Selim Jochim, Universität Heidelberg Ultracold fermions: A bottom-up approach Selim Jochim, Universität Heidelberg

A quick advertisement: Our 2-D Fermi gas experiment

Momentum Distribution Imaging High T Low T Temperature Macroscopic occupation of low-momentum states x y kx ky T/4 = 25ms in-situ density distribution n(x,y) momentum distribution ñ(kx,ky) P. Murthy et al., PRA 90, 043611 (2014)

Phase Diagram normal phase exp.: Tc/TF condensed phase Non-Gaussian fraction normal phase exp.: Tc/TF condensed phase Measured phase diagram: x-axis normalized interaction strength in 2D relevant parameter ln(kf a2d) where kf is the fermi wavevector ( related to the sqrt of density) Y-axis temperