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Few-body physics with ultracold fermions

Few-body physics with ultracold fermions Selim Jochim Physikalisches Institut Universität Heidelberg. The matter we deal with. T =40nK … 1µK Density n =10 9 … 10 14 cm -3 Pressures as low as 10 -17 mbar k B T ~ 5peV Extremely dilute gases , which can be strongly interacting !.

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Few-body physics with ultracold fermions

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  1. Few-bodyphysics with ultracold fermions Selim JochimPhysikalisches Institut Universität Heidelberg

  2. The matter we deal with • T=40nK … 1µK • Densityn=109 … 1014cm-3 • Pressures aslowas 10-17mbar • kBT ~ 5peV • Extremelydilutegases, whichcanbestronglyinteracting! Extreme matter!

  3. Importantlengthscales • interparticle separation sizeoftheatoms • de Broglie wavelength sizeoftheatoms • scatteringlengtha , onlyonelengthdeterminesinteractionstrength • → Universal properties, independentof a particularsystem! • → Wecan tune all theaboveparameters in ourexperiments!

  4. Tunability of ultracold systems Feshbach resonance: Magnetic-fielddependenceof s-wavescatteringlength Few-bodysystem: Tune thebindingenergyof a weaklyboundmolecule: Size (>> rangeofinteraction): Binding energy:

  5. Ultracold Fermi gases • At ultracold temperatures, a gas ofidenticalfermionsisnoninteracting • Ideal Fermi gas

  6. Ultracold Fermi gases • Need mixturestostudyinterestingphysics! • Simplestimplementation: spinmixtures (↑,↓)

  7. Ultracold Fermi gases • Two (distinguishable) fermions form a boson ….. • … moleculescan form a Bose condensate … → realize the BEC-BCS crossover!

  8. Ultracold Fermi gases • Two (distinguishable) fermions form a boson ….. • … moleculescan form a Bose condensate … • … tune fromstronglyboundmoleculestoweaklybound Cooper pairs From A. Cho, Science 301, 751 (2003) → realize the BEC-BCS crossover!

  9. A picturefromthe lab …

  10. What’s going on in our lab • Universal three-bodyboundstates „Efimov“ trimers T. Lompe et al., Science 330, 940 (2010) • Finite Fermi systemswithcontrolled interactions A newplaygroundwithcontrolatthesingleatomlevel! F. Serwane et al., Science 332, 336 (2011)

  11. The Efimov effect • An infinite numberof 3-body boundstatesexistswhenthescatteringlengthdiverges: (3 identicalbosons) 1/a (strengthofattraction) • At infinite scatteringlength:En=22.72En+1 • Scatteringlengthvalueswhere Efimov trimers becomeunboundan+1=22.7an

  12. Observing an EfimovSpectrum? 10nm (1st state) 227nm (2nd state) 5.2µm (3rd state) 0.12mm (4th state) 2.7mm (5th state)

  13. Whatisobserved in experiments? • three-bodyrecombination deeplyboundmolecule

  14. Enhanced recombination • With an (Efimov) trimeratthresholdrecombinationisenhanced: 1/a (strengthofattraction) deeplyboundmolecule

  15. Whathasbeendone in experiments? • Observeandanalyzecollisionalstability in ultracold gases • seminalexperimentwith ultracold Cs atoms (Innsbruck): T. Krämer et al., Nature 440, 315 (2006)

  16. The 6Li atom a12 |2> |1> Need three distinguishable fermions with(in general) different scattering lengths: (S=1/2, I=1 -> half-integer total angular momentum) 16

  17. The 6Li atom a12 |2> |1> Need three distinguishable fermions with(in general) different scattering lengths: a23 a13 |3> couple Zeeman sublevelsusing Radio-frequency B-fields: „Radio Ultracold“ 17

  18. 2- and 3-body boundstates …. Binding energiesofdimersandtrimers: • Threedifferent universal dimerswithbindingenergy • Wherearetrimerstates? 1/a (strengthofattraction)

  19. Wherearethe trimer states? Observecrossingsasinelasticcollisions T. Ottenstein et al., PRL 101, 203202 (2008) T. Lompe et al., PRL 105, 103201 (2010) Also: Penn State: J. Huckans et al., PRL 102, 165302 (2009) J. Williams et al. PRL 103, 130404 (2009) University of Tokyo: Nakajima et al., PRL 105, 023201 (2010) RG basedtheory: R. Schmidt, S. Flörchinger et al. Phys. Rev. A 79, 053633 (2009) Phys. Rev. A 79, 042705 (2009) Phys. Rev. A 79, 013603 (2009)

  20. Can we also measurebindingenergies? Measurebindingenergiesusing RF spectroscopy |1> |2> |2> RF field |1> |2> |3> Attach a thirdatomto a dimer Theorydatafrom: Braaten et al., PRA 81, 013605 (2010)

