Few-body physics with ultracold fermions Selim Jochim Physikalisches Institut Universität Heidelberg

The matter we deal with T=40nK … 1µK Density n=10 9 … cm -3 Pressures as low as mbar k B T ~ 5peV Extremely dilute gases, which can be strongly interacting! Extreme matter!

Important length scales interparticle separation size of the atoms de Broglie wavelength size of the atoms scattering length a, only one length determines interaction strength → Universal properties, independent of a particular system! → We can tune all the above parameters in our experiments!

Few-body system: Tune the binding energy of a weakly bound molecule: Tunability of ultracold systems 4 Size (>> range of interaction): Binding energy: Feshbach resonance: Magnetic- field dependence of s-wave scattering length

Ultracold Fermi gases At ultracold temperatures, a gas of identical fermions is noninteracting Ideal Fermi gas 5

Ultracold Fermi gases 6 Need mixtures to study interesting physics! Simplest implementation: spin mixtures (↑,↓)

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

Ultracold Fermi gases Two (distinguishable) fermions form a boson ….. … molecules can form a Bose condensate … … tune from strongly bound molecules to weakly bound Cooper pairs 8 From A. Cho, Science 301, 751 (2003) → realize the BEC-BCS crossover!

A picture from the lab …

What’s going on in our lab 1.Universal three-body bound states „Efimov“ trimers T. Lompe et al., Science 330, 940 (2010) 2.Finite Fermi systems with controlled interactions A new playground with control at the single atom level! F. Serwane et al., Science 332, 336 (2011)

The Efimov effect An infinite number of 3-body bound states exists when the scattering length diverges: (3 identical bosons) At infinite scattering length: E n = E n+1 Scattering length values where Efimov trimers become unbound a n+1 =22.7a n 1/a (strength of attraction)

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

What is observed in experiments? three-body recombination deeply bound molecule

Enhanced recombination With an (Efimov) trimer at threshold recombination is enhanced: deeply bound molecule 1/a (strength of attraction)

What has been done in experiments? Observe and analyze collisional stability in ultracold gases seminal experiment with ultracold Cs atoms (Innsbruck): T. Krämer et al., Nature 440, 315 (2006)

The 6 Li atom 16 |1> |2> a 12 Need three distinguishable fermions with (in general) different scattering lengths: (S=1/2, I=1 -> half-integer total angular momentum)

The 6 Li atom 17 |1> |3> |2> a 13 a 12 a 23 Need three distinguishable fermions with (in general) different scattering lengths: couple Zeeman sublevels using Radio-frequency B- fields: „Radio Ultracold“

2- and 3-body bound states …. Binding energies of dimers and trimers: Three different universal dimers with binding energy Where are trimer states? 1/a (strength of attraction)

Where are the trimer states? Observe crossings as inelastic collisions T. Ottenstein et al., PRL 101, (2008) T. Lompe et al., PRL 105, (2010) Also: Penn State: J. Huckans et al., PRL 102, (2009) J. Williams et al. PRL 103, (2009) University of Tokyo: Nakajima et al., PRL 105, (2010) RG based theory: R. Schmidt, S. Flörchinger et al. Phys. Rev. A 79, (2009) Phys. Rev. A 79, (2009) Phys. Rev. A 79, (2009)

Can we also measure binding energies? Theory data from: Braaten et al., PRA 81, (2010) RF field Attach a third atom to a dimer Measure binding energies using RF spectroscopy |2> |1> |3>

RF-association of trimers dimer trimer T. Lompe et al., Science 330, 940 (2010) radio frequency radio frequency [MHz]

RF-association of trimers 22 T. Lompe et al., Science 330, 940 (2010) T. Lompe et al., PRL 105, (2010) With our precision: theoretical prediction of the binding energy confirmed: Need to include finite range corrections for dimer binding energies Same results for two different initial systems More recent results: Nakajima et al., PRL 106, (2011)

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

An ultracold three-component Fermi gas 24 Color Superfluid Starting grant

What’s going on in our la ｂ 1.Three component Fermi gases RF-spectroscopy of Efimov trimers T. Lompe et al., Science 330, 940 (2010) 2.Finite Fermi systems with controlled interactions A new playground with control at the single atom level! F. Serwane et al., Science 332, 336 (2011)

Our motivation Extreme repeatability and control over all degrees of freedom, but limited tunability Quantum dots, clusters … Wide tunability, but no „identical“ systems Atoms, nuclei …

Conventional trap like a soup plate! Shot glass type trap Creating a finite gas of fermions Control the number of quantum states in the trap! …small density of statesLarge density of states …

Transfer atoms to a microtrap …

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

Atoms in a microtrap Transfer a few 100 atoms into a tightly focused trap (~1.8µm in size, 1.4kHz axial, 15kHz radial trap frequencies) 100µm Trap potential is proportional to intensity, good approximation: harmonic at the center

Single atom detection CCD distance between 2 neighboring atom numbers : ~ 6  1-10 atoms can be distinguished with high fidelity > 99% one atom in a MOT 1/e-lifetime: 250s Exposure time 0.5s

Starting conditions Reservoir temperature ~250nK Depth of microtrap: ~3µK  Expect  Occupation probability of the lowest energy state: > µm L. Viverit et al. PRA 63, (2001)

1.Spill atoms in a controlled way 2.Recapture prepared atoms into magneto-optical trap Preparation sequence

Spilling the atoms …. We can control the atom number with exceptional precision! Note aspect ratio 1:10: 1-D situation 1kHz ~400feV

A green laser pointer trap

We have decent control over the motional degrees of freedom! What about interactions?

The 6 Li atom 37 |1> |2> a 12 (S=1/2, I=1 -> half-integer total angular momentum)

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

First few-body interactions What happens if we bring the two atoms in the ground state across the Feshbach resonance One atom is observed in =2 a~0 a>0

Interactions in 1D Feshbach resonance Confinement induced resonance (for radial harmonic confinement) M. Olshanii, PRL 81, 938 (1998). 1D 3D Trap has aspect ratio 1:10

Energy of 2 atoms in the trap Relative kinetic energy of two interacting atoms (exact solution!) x 2 -x 1 (relative coordinate) T. Busch et al., Foundations of Physics 28, 549 (1998)

2 distinguishable vs. 2 identical fermions Tunneling time equal to case of two identical fermions: the system is „fermionized“ 2 distinguishable fermions 2 identical fermions

Tunneling dynamics

Fermionization relative wave function 2 distinguishable fermions 2 identical fermions (2-particle limit of a Tonks-Girardeau gas) ground state Wave function square, and energy are identical!

Conclusion We detect and count single atoms with very high fidelity We prepare few-fermion systems with unprecedented control We control the interactions in the few-fermion system  A toolbox for the study of few-body systems

The future Investigate interacting few-body systems in the ground state: Few- body „quantum simulator“ Realize multiple interacting wells Measure pairing in a finite system Study dynamics of few- fermion systems: How many atoms do we need to have a thermal ensemble?

Thank you very much for your attention!