“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.
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“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