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

Quantum magnetism with few cold atoms Gerhard Zürn Graduiertenkolleg Hannover, 17.12.2015

States of matter http://en.wikipedia.org/wiki/high-temperature_superconductivity What are the key ingredients for high-tc supercondutivity? Can we simulate some of them?

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, 230401 (2015) P. Murthy et al., PRL 115, 010401 (2015) The Heisenberg model: picture: T. Fukuhara et al., Nat.Phys. 9, 235 241 (2013)

Spin order on a lattice Many body system at high low temperature For positive J: 1D: (Bethe-Ansatz, DMRG,...) 2D and large N, anisotropic J ex, difficult

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 s-wave scattering length a by Feshbach resonances - Shape of the external confinement (optical dipole traps, lattices)

A lattice for ultracold atoms Shape a lattice potential with light J t

A lattice for ultracold atoms Shape a lattice potential with light Tunneling J t On-site interaction U

A lattice for ultracold atoms For large enough U/J t : Mott-insulating state is reached, fixed particle number per site Tunneling J t On-site interaction U

D. Greif et al., arxiv:1511.06366 M. Greiner group, Harvard Fermionic Mott insulators

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

Outline Preparation and control of few-fermion systems Two fermions in a double well potential Finite antiferromagnetic spin chains without a lattice

Outline Preparation and control of few-fermion 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

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

High Fidelity Preparation E 2-component mixture in reservoir T=250nK superimpose microtrap scattering thermalisation expected degeneracy: T/T F = 0.1 switch off reservoir 1 P(E) p 0 = 0.9999 count + magnetic field gradient in axial direction

Counts Single atom detection CCD 1/e-lifetime: 250s Exposure time 0.5s 50 CCD 40 30 20 1-10 atoms can be distiguished with high fidelity. (> 99% ) F. Serwane et al., Science 332, 336 (2011) 10 0 0 1 2 3 4 5 6 7 8 9 10 Flourescence normalized to atom number

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)

g 1D a [10 3D [10 a 3 perp a ħ 0 ] w perp ] a 3D [10 3 a 0 ] Interaction in 1D 3D 20 10 radially strongly confined 0-10 -20 750 800 850 900 magnetic field [G] 1D 20 1 10 aspect ratio: w II / w perp 1:10 1D Z. Idziaszek and T. Calarco, PRA 74, 022712 (2006) 0-10 -1-20 2 2 a3d 1 1D 2 3D g = ma 1 Ca / a 750 800 850 900 magnetic field [G] M. Olshanii, PRL 81, 938 (1998) G. Zürn et al., PRL 110, 135301 (2013)

Few atoms in a harmonic trap control of the particle number tunability of the interpart. interaction imbalanced balanced 2 E [hw ll ] 0-2 -3-2 -1 0 1 2 3-1/g [a ll hw ll ] -1 T. Busch et al., Found. Phys. 28, 549 (1998)

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] 0,0 0 1 2 3 4 5 N Determine: how many is many? Resolution: ~ 1% of E F A. Wenz et al., Science 342, 457 (2013)

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

Outline Preparation and control of few-fermion systems Two fermions in a double well potential Finite antiferromagnetic spin chains without a lattice

Acoustooptic deflector Creating a tunable potential

Tunneling in a double-well Preparation J t Detection scheme U = 0 Single-part. tunneling Calibration of J, J << w

Tunneling in a double-well Preparation J Detection scheme U 0 Correlated tunneling 9

Measuring Energies in a double well Conditional single-particle tunneling Resonant pair tunneling U>>J Measure amplitudes of single-particle and pair tunneling as a function of tilt

Preparation of the ground state

Two site Hubbart model - eigenstates Spectrum of eigenenergies ( =0)

Occupation statistics Number statistics for the balanced case depending on the interaction strength: Single occupancy Double occupancy S. Murmann et al., PRL 114, 080402 (2015) 12

Occupation statistics Number statistics for the balanced case depending on the interaction strength: Single occupancy Double occupancy S. Murmann et al., PRL 114, 080402 (2015) 12

Measuring energy differences E [J] Method: Trap modulation spectroscopy 5 U ~ c> 0-5 0 5 U [J] b> a> -5 S. Murmann et al., PRL 114, 080402 (2015)

Next Basic building block is realized: - S=0 state. - one particle per site - control of super-exchange energy Assemble antiferromagnetic ground state by merging several double wells M. Lubasch et al., 107, 165301 (2011)

Outline Preparation and control of few-fermion systems Two fermions in a double well potential Finite antiferromagnetic spin chains without a lattice

A Heisenberg spin chain without a lattice. in a single 1-D tube through strong repulsion!

Fermionization Non-interacting Repulsive G. Zuern et al., PRL 108, 075303 (2012)

A spin chain without a lattice A Wigner-crystal-like 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, 013611 (2014) Volosniev et al., Nature Comm 5, 5300 (2014) 2

Realization of spin chain Non-interacting Repulsive Attractive Non-interacting Non-interacting 1 g 1D a ħω 1 Gharashi, Blume, PRL 111, 045302 (2013) Lindgren et al., New J. Phys. 16 063003 (2014) Bugnion, Conduit, PRA 87, 060502 (2013) 5

Realization of spin chain Non-interacting Repulsive Attractive Non-interacting Fermionization Non-interacting 1 g 1D a ħω 1 Gharashi, Blume, PRL 111, 045302 (2013) Lindgren et al., New J. Phys. 16 063003 (2014) Bugnion, Conduit, PRA 87, 060502 (2013) 5

Realization of spin chain Non-interacting Repulsive Attractive Non-interacting Non-interacting Fermionization 1 g 1D a ħω 1 Gharashi, Blume, PRL 111, 045302 (2013) Lindgren et al., New J. Phys. 16 063003 (2014) Bugnion, Conduit, PRA 87, 060502 (2013) 5

Realization of spin chain Non-interacting Repulsive Attractive Non-interacting At resonance: Spin orientation of rightmost particle allows for identification Fermionization of state Non-interacting Antiferromagnet Ferromagnet 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) 5

Measurement of spin orientation Ramp on interaction strength Non-interacting system 1 g 1D a ħω 1

Measurement of spin orientation Ramp on interaction strength Spill of one atom Non-interacting system Minority tunneling Majority tunneling 1 g 1D a ħω 1

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, 215301 (2015) Note: data points in gray can be explained by CoM-Rel motion coupling

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, 215301 (2015)

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, 215301 (2015)

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

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:

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, 230401 (2015) P. Murthy et al., PRL 115, 010401 (2015) I. Boettcher et al. arxiv:1509.03610, PRL, in press

Precise energy measurements Radio Frequency spectroscopy bare RF transition RF photon RF transition with interaction RF photon+ ΔE

CoM Rel. motion coupling cubic and quartic terms in the potential 2-1 sample, detect majority

Creating imbalanced samples

Eigenstates Antiferromagnet Intermediate Ferromagnet - 3J 0 0 0 - J 0 0 0 0

Tunneling Model Tunneling rate: Overlap of spin chains Gamma-factor Probabilty to tunnel from i> f>

AOD setup Light intensity distribution