
High-temperature superfluidity at 100 nK?
Transition temperature
Fermi temperature

Binding energy of pairs
Fermi energy
(density)2/3
10-5 … 10-4
10-3
10-2
normal superconductors
superfluid 3He
high Tc superconductors
0.3
high Tc superfluid
Scaled to the density of electrons in a solid:
Superconductivity far above room temperature!
Preparation of an interacting Fermi system in Lithium-6
Optical trapping @ 1064 nm
States |1> and |2> correspond to
|> and |>
naxial = 10-20 Hz
nradial= 50–200 Hz
Etrap = 0.5 - 5 mK
How to show that these gases
are superfluid?
Quantization: Integer number of matter waves on a circle
Spinning a strongly interacting Fermi gas
Container is an optical trap
at high bias field!
Makes life hard …..
Have to fight against:
• Imperfections of the beam
• Anisotropy
• Anharmonicity
• Stray magnetic field gradients
• Gravity
• etc…
Vortex lattices in the BEC-BCS crossover
This establishes phase coherence and superfluidity
in gases of molecules and of fermionic atoms
Astrophysical significance:
• Superfluidity of neutron in neutron stars
• Pulsar glitches
M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle,
Nature 435, 1047-1051 (2005)
Gallery of superfluid gases
Atomic Bose-Einstein
condensate (sodium)
Molecular Bose-Einstein
condensate (lithium 6Li2)
Pairs of fermionic
atoms (lithium-6)
Fermionic Superfluidity with
Imbalanced Spin Populations
Astrophysical significance:
• Superfluidity of quarks in neutron stars
Energy
BCS Pairing of Fermions
m1
m2
BCS Pairing of Fermions
Energy
Pairing costs kinetic energy, but there is gain in potential
energy (attractive interaction between fermions)
m1
m2
Pairing energy D
BCS Pairing of Fermions
Unequal Fermi energies (non-interacting)
(example: Apply magnetic field to a normal conductor)
Energy
m1
m2
BCS Pairing of Fermions
Interacting case, fixed particle number:
Phase separation! (Bedaque, Caldas, Rupak 2003)
Breakdown of the BCS state
when D  m1 –m2
Superfluid gap
is now smaller
m1
Energy
Clogston 1962
m2
N
S
N
FFLO/
LOFF-State
Distorted Fermi
Surface
Breached
Pair State
Phase
Separation
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
Fermionic Superfluidity with Imbalanced Spin Populations
BEC-Side
1/kFa = 0.2
|1>
|2>
0%
6%
12%
22%
30%
56%
Population Imbalance: d = (N2-N1)/(N2+N1)
BCS-Side
90%
94%
1/kFa = -0.15
|1>
|2>
0%
-2%
-16%
-32%
-48%
-58%
-74%
-100%
Momentum distribution after magnetic field sweep to the BEC side
|2>
|1>
Increase population imbalance
Decreasing Interaction
Condensate Fraction
The Window of Superfluidity
1/kFa
BEC
0.11
0
– 0.27
– 0.44
BCS
Population Imbalance
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
Phase Diagram for Unequal Mixtures
EKin = 310 nK
350 nK
400 nK
430 nK
D
Superfluid
BEC
BCS
Critical Population Imbalance
Normal
Breakdown: Critical mismatch in Fermi energies DEF  Gap D
What is the nature of
the superfluid state?
Energy
m1
m2
N
S
N
Phase Contrast Imaging
• Imaging beam red-detuned for |1>,
blue-detuned for |2>
|3>
• Optical signal of phase-contrast imaging
directly measures density difference Dn=n2-n1
n2
|2>
80 MHz
|1>
n1
|1>
Li linewidth: G= 6 MHz
Equal
mixture
|2>
In-trap images
Direct imaging of the density difference
-50%
-37%
-30%
-24%
0%
20%
30%
40%
Population imbalance
The shell structure is a hint of the phase separation.
50%
Reconstruction of 3D density profile
d=0.6
Only assumption: cylindrical symmetry
Phase Separation !!
Atomic physics “knobs” to control many-body physics
Density 1011 to 1015 cm-3
Temperature 500 pK to 1 mK
Interactions: scattering length a -  to +
a
DB
Choice of hyperfine state(s): |, |; spinors
Optical traps and lattices: 1D, 2D systems
Optical lattices with different symmetries
Use the tools and precision of atomic physics
Spin dependent lattices
to realize new phenomena (Hamiltonians)
Rotation
of many-body physics
Disorder
Condensed-matter
physics at ultra-low densities
(100,000 times thinner than air)
BEC I
Ultracold
fermions
Martin Zwierlein
Christian Schunck
Andre Schirotzek
Peter Zarth
Ye-ryoung Lee
Yong-Il Shin
$$
NSF
ONR
NASA
DARPA
BEC II
Na2 molecules
BEC III
Na-Li mixture
Optical Lattices Atom chips,
surface atom
optics
Kaiwen Xu
Jit Kee Chin
Daniel Miller
Yingmei Liu
Widagdo Setiawan
Christian Sanner
Opening
BEC IV
Atom optics
and optical
lattices
Tom Pasquini
Gyu-Boong Jo
Michele Saba
Caleb Christensen
Micah Boyd
Sebastian Will
Erik Streed
D.E. Pritchard
Gretchen Campbell
Jongchul Mun
Patrick Medley
D.E. Pritchard
for postdoc