  21. RF-associationoftrimers radio frequency trimer dimer radiofrequency [MHz] T. Lompe et al., Science 330, 940 (2010)

  22. RF-associationof trimers • Withourprecision: theoreticalpredictionofthebindingenergyconfirmed: Need toinclude finite rangecorrectionsfor dimer bindingenergies • Same resultsfortwo different initialsystems T. Lompe et al., Science 330, 940 (2010) T. Lompe et al., PRL 105, 103201 (2010) More recentresults: Nakajima et al., PRL 106,143201 (2011) 22

  23. An ultracold three-component Fermi gas Fermionic trions, „Baryons“

  24. An ultracold three-component Fermi gas Startinggrant Color Superfluid

  25. What’s going on in our laｂ • Threecomponent Fermi gases RF-spectroscopyof Efimov trimers T. Lompe et al., Science 330, 940 (2010) • Finite Fermi systemswithcontrolled interactions A newplaygroundwithcontrolatthesingleatomlevel! F. Serwane et al., Science 332, 336 (2011)

  26. Ourmotivation • Atoms, nuclei … • Quantum dots, clusters … • Extreme repeatabilityandcontrolover all degreesoffreedom, but limited tunability • Wide tunability, but no „identical“ systems

  27. Creating a finite gas offermions Control the number of quantum states in the trap! Conventionaltrap like a soupplate! Shotglass type trap Large densityofstates … …smalldensityofstates

  28. Transfer atoms to a microtrap …

  29. Spill most of the atoms: Lower trap depth Use a magnetic field gradient to spill: ~600 atoms µ x B ~2-10 atoms “laser culling of atoms”: M. Raizenet al., Phys. Rev. A 80, 030302(R)

  30. Atoms in a microtrap Transfer a few 100 atomsinto a tightlyfocusedtrap (~1.8µm in size, 1.4kHz axial, 15kHz radial trapfrequencies) 100µm 100µm Trap potential is proportional tointensity, goodapproximation: harmonicatthecenter

  31. Single atomdetection oneatom in a MOT 1/e-lifetime: 250s Exposure time 0.5s CCD distancebetween 2 neighboringatomnumbers : ~ 6s 1-10 atomscanbedistinguishedwith high fidelity > 99%

  32. Startingconditions • Reservoir temperature ~250nK • Depthofmicrotrap: ~3µK • Expect • Occupationprobabilityofthelowestenergystate: > 0.9999 100µm 100µm L. Viverit et al. PRA 63, 033603 (2001)

  33. Preparationsequence Spill atoms in a controlledway Recapturepreparedatomsintomagneto-opticaltrap

  34. Spilling theatoms …. • Wecancontroltheatomnumberwithexceptionalprecision! • Note aspectratio 1:10: 1-D situation 1kHz~400feV

  35. A greenlaserpointertrap • Output power: • Total output ~70mW • Most ofitgreen, 532nm • About 10mW at 1064nm, • Some pump lightat 808nm. Atsuitable pump current: • Itemits a single longitudinal mode (singlefrequency) • Hasverylownoise: RIN < -110dB/Hz

  36. Wehavedecentcontroloverthemotionaldegreesoffreedom! • Whatabout interactions?

  37. The 6Li atom a12 |2> |1> (S=1/2, I=1 -> half-integer total angular momentum) 37

  38. First few-body interactions … Interaction-inducedspilling! F. Serwane et al., Science 332, 336 (2011)

  39. First few-body interactions • Whathappensifwe bring thetwoatoms in thegroundstateacrosstheFeshbachresonance • Oneatomisobserved in n=2 a>0 a~0

  40. Interactions in 1D Confinementinducedresonance 1D Trap hasaspectratio 1:10 3D M. Olshanii,PRL 81, 938 (1998). (for radialharmonicconfinement) Feshbachresonance

  41. Energyof 2 atomsin thetrap Relative kineticenergyoftwointeractingatoms (exactsolution!) T. Busch et al., Foundations of Physics 28, 549 (1998) x2-x1 (relative coordinate)

  42. 2 distinguishable vs. 2 identicalfermions 2 distinguishablefermions 2 identicalfermions Tunneling time equaltocaseoftwoidenticalfermions: thesystemis „fermionized“

  43. Tunneling dynamics

  44. Fermionization relative wavefunction groundstate 2 distinguishablefermions 2 identicalfermions Wave functionsquare, andenergyareidentical! (2-particle limitof a Tonks-Girardeau gas)

  45. Conclusion • Wedetectandcountsingleatomswithveryhighfidelity • Wepreparefew-fermionsystemswithunprecedentedcontrol • Wecontrolthe interactions in thefew-fermionsystem • A toolboxforthestudyoffew-bodysystems

  46. The future • Investigateinteractingfew-bodysystems in thegroundstate: Few-body „quantumsimulator“ • Realize multiple interactingwells Study dynamicsoffew-fermionsystems: Howmanyatoms do weneedtohave a thermal ensemble? Measurepairing in a finite system

  47. Thankyouverymuchforyourattention! Friedhelm Serwane Johanna Bohn Martin Ries Thomas Lompe Gerhard Zürn Selim Jochim André Wenz

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