D. Jin JILA, NIST and the University of Colorado $ NIST, NSF Using a Fermi gas to create Bose-Einstein condensates

Outline I.Intro and motivation a)A little quantum physics b)Basics of the experiment II.Interactions - An amazing new knob a)Experimental demonstration b)Implications (more motivation) III.Condensates of correlated fermion pairs

Outline I.Intro and motivation a)A little quantum physics b)Basics of the experiment II.Interactions - An amazing new knob a)Experimental demonstration b)Implications (more motivation) III.Condensates of correlated fermion pairs

Quantum Gases high T low T deBroglie  d classical behaviorquantum behavior matter waves

 There are two types of quantum particles found in nature - bosons and fermions. Bosons like to do the same thing. Fermions are independent-minded.  Atoms, depending on their composition, can be either. bosons: 87 Rb, 23 Na, 7 Li, H, 39 K, 4 He*, 85 Rb, 133 Cs fermions: 40 K, 6 Li Quantum Particles

Bosons and Fermions  half-integer spin other fermions: protons, electrons, neutrons, liquid 3 He  integer spin T = 0 Atoms in a harmonic potential. Bose-Einstein condensation 1995 other bosons: photons, liquid 4 He Fermi sea of atoms 1999 E F = k b T F (two spin states)

Ultracold atomic gases  low density n ~ – cm -3 N~10 6  ultralow T ~ 100 n K amenable to theoretical analysis unique experimental control dramatic detection of condensation

Bose-Einstein condensation BEC shows up in condensed matter, nuclear physics, elementary particle physics, astrophysics, and atomic physics. Excitons, biexcitons in semiconductors Cooper pairs of electrons in superconductors 4 He atoms in superfluid liquid He 3 He atom pairs in superfluid 3 He-A,B Neutron pairs, proton pairs in nuclei and neutron stars Mesons in neutron star matter Alkali atoms in ultracold atom gases

Condensates with Fermions?  Condensation requires bosons.  Material bosons are composite particles, made up of fermions.  Starting with a gas of bosonic atoms, you can only explore the behavior of bosons. 87 Rb, 23 Na, …  By starting with a gas of fermionic atoms we can explore the behavior of fermions AND BOSONS. 40 K, 6 Li, …

Cooling a gas of atoms 1. Laser cooling and trapping 2.Magnetic trapping and evaporative cooling 300 K to 1 mK  10 9 atoms 1 mK to 1  K  10 8 → 10 6 atoms spin 1 spin 2

3.Optical trapping and evaporative cooling 4.Probing the atoms Cooling a gas of atoms 1  K to 50 nK 10 6 → 10 5 atoms  can confine any spin-state  can apply arbitrary B-field

Quantum degeneracy velocity distributions T/T F =0.77 T/T F =0.27 T/T F =0.11 Fermi sea of atoms EFEF EFEF n 0 = 0.28 n 0 = n 0 =

Outline I.Intro and motivation a)A little quantum physics b)Basics of the experiment II.Interactions - An amazing new knob a)Experimental demonstration b)Implications (more motivation) III.Condensates of correlated fermion pairs

Interactions  Interactions are characterized by the s-wave scattering length, a  In an ultracold atomic gas, we can control a! a > 0 repulsive, a < 0 attractive Large |a| → strong interactions 0  scattering length

Magnetic-field Feshbach resonance C. A. Regal and D. S. Jin, PRL 90, (2003) repulsive attractive  spectroscopic measurement of the mean-field energy shift

Magnetic-field Feshbach resonance R V(R) R R R a<0, attractive a>0, repulsive

Magnetic-field Feshbach resonance R V(R) R R R a<0, attractive a>0, repulsive molecules → ← BB > atoms

Turning atoms into molecules Ramp across Feshbach resonance from high to low B The atoms reappear if we sweep back to high B energy B → ← up to 90% conversion to molecules!

molecules are extremely weakly bound ! molecules can survive many collisions ! Bosonic molecules Interesting regime Theory: D.S. Petrov et al., cond-mat/ , Expts: Rice, ENS, Innsbruck, JILA rf photodissociation C. Regal et al. Nature 424, 47 (2003)

 BEC of diatomic molecules  BCS superconductivity/superfluidity  Something in between? Making condensates with fermions 1. Bind fermions together. 2. BEC Condensation of Cooper pairs of atoms (pairing in momentum space, near the Fermi surface) EFEF spin  spin  BCS-BEC crossover (“generalized Cooper pairs”)

BCS-BEC landscape energy to break fermion pair transition temperature BEC BCS superfluid 4 He alkali atom BEC high T c superconductors superfluid 3 He superconductors M. Holland et al., PRL 87, (2001) interactions

Outline I.Intro and motivation a)A little quantum physics b)Basics of the experiment II.Interactions - An amazing new knob a)Experimental demonstration b)Implications (more motivation) III.Condensates of correlated fermion pairs

Magnetic-field Feshbach resonance molecules → ← attractive repulsive BB > free atoms

repulsive Changing the interaction strength in real time molecules attractive BB > EFEF 2  s/G : FAST

Changing the interaction strength in real time: SLOW molecules attractive BB > EFEF 40  s/G

Changing the interaction strength in real time: SLOWER molecules attractive BB > EFEF 4000  s/G Cubizolles et al., PRL 91, (2003); L. Carr et al., cond-mat/

Molecular Condensate M. Greiner, C.A. Regal, and D.S. Jin, Nature 426, 537 (2003). Time of flight absorption image initial T/T F :

repulsive 40  s/G Observing a Fermi condensate attractive BB > EFEF ? 4000  s/G ?

Condensates w/o a two-body bound state C. Regal, M. Greiner, and D. S. Jin, PRL 92, (2004) Dissociation of molecules at low density  B = 0.12 G  B = 0.25 G  B=0.55 G T/T F =0.08  B (gauss)

Fermionic condensate  Clearly see condensation on the “atom-side” of the resonance! T/T F =0.08  molecules atoms  two-body molecules pairing due to many-body effects

BCS-BEC Crossover  BCS (atoms) BEC (molecules)  N 0 /N 0 C. Regal, M. Greiner, and D. S. Jin, PRL 92, (2004)

Conclusion  An atomic Fermi gas provides experimental access to the BCS-BEC crossover region.  Fermi gas ↔ molecular BEC interconversion has been explored.  Condensates of correlated fermionic atom pairs have been achieved ! generalized “Cooper pairs” with strong interactions Many opportunities for further experimental and theoretical work... Next…

Current group members: M. Greiner J. Goldwin S. Inouye C. Regal J. Smith M. Olsen