1 Ultracold few-fermion systems with tunable interactions Selim Jochim Physikalisches Institut Universität Heidelberg
2 The matter we deal with T=40nK 1µK Density n= cm -3 Pressures as low as mbar k B T ~ 5peV Extremely dilute gases, which can be strongly interacting! Extreme matter!
3 Important length scales interparticle separation 3 1/n de Broglie wavelength 2 h 2 mkt size of the atoms 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!
4 Scattering length (1000 a 0 ) Tunability of ultracold systems Feshbach resonance: Magneticfield dependence of s-wave scattering length Few-body system: Tune the binding energy of a weakly bound molecule: Magnetic field (G) Size (>> range of interaction): () / r e ra Binding energy: E B 2 ma 2 4
5 Ultracold Fermi gases At ultracold temperatures, a gas of identical fermions is noninteracting Ideal Fermi gas 5
6 Ultracold Fermi gases Need mixtures to study interesting physics! Simplest implementation: spin mixtures (, ) 6
7 Ultracold Fermi gases Two (distinguishable) fermions form a boson.. molecules can form a Bose condensate realize the BEC-BCS crossover! 7
8 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 From A. Cho, Science 301, 751 (2003) realize the BEC-BCS crossover! 8
9 A picture from the lab
10 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)
11 Binding energy / h (khz) Three-component Fermi gas: Experiments 0 Study of universal three-body bound states: Efimov trimers First direct observation by measurement of the binding energy Magnetic field (G) Three-body loss prohibits study of many-body physics in free space T. Lompe et al., Science 330, 940 (2010) T. Lompe et al., PRL 105, (2010) A. Wenz et al., PRA 80, (R) (2009) T. Ottenstein et al., PRL 101, (2008) 11
12 An ultracold three-component Fermi gas Fermionic trions, Baryons Color Superfluidity and Baryon Formation in Ultracold Fermions: A. Rapp et al., PRL 98, (2007) Jochim 3FLEX 12
13 An ultracold three-component Fermi gas A color superfluid Color Superfluidity and Baryon Formation in Ultracold Fermions: A. Rapp et al., PRL 98, (2007) Jochim 3FLEX 13
14 Atomic color superfluid Starting grant realize this in a 2 - dimensional lattice for optimal in-situ diagnostics Jochim 3FLEX 14
15 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)
16 Motivation An isolated quantum system in which all degrees of freedom can be controlled Study pairing in different interaction regimes, weak or strong Study the time evolution of an isolated system (transition from a deterministic to thermal system)
17 Motivation An isolated quantum system in which all degrees of freedom can be controlled Study pairing in different interaction regimes, weak or strong Study the time evolution of an isolated system (transition from a deterministic to thermal system)
18 Motivation An isolated quantum system in which all degrees of freedom can be controlled Study pairing in different interaction regimes, weak or strong Study the time evolution of an isolated system (transition from a deterministic to thermal system)
19 Outline 1. Preparation and manipulation of deterministic microscopic ensembles 2. Study of the repulsive few-particle system: Fermionization and magnetism 3. Study of the attractive system: correlated tunnelling, and odd-even effect
20 Creating a finite gas of fermions 1. A conventional ultracold Fermi gas T~250nK, T F ~0.5µK ~100µm 2. Superimpose microtrap, depth U~3µK T F ~U~3µK, T/T F ~ Occupation probability of the lowest energy state: > (assuming thermal equilibrium) few µm L. Viverit et al. PRA 63, (2001)
21 Creating a finite gas of fermions Lower trap depth Use a magnetic field gradient to spill: ~600 atoms µ x B ~2-10 atoms M. Raizen et al., Phys. Rev. A 80, (R)
22 Classical atom culling machine
23 counts counts Spilling the atoms % % % 6.5% 2% 2% fluorescence signal signal We can control the atom number with exceptional precision! Note aspect ratio 1:10: 1-D situation
24 Outline 1. Preparation and manipulation of deterministic microscopic ensembles 2. Study of the repulsive few-particle system: Fermionization and magnetism 3. Study of the attractive system: correlated tunnelling, and odd-even effect
