Quantum magnetism with few cold atoms. Gerhard Zürn Graduiertenkolleg Hannover,


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1 Quantum magnetism with few cold atoms Gerhard Zürn Graduiertenkolleg Hannover,
2 States of matter What are the key ingredients for hightc supercondutivity? Can we simulate some of them?
3 Related phenomena  2D structure: study phase transition and phase correlation first order correlation function g 1 (r)  effective magnetic interaction exchange interaction M. Ries et al., PRL 114, (2015) P. Murthy et al., PRL 115, (2015) The Heisenberg model: picture: T. Fukuhara et al., Nat.Phys. 9, (2013)
4 Spin order on a lattice Many body system at high low temperature For positive J: 1D: (BetheAnsatz, DMRG,...) 2D and large N, anisotropic J ex, difficult
5 The cold gases approach  Reduce the complexity of a system as much as possible until only the essential parts remain! (e.g. consider only nearest neighbor interaction)  Tunability of interaction: vary swave scattering length a by Feshbach resonances  Shape of the external confinement (optical dipole traps, lattices)
6 A lattice for ultracold atoms Shape a lattice potential with light J t
7 A lattice for ultracold atoms Shape a lattice potential with light Tunneling J t Onsite interaction U
8 A lattice for ultracold atoms For large enough U/J t : Mottinsulating state is reached, fixed particle number per site Tunneling J t Onsite interaction U
9 D. Greif et al., arxiv: M. Greiner group, Harvard Fermionic Mott insulators
10 Control ordering? Energy scale relevant for ordering: Superexchange J t 2 /U J ex = 4 J t 2 /U Challenge: low enough entropy to observe long range correlation Our Idea  Bottom up approach: Create this fundamental building block and scale system up
11 Outline Preparation and control of fewfermion systems Two fermions in a double well potential Finite antiferromagnetic spin chains without a lattice
12 Outline Preparation and control of fewfermion systems Two fermions in a double well potential Finite antiferromagnetic spin chains without a lattice Prepare finite, deterministic samples, where all degrees of freedom are controlled
13 Requirements for Control Pauli principle: each single particle state not occupied by more than one Fermion Control over the quantum states of the trap Control over particle number Requirement: highly degenerate Fermi gas control over the trap depth more precise then level spacing
14 High Fidelity Preparation E 2component mixture in reservoir T=250nK superimpose microtrap scattering thermalisation expected degeneracy: T/T F = 0.1 switch off reservoir 1 P(E) p 0 = count + magnetic field gradient in axial direction
15 Counts Single atom detection CCD 1/elifetime: 250s Exposure time 0.5s 50 CCD atoms can be distiguished with high fidelity. (> 99% ) F. Serwane et al., Science 332, 336 (2011) Flourescence normalized to atom number
16 High Fidelity Preparation 2 atoms 8 atoms count the atoms fluorescence normalized to atom number Lifetime in ground state ~ 60s >> 1/w F. Serwane et al., Science 332, 336 (2011)
17 g 1D a [10 3D [10 a 3 perp a ħ 0 ] w perp ] a 3D [10 3 a 0 ] Interaction in 1D 3D radially strongly confined magnetic field [G] 1D aspect ratio: w II / w perp 1:10 1D Z. Idziaszek and T. Calarco, PRA 74, (2006) a3d 1 1D 2 3D g = ma 1 Ca / a magnetic field [G] M. Olshanii, PRL 81, 938 (1998) G. Zürn et al., PRL 110, (2013)
18 Few atoms in a harmonic trap control of the particle number tunability of the interpart. interaction imbalanced balanced 2 E [hw ll ] /g [a ll hw ll ] 1 T. Busch et al., Found. Phys. 28, 549 (1998)
19 Transferred fraction E [ħw ll ] Measure the interaction energy vary the number of majority particles repulsive interaction 2,0 1,5 0,6 1,0 0,4 0,2 0,5 0,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 interaction shift [khz] 0, N Determine: how many is many? Resolution: ~ 1% of E F A. Wenz et al., Science 342, 457 (2013)
20 Realize systems with magnetic ordering We have full control of a harmonically trapped system. Can we prepare an ordered state with similar fidelity and control? We have very low entropy per particle! Further requirement: Shape the trapping potential: Start with the smallest possible system
21 Outline Preparation and control of fewfermion systems Two fermions in a double well potential Finite antiferromagnetic spin chains without a lattice
22 Acoustooptic deflector Creating a tunable potential
23 Tunneling in a doublewell Preparation J t Detection scheme U = 0 Singlepart. tunneling Calibration of J, J << w
24 Tunneling in a doublewell Preparation J Detection scheme U 0 Correlated tunneling 9
25 Measuring Energies in a double well Conditional singleparticle tunneling Resonant pair tunneling U>>J Measure amplitudes of singleparticle and pair tunneling as a function of tilt
26 Preparation of the ground state
27 Two site Hubbart model  eigenstates Spectrum of eigenenergies ( =0)
28 Occupation statistics Number statistics for the balanced case depending on the interaction strength: Single occupancy Double occupancy S. Murmann et al., PRL 114, (2015) 12
29 Occupation statistics Number statistics for the balanced case depending on the interaction strength: Single occupancy Double occupancy S. Murmann et al., PRL 114, (2015) 12
30 Measuring energy differences E [J] Method: Trap modulation spectroscopy 5 U ~ c> U [J] b> a> 5 S. Murmann et al., PRL 114, (2015)
31 Next Basic building block is realized:  S=0 state.  one particle per site  control of superexchange energy Assemble antiferromagnetic ground state by merging several double wells M. Lubasch et al., 107, (2011)
32 Outline Preparation and control of fewfermion systems Two fermions in a double well potential Finite antiferromagnetic spin chains without a lattice
33 A Heisenberg spin chain without a lattice. in a single 1D tube through strong repulsion!
34 Fermionization Noninteracting Repulsive G. Zuern et al., PRL 108, (2012)
35 A spin chain without a lattice A Wignercrystallike state: Distinguishable fermions with strong repulsive interactions Fermionization Identical fermions: Pauli principle Mapping on a Heisenberg Hamiltonian  Theory by Frank Deuretzbacher Deuretzbacher et al., PRA 90, (2014) Volosniev et al., Nature Comm 5, 5300 (2014) 2
36 Realization of spin chain Noninteracting Repulsive Attractive Noninteracting Noninteracting 1 g 1D a ħω 1 Gharashi, Blume, PRL 111, (2013) Lindgren et al., New J. Phys (2014) Bugnion, Conduit, PRA 87, (2013) 5
37 Realization of spin chain Noninteracting Repulsive Attractive Noninteracting Fermionization Noninteracting 1 g 1D a ħω 1 Gharashi, Blume, PRL 111, (2013) Lindgren et al., New J. Phys (2014) Bugnion, Conduit, PRA 87, (2013) 5
38 Realization of spin chain Noninteracting Repulsive Attractive Noninteracting Noninteracting Fermionization 1 g 1D a ħω 1 Gharashi, Blume, PRL 111, (2013) Lindgren et al., New J. Phys (2014) Bugnion, Conduit, PRA 87, (2013) 5
39 Realization of spin chain Noninteracting Repulsive Attractive Noninteracting At resonance: Spin orientation of rightmost particle allows for identification Fermionization of state Noninteracting Antiferromagnet Ferromagnet Distinguish states by: Spin densities Level occupation Gharashi, Blume, PRL 111, (2013) Lindgren et al., New J. Phys (2014) Bugnion, Conduit, PRA 87, (2013) 5
40 Measurement of spin orientation Ramp on interaction strength Noninteracting system 1 g 1D a ħω 1
41 Measurement of spin orientation Ramp on interaction strength Spill of one atom Noninteracting system Minority tunneling Majority tunneling 1 g 1D a ħω 1
42 Measurement of spin orientation spin orientation determines state AFM Theory by Frank Deuretzbacher, Luis Santos, Johannes Bjerlin, Stephie Reimann S. Murmann et al., PRL 115, (2015) Note: data points in gray can be explained by CoMRel motion coupling
43 Measurement of occupation probabilities Remove majority component with resonant light Spill technique to measure occupation numbers IM exp. data AFM AFM has most symmetric spatial wavefunction FM many levels required to describe the kink S. Murmann et al., PRL 115, (2015)
44 We can prepare an AFM spin chain! 1 g 1D a ħω 1 Important: We don t really need to resolve this energy scale in our experiment! spin symmetry is fixed by initial preparation S. Murmann et al., PRL 115, (2015)
45 Can we scale it up? It will be extremely challenging to produce longer spin chains But: Can we couple many individual spin chains? J Ex 1 J Ex 2 Current work in progress
46 In collaboration with: Frank Deuretzbacher, Luis Santos Leibniz Universität Hannover Johannes Bjerlin, Stephanie Reimann Lund University Mathias Neidig Andrea Bergschneider Thank you for your attention! Simon Murmann Luca Bayha Dhruv Kedar Vincent Klinkhamer Andre Wenz Martin Ries Michael Justin Bakircioglu Niedermeyer Selim Jochim Puneet Murthy Funding:
47 Combine 2D and lattice geometry We have another experiment: 2D gas with a lattice! J Ex 2? J Ex 1 M. Ries et al., PRL 114, (2015) P. Murthy et al., PRL 115, (2015) I. Boettcher et al. arxiv: , PRL, in press
48 Precise energy measurements Radio Frequency spectroscopy bare RF transition RF photon RF transition with interaction RF photon+ ΔE
49 CoM Rel. motion coupling cubic and quartic terms in the potential 21 sample, detect majority
50 Creating imbalanced samples
51 Eigenstates Antiferromagnet Intermediate Ferromagnet  3J J
52 Tunneling Model Tunneling rate: Overlap of spin chains Gammafactor Probabilty to tunnel from i> f>
53 AOD setup Light intensity distribution
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