Strong correlations in few-atom systems Selim Jochim, Universität Heidelberg
Control over few atoms IBM, 1989: Control over individual atoms Our vision: Control also all correlations between atoms 1 2 3 4 5 6 7 8 9
Outline How do we prepare our samples? How do they interact An antiferromagnet without a lattice Two atoms in a double well Assemble many body systems from individual building blocks?
Creating a finite gas of fermions Fermi-Dirac dist. E ~100µm 1 n p 0 = 0.9999 2-component mixture in reservoir superimpose microtrap (~1.8 µm waist)
Creating a finite gas of fermions switch off reservoir p 0 = 0.9999 + magnetic field gradient in axial direction
Our experimental setup Quasi-1D trap: Aspect ratio F. Serwane et al., Science 332, 336 (2011)
Prepare atom number states We prepare the many-body ground state! F. Serwane et al., Science 332, 336 (2011)
Interactions between the atoms 6 Li ground state Tuning interactions: Feshbach resonance in 6 Li a S=1/2, I=1 half-integer total angular momentum 6 Li is a fermion NO interaction between identical particles in the s-wave limit! 8
Interactions in 1D Confinement induced resonance 2 2 a3d 1 1D 2 3D g = ma 1 Ca / a M. Olshanii, PRL 81, 938 (1998) 1D 3D
Precise energy measurements Radio Frequency spectroscopy bare RF transition RF photon RF transition with interaction RF photon+ ΔE
Measure the interaction energy vary the number of majority particles: Determine: how many is many? A. Wenz et al., Science 342, 457 (2013)
Realize systems with magnetic ordering.. with similar fidelity and control? We have very low entropy per particle!
A Heisenberg spin chain infinite repulsion antisymmetry of the wave function. in a single 1-D tube through strong repulsion! With help from many theorists: Dörte Blume, Nikolaj Zinner, Frank Deuretsbacher, Pietro Massignan, Meera Parish, Jesper Levinsen
Energy of 2 atoms in a harmonic trap Center of mass motion! repulsive attractive B-field T. Busch et al., Foundations of Physics 28, 549 (1998)
Energy of 2 atoms in a harmonic trap Center of mass motion! repulsive attractive B-field T. Busch et al., Foundations of Physics 28, 549 (1998)
Energy of 2 atoms in a harmonic trap Center of mass motion! fermionization repulsive attractive B-field T. Busch et al., Foundations of Physics 28, 549 (1998) G. Zürn et al. PRL 108, 075303 (2012)
Energy of more than two atoms? B-field repulsive attractive
Realization of a spin chain Fermionization Non-interacting Ferromagnet Antiferromagnet repulsive attractive Distinguish states by: Spin densities Level occupation Gharashi, Blume, PRL 111, 045302 (2013) Lindgren et al., New J. Phys. 16 063003 (2014) Bugnion, Conduit, PRA 87, 060502 (2013)
Measurement of spin orientation Ramp on interaction strength Non-interacting system Spin chain
Measurement of spin orientation Ramp on interaction strength Non-interacting system Spill the atom on the right Spin chain Minority tunneling Majority tunneling Remove minority atom N = 2 N = 1
Measurement of spin order At resonance: Spin orientation of rightmost particle allows identification of state Theory by Frank Deuretzbacher et al. S. Murmann et al., Phys. Rev. Lett. 115, 215301
We prepare an AFM spin chain! Important: We don t really need to resolve this energy scale in our experiment!!! S. Murmann et al., Phys. Rev. Lett. 115, 215301 9
Can we scale it up?? It will be extremely challenging to produce longer spin chains But: Can we couple many individual spin chains? S=0 S=0 S. Murmann, A. Bergschneider et al., PRL 114, 080402 (2015)
Can we scale it up?? It will be extremely challenging to produce longer spin chains But: Can we couple many individual spin chains? S=0 S=0 S=0 S=0 S. Murmann, A. Bergschneider et al., PRL 114, 080402 (2015)
Our experimental setup Aspect ratio
A tunable double well Interactions switched off: well L> J well R>
Two interacting atoms Interaction leads to entanglement: well L> J well R> U
Preparing stationary states If we ramp on the second well slowly enough, the system will remain in its ground state:
The eigenstates Spectrum of eigenenergies for the balanced double well: Mott insulator superfluid charge density wave
Preparing stationary states Number statistics for the balanced case depending on the interaction strength:
Preparing stationary states Number statistics for the balanced case depending on the interaction strength: S. Murmann, A. Bergschneider et al., PRL 114, 080402 (2015)
What s next? Fill the double well with two atoms per well: Can an effective plaquette be realized?
What are we excited about? We have another experiment: 2D gas with a lattice Can we realize this idea of coupled spin chains on a large scale? M. Ries et al., PRL 114, 230401 (2015) Viewpoint: P. Pierbiagi, Physics 8, 53 (2015) P. Murthy et al., PRL 115, 010401 (2015) I. Boettcher et al. PRL 116, 045303 (2016) Viewpoint: M. Parish: Physics 9,10 (2016)