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Ultracold Fermions

Ultracold Fermions. Erich Mueller Cornell University. Sourish Basu Stefan Baur Stefan Natu Theja De Silva (Binghampton) Dan Goldbaum Kaden Hazzard. David Huse (Princeton) Meera Parish (Princeton) Francesco Fumarola (Columbia). Fermi Systems. Neutrons in Nuclear Matter.

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Ultracold Fermions

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  1. Ultracold Fermions Erich Mueller Cornell University Sourish Basu Stefan Baur Stefan Natu Theja De Silva (Binghampton) Dan Goldbaum Kaden Hazzard David Huse (Princeton) Meera Parish (Princeton) Francesco Fumarola(Columbia)

  2. Fermi Systems Neutrons in Nuclear Matter Strong overlap in relevant models and phenomena (magnetism, superconductivity…) Electrons in Metals Hard problems:emergent physics Lithium atoms in optical traps (record temp: 500pK) Unity of description: why we love physics.

  3. Outline Recent Progress BCS-BEC crossover Revisiting superconductivity Near future Pseudogap physics Modulated superfluidity(FFLO) Supressing superfluidity (Polarization and surface tension) Use atomic systems to explore most exciting ideas in many body physics Many other exciting phenomena:spin models, quantum hall effects, artificial light, Hubbard models… Other directions: metrology, quantum computing…

  4. Quantum Statistics High T: Boltzmann distribution Low T: Degenerate gas Hulet

  5. Superfluidity Bosons: cold hot Atoms delocalized (Heisenberg) Collective transport: no dissipation BEC: state “unchanged” by adding/removing boson Fermions: Interactions drive pairing: Pairs are Bosons: Superfluid

  6. BCS-BEC Crossover Leggett Weak attractive interactions BCS No bound state in free space Pairing is many-body effect(Fermi surface reduces dimensionality) V r V0 Pairing and superfluidity occur simultaneously r0 Continuously connected (Experiment: tune interactions with magnetic field) Strong attractive interactions Pairing (crossover) precedes superfluidity (phase transition) V r BEC

  7. BCS-BEC crossover regime High Tc superconductors Superfluid 3He Superconductors (Cooper pairs) Figure:M. Holland et al., PRL 87, 120406 (2001) BCS-BEC landscape BEC BCS 0 10 Alkali BEC Superfluid 4He -2 10 Transition temperature Tc/TF -4 10 -6 10 10 5 -5 10 10 10 Binding energy of Fermionic pairs or gap energy in units of Fermi Energy 2/ kT D BF

  8. V r Phase diagram 6Li or 40K Pairs shrink Normal BEC BCS Superfluid B V B0 V r r Free space: bound state at threshold(universal thermodynamics) Most theory and experiment done here Experiments confirm phase diagram

  9. V r Universality and Unitarity Bound state has infinite size:no energy scale from potential Cross-section as large as possible (determined by conservation laws) Thermodynamic functions -- universal functions of density and temperature Ex: Same for nucleons as for atoms!

  10. How to experimentally detect superfluidity? Vortices Ketterle group:Nature 435 , 1047-1051 (2005). Q: Nature of normal state Pseudogap Specific heat: Thomas group: Phys. Rev. Lett. 98, 080402 (2007)

  11. What is pseudogap? (in BCS-BEC crossover literature) Gap: SuperfluidNo low energy fermionic excitations Atoms bound in condensed pairs Colloquial pic: energy cost of breaking pairs gives gap More precise: quantum interference of particle and hole states Pseudogap: Normal Few low energy fermionic excitations Atoms bound in non-condensed pairs: Gap “blurred out” by incoherently adding contributions from pairs with different momenta

  12. What is pseudogap? (in BCS-BEC crossover literature) BCS spectral density(what is energy of excitations with momentum k?) Idea: two ways to add particle Simply insert particle

  13. What is pseudogap? (in BCS-BEC crossover literature) BCS spectral density(what is energy of excitations with momentum k?) Idea: two ways to add particle Simply insert particle Insert pair, and a hole (adding pair leaves state unchanged-- Condensate)

  14. What is pseudogap? (in BCS-BEC crossover literature) BCS spectral density(what is energy of excitations with momentum k?) Idea: two ways to add particle Simply insert particle Insert pair, and a hole States hybridize

  15. What is pseudogap? (in BCS-BEC crossover literature) BCS spectral density(what is energy of excitations with momentum k?) Idea: two ways to add particle Simply insert particle Insert pair, and a hole States hybridize Add “coherence factors”

  16. What is pseudogap? Superfluid (in BCS-BEC crossover literature) Pseudogap spectral density(what is energy of excitations with momentum k?) Normal Insert particle

  17. What is pseudogap? Superfluid (in BCS-BEC crossover literature) Pseudogap spectral density(what is energy of excitations with momentum k?) Normal • Simply insert particle • Insert hole and pair • Many ways to do this

  18. What is pseudogap? Superfluid (in BCS-BEC crossover literature) Pseudogap spectral density(what is energy of excitations with momentum k?) Normal • Simply insert particle • Insert hole and pair • Many ways to do this • Hybridize + + + …

  19. What is pseudogap? Superfluid (in BCS-BEC crossover literature) Pseudogap spectral density(what is energy of excitations with momentum k?) Normal Structures persist at weaker coupling:(less broadening)

  20. How to experimentally see pseudogap? Continuum of final state k -k RF spectroscopy Grimm group, Science 305, 1128 (2004) 7Li Empty Decreasing T Pairs B [Gauss] dn [kHz] Challenges:final state interactions, trap inhomogeneities(current controversies) (example with tightly bound pairs) Mueller, ArXiv:0711.0182; Basu and Mueller, arXiv:0712.1007

  21. x Is crossover pseudogap a novel quantum Liquid? T>Tc~0.5 TF -- Not very degenerate (metal at 105 K) No sharp quasiparticles: thermal effect? Need to suppress TC Solution: Polarize gas (spin relaxation negligible) Connected to questions of interplay of superconductivity and magnetism Fulde-Ferrel [1964], Larkin and Ovchinnikov [1965] History: Looking for FFLO state is among goals of future experiments Buzdin, Nature Materials (2004)

  22. Observation: Phase separation MW. Zwierlein, A. Schirotzek, C.H. Schunck, and W, Ketterle: Science 311, 492-496 (2006) Superfluid core with polarized halo

  23. Phase diagram (at unitarity) Comparison:liquid-gas (cf: 3He-4He) Ketterle group: Nature (Feb 7, 2008)

  24. Surface Tension 60 mm • Phase Coexistence -> Surface Tension 1 mm Aspect Ratio of Cloud: 50:1 Aspect Ratio of Superfluid: 5:1 Data: Hulet (unpublished) Amusing aside: Initial experiments: axial density -- discrepancy between experiments

  25. More Data Data: Hulet group -- Nuclear Physics A (2007)

  26. E D D0 Origin of Surface Tension SF Normal Order parameter passes over barrier in going between spatially separated phases

  27. Numerical Calculation kfa=-20 At unitarity, surface tension parameterized by single universal number- extract approx value from BdG Normal Stefan Baur

  28. Global consequences: soap bubble physics z Why “square” ends? Interplay of trapand surface tension Data: Hulet group -- Nuclear Physics A (2007) Large anisotropy: at each z imagine infinite cylindrical bubble E Criticaldroplet Bubble radius Natu and Mueller, arXiv:0802.2083

  29. Soap bubble physics z Why “square” ends? Data: Hulet group -- Nuclear Physics A (2007) Minimum moves up as z increases: “1st order transition” E Criticaldroplet Bubble radius Natu and Mueller, arXiv:0802.2083

  30. How does pseudogap evolve with polarization? Fumarola and Mueller, arXiv:0706.1205 T N S Forbidden • Sharp fermions at Fermi energy • Pseudogap smearing pushed to finite energy • Pairs exist as excitations Polarization

  31. How does pseudogap evolve with polarization? Fumarola and Mueller, arXiv:0706.1205 T N S Forbidden • Sharp fermions at Fermi energy • Pseudogap smearing pushed to finite energy • Pairs exist as excitations Polarization

  32. x Summary/Outlook • Recent work: Strong coupling superfluidity • BCS-BEC Crossover • Pseudogap • Polarization: phase separation • More General • Cold atoms: controlled environment for studying collective effects in degenerate quantum systems • Future • FFLO

  33. Analogies • “Pasta” phases of nuclear matter • “Stripe phases” of high temperature superconductors

  34. x Stability of FFLO? Short range interactions:generally favor bulk phase sep T=0 Mean-field calculation Normal Superfluid FFLOred region

  35. Future experiments -- Quasi-1D enhance CDW/SDW instability Arrays of coupled tubes 1D--fluctuating FFLO phase very stable FFLO S N Boost Tc by coupling tubes (Bethe Ansatz)

  36. Phase diagram for coupled tubes Meera M. Parish, Stefan K. Baur, Erich J. Mueller, David A. Huse Phys. Rev. Lett. 99, 250403 (2007)

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