25 a 3D [10 3 a 0 ] g 1D [10 a perp ħ perp ] Interactions in 1D Trap has aspect ratio 1:10 Confinement induced resonance 1 1D a a3d 1 1D 2 3D g = ma 1 Ca / a M. Olshanii, PRL 81, 938 (1998). (for radial harmonic confinement) D magnetic field [G]
26 Our major tool: Observe tunneling dynamics: Tilt the trap so much that the highest-lying states have an experimentally accessible tunneling time (~ ms). From observed tunneling time scale infer total energy of the system
27 Mean atom number Repulsive few-body interactions 2,00 1,75 1,50 1,25 1, Hold time [ms] One atom tunnels out of the trap with time τ while the second remains trapped. G. Zürn et al., PRL 108, (2012)
28 tunneling time [ms] g 1D [10 a perp ħ perp ] 2 distinguishable vs. 2 identical fermions distinguishable atoms distiguishable fermions identical fermions linear fit identical fermions identical fermions magnetic field [G] Tunneling time equal to case of two identical fermions: the system is fermionized G. Zürn et al., PRL 108, (2012)
29 Mean atom number Tunneling dynamics 2,00 1,75 1,50 1,25 1, Hold time [ms] G. Zürn et al., PRL 108, (2012)
30 E [ħ a ] Energy of 2 atoms in the trap Relative kinetic energy of two interacting atoms (exact solution!) T. Busch et al., Foundations of Physics 28, 549 (1998) x 2 -x 1 (relative coordinate) /g 1D 1D
31 Fermionization ground state 2 distinguishable fermions 2 identical fermions relative wave function From equal tunneling time in 1D we infer: Wave function square modulus, and energy are identical
32 Three particles? What s the probability for a spin down particle to tunnel first?
33 propability of minority tunneling Three particles 60 3 particles one minority preliminary data error ~ +-5% 0-1,0-0,8-0,6-0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0-1/g1d On resonance, expect 1/3 Preliminary data!
34 propability of minority tunneling more particles particles one minority 4 particles one minority 5 particles one minority preliminary data error ~ +-5% 0-1,0-0,8-0,6-0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0-1/g1d On resonance, expect 1/3 and 1/4, and so on. Preliminary data!
35 probability of creating a spin polarized sample balanced samples 60 3 particles one minority 4 particles one minority 5 particles one minority 4 balanced ferromagnetic antiferromagnetic ,0-0,8-0,6-0,4-0,2 0,0 0,2 0,4 0,6 0,8 1,0-1/g1d Crossover from antiferromagnetic to ferromagnetic correlations! Preliminary data!
36 Outline 1. Preparation and manipulation of deterministic microscopic ensembles 2. Study of the repulsive few-particle system: Fermionization and magnetism 3. Study of the attractive system: correlated tunnelling, and odd-even effect
37 Mean atom number Attractive interactions 2,0 1, G g [a ll h ll ] 0.04 [a ll h ll ] = G g [a [a ll h ll h ll ] ll = G g [a ll h ll ] = ,0 0,5 0, Hold time(ms) Tunneling out of an interacting system is more complex, as the two particles can influence each other. What can we learn from correlated tunneling? Preliminary data
38 P(1) Correlated tunneling N=2 Depending on the interaction strength, the two atoms can tunnel independently, correlated in time or as pairs N=1 0,6 0,5 0,4 uncorrelated g [a ll h ll ] = 0.04 uncorrelated g [a ll h ll ] = 0.04 g [a ll h ll ] = 0.63 g [a ll h ll ] = ,3 N=0 0,2 0,1 N=0 0,0 0,0 0,5 1,0 1,5 2,0 <N> Preliminary data
39 Odd-even effect with ultracold fermions How does the energy of the system evolve for larger systems? 10 g =-0.63[a ll h ll ] 8 int / 0 [db] atom number Systems with closed shells are more stable against decay Preliminary data
40 counts Summary % We prepare few-fermion systems with unprecedented control Control over both attractive and repulsive interactions a) We fermionized two distinguishable atoms 25 2% 2% fluorescence signal b) Observe magnetic correlations in the repulsive fewbody system c) Observe correlated tunneling and odd-even effect with attractive interactions
41 Thank you very much for your attention! Vincent Klinkhamer
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