Title “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

Title The ongoing revolution in atomic physics …

Title Enabling technology: Nanokelvin temperatures

The concepts The cooling methods Laser cooling Evaporative cooling

Sodium BEC I experiment (2001)

Guinness Book Record

Height of atmosphere How to measure temperature Height of the atmosphere 300 K h=10 km 300  K h=1 cm e -(10 6 ) Potential (gravitational) energy mgh = k B T/2 (g: gravitational acceleration) In thermal equilibrium: Potential energy ~ kinetic energy 1 nK h= 30 nm

1.05 nK 780 pK 450 pK Trapping a sodium BEC with 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 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 at JILA and MIT JILA, June ‘95 (Rubidium) 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, (2004) Preprint (2006)

Silicon surface Sodium BEC

Quantum Reflection from Nanopillars Reflection Probability Velocity (mm/s) Solid Si surface Reduced density Si surface 1 mm/s is 1.5 nK x k B kinetic energy

What distinguishes nanokelvin? Physics BEC Phase transition Quantum reflection Interactions Ease of Manipulation

Moving condensates Loading sodium BECs into atom chips with optical tweezers BEC production BEC 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, (2002). Atom chip with waveguides

Splitting of condensates 15ms Expansion Two condensates 1mm One trapped condensate

Trapped 15ms expansion 1mm Two condensates Splitting of condensates

Two condensates Splitting of 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, (R) (2005). Very recent progress: 200 ms coherence time for an atom chip interferometer

Two condensates Splitting of condensates The goal: Atom interferometry: 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

Title Particle A Particle B Pair A-B How to get strong interactions?

Title Particle A Particle B Pair A-B Resonant interactions have 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 other Atoms repel each other Free atoms

Force between atoms Scattering length Feshbach resonance Magnetic field Atoms attract each other Atoms repel each other

Title Observation of High- Temperature Superfluidity in Ultracold Fermi Gases

Bosons Particles with an even number of protons, neutrons and electrons Fermions Particles 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 Fermi sea:  Atoms are not coherent  No superfluidity Pairs of fermions Particles with an even number of protons, neutrons and electrons

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

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

Bose Einstein condensate of molecules BCS Superconductor Atom pairs Electron pairs

Molecules Atoms Energy Magnetic field Molecules are unstable Atoms form stable molecules Atoms repel each other a>0 Atoms attract each other a<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  … normal superconductors superfluid 3 He high T c superconductors 0.3 high T c superfluid Fermi energy Fermi temperature  (density) 2/3 Scaled to the density of electrons in a solid: Superconductivity far above room temperature!

Optical 1064 nm axial = Hz radial = 50–200 Hz E trap =  K States |1> and |2> correspond to |  > and |  > Preparation of an interacting Fermi system in Lithium-6

Title How to show that these gases are superfluid?

Rotating buckets

Quantized circulation Quantization: Integer number of matter waves on a circle

Vortex structure

Spinning a strongly interacting Fermi gas Makes life hard ….. Container is an optical trap at high bias field! Imperfections of the beam Anisotropy Anharmonicity Stray magnetic field gradients Gravity etc… Have to fight against:

Vortices in the BEC-BCS Crossover Vortex lattices in the BEC-BCS crossover M.W. Zwierlein, J.R. Abo-Shaeer, A. Schirotzek, C.H. Schunck, W. Ketterle, Nature 435, (2005) This establishes phase coherence and superfluidity in gases of molecules and of fermionic atoms Astrophysical significance: Superfluidity of neutron in neutron stars Pulsar glitches

Atomic Bose-Einstein condensate (sodium) Molecular Bose-Einstein condensate (lithium 6 Li 2 ) Pairs of fermionic atoms (lithium-6) Gallery of superfluid gases

Fermionic Superfluidity with Imbalanced Spin Populations Astrophysical significance: Superfluidity of quarks in neutron stars

BCS Pairing of Fermions Energy 22 11

Pairing costs kinetic energy, but there is gain in potential energy (attractive interaction between fermions) BCS Pairing of Fermions Energy 22 11 Pairing energy 

Unequal Fermi energies (non-interacting) (example: Apply magnetic field to a normal conductor) BCS Pairing of Fermions Energy 22 11

BCS Pairing of Fermions 22 11 Interacting case, fixed particle number: Phase separation! (Bedaque, Caldas, Rupak 2003) Breakdown of the BCS state when   1 –  2 Superfluid gap is now smaller NNS Clogston 1962

FFLO/ LOFF-State Breached Pair State Distorted Fermi Surface 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

94%90%56%30%22%12%6% Fermionic Superfluidity with Imbalanced Spin Populations Population Imbalance:  = (N 2 -N 1 )/(N 2 +N 1 ) |2> 0% |1> BEC-Side1/k F a = %-74%0%-2%-32%-16%-58%-48% |2> |1> BCS-Side1/k F a = -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 Decreasing Interaction 1/k F a – 0.27 – 0.44 BEC BCS Condensate Fraction Population Imbalance

Phase Diagram for Unequal Mixtures Breakdown: Critical mismatch in Fermi energies  E F  Gap   E Kin = 310 nK 350 nK 400 nK 430 nK Superfluid Normal BCSBEC Critical Population Imbalance

Energy What is the nature of the superfluid state? 22 11 NNS

Phase Contrast Imaging |1> |2> |3> n2n2 n1n1 80 MHz Imaging beam red-detuned for |1>, blue-detuned for |2> Optical signal of phase-contrast imaging directly measures density difference  n=n 2 -n 1 Li linewidth:  = 6 MHz |1>|2> Equal mixture 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 to cm -3 Temperature 500 pK to 1 mK Interactions: 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 Rotation Disorder BB a Use the tools and precision of atomic physics to 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 Zwierlein Christian Schunck Andre Schirotzek Peter Zarth Ye-ryoung Lee Yong-Il Shin BEC II Na 2 molecules Na-Li mixture Optical Lattices Kaiwen Xu Jit Kee Chin Daniel Miller Yingmei Liu Widagdo Setiawan Christian Sanner BEC III Atom chips, surface atom optics Tom Pasquini Gyu-Boong Jo Michele Saba Caleb Christensen Sebastian Will D.E. Pritchard BEC IV Atom optics and optical lattices Micah Boyd Erik Streed Gretchen Campbell Jongchul Mun Patrick Medley D.E. Pritchard $$ NSF ONR NASA DARPA Opening for postdoc