Outline. Magnetic field dependence (e.g. 40 K) Fermionic Alkalis. Creating new states of matter: Experiments with ultra-cold Fermi gases
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1 Outline Creating new states of matter: Experiments with ultra-cold Fermi gases Cooling (difficulties) with Fermions Scattering Concept of Feshbach resonances Ultracold molecules Making a BEC of molecules Selim Jochim, Henning Moritz MPI für f r Kernphysik, HD ETH ZürichZ moritz@phys.ethz.ch Fermionic Alkalis Magnetic field dependence (e.g. 40 K) Only Li and 40 K stable fermions Li level scheme F P 3/ 0 GHz.7 MHz.8 MHz / 3/ 5/ Г= MHz P / D-Line: nm F MOT transition 3/ S / 8. MHz repumping transition / Li, rel. isotope abundancy in Li=7% I=, melting point ~80 C 40 K, abundancy=0.0% I=4, melting point ~0 C
2 Cooling Methods Ideal Fermi Gas in an harmonic trap Evaporative cooling in magnetic trap or dipole trap T< 00 nk< T F, 0 atoms Laser cooling ~0. mk ~ 0 9 atoms f(ε) = D(ε) = N = exp( ε μ kt ) ε (~ ω) 3 Z 0 D(ε)f(ε) 3D harmonic oscillator E F = k B T F = ~ω(n) /3 0. μk Absorption imaging k F = p me F =(π n 0 ) /3 n / μm R F = a ho (48N) / 0 00μm Sympathetic Cooling The difficulty in cooling fermions Collisions are required for cooling, but at low T spin polarised fermions stop colliding Two particle wavefunction: Ψ, = χ spin ψ space Partial wave expansion: ψ space = ψ s-wave + ψ p-wave symmetric anti-symmetric Bosons BEC has no entropy, only thermal atoms î heat capacity vanishes for T 0 For Fermions ~kt Fermions ³ N th,c BEC C Fermi T TF 3 T TC A. G. Truscott, K. E. Strecker, W. I. McAlexander,G. B. Partridge, R. G. Hulet, Science 9, 570 (00); E Emin mv r eff = ~ E min = /mv = ~ mreff 0 00μK Only s-wave collisions energetically possible fi χ spin antisymmetric fi spin mixture ψ(r) e ikr + f (k, θ) eikr Z r σ = f (k, θ) dω Ω σ l k l ; σ s =4πa
3 Collision cross-sections sections Pauli Blocking of Collisions Collisions die out at low T Cooling difficult! Limit T~ 0% T F B. demarco, S. Papp, D. S. Jin, PRL 8, 5409 (00); Condition for Superfluidity Scattering length and bound states T BCS 0. T F exp( a<0 attractive interaction k F k a π k F a ) n /3 /mean distance < T BCS T F rψ rψ Still a long way to go: Interaction strength ~ a an important parameter: increases T C makes cooling more efficient E B = ~ ma size a very large 3
4 Feshbach resonance Scattering length and bound states Interaction between spins of atoms at close distance may couple states m tot conserved E Tune bound state of a closed channel into degeneracy with the continuum Convenient tuning by mag. field: the two states have different mag. moment closed channel E Kin r open channel ΔE = Δμ x B B B 0 magnetic field Composite Bosons Free Fermions How to see the molecules? How to see the molecules? Molecules have different optical transition frequency Why: If on constituent is excited, its dipole couples resonantly polarises the other fi Potential between two dipoles ~R -3, R molecule size Shift ~Γ λ 3 π R 4
5 RF Photodissociation Molecule Fraction and Temperature OD(x, y) = OD 0 Li ( ζ e x σ x ζ = exp( T/T F ) Li n(x) = y σ y )/Li ( ζ) X k= x k /k n E. Hodby et al. PRL 94, 040 (005); From Jin Group, JILA, Boulder Stability of molecules Short summary Fermionic molecules are surprisingly stable Bosonic not Pauli Blocking prevents the atoms from coming close Decay rate Size of Potential 3 Molecule size a 3 E r The bad news: Sympathetic colling difficult, because heat capacity of BEC vanishes Direct cooling of Fermions: Only s-wave collisions at low T Become Pauli blocked at low T The good news T C and rethermalisation depends on a a tunable via Feshbach resonance Two fermions transform into one composite Boson across resonance molecules long lived Two Solutions End of 00 Spring of 003 Cool very hard with Fermions Cooling on the Bosonic side 5
6 A machine to produce cold Fermions Experimental procedure Magnetooptical Trap Optical dipole traps Different sizes Dipole potential: U dip = p E 00 million atoms 00 μk Radius ~mm focused beam trap cooling performed by evaporation: simply lower the trap power!
7 Funnel Dimple Potential Use resonant enhancement in an optical resonantor: ~30-fold enhancement Deep and large volume trap 0.4 mm Mosk et al., Opt. Lett, (00) Evaporative cooling results number of quantum states for atoms scattering length (000 a 0 ) magnetic field (G) Three body recombination create molecules by collisions! three atoms trapped particles (0 5 atoms) 0 spilling the fermi sea! 0. 7G (only atoms) dimple laser power [W] three- body process E kin = E b /3 atom molecule (binding energy E b ) E kin = E b /3 7
8 Evaporative cooling results field where a weakly bound molecular state exists! ~ molecules per quantum state!!! critical temperature number of quantum states for molecules trapped particles (0 5 atoms) G (only atoms) 74G (atoms-molecules) dimple laser power [W] S. Jochim et al., Science 30, 0 (003) scattering length (000 a 0 ) magnetic field (G) quantum degeneracy! very long lifetime (~40s) thermalization These molecules must form a BEC! Bose-Einstein condensation In-situ images of the molecules thermal cloud condensed fraction x0 5 molecules axial profiles 0.5 mm in-situ images molecular BEC was simultaneously achieved at JILA, Boulder Laser power 40mW mw Molecular BEC gallery Li in situ Innsbruck Bartenstein et al., PRL 9, 040 (004) expansion JILA Greiner et al., Nature 4, 537 (003) 40 K BEC BCS crossover molecules strong coupling crossover Cooper pairs weak coupling MIT Zwierlein et al., PRL 9, 5040 (003) Li Li ENS Bourdel et al., PRL 93, (004) Rice Partridge et al., PRL 93, (005) Li drawing from Cho, Science 30, 750 (003) 8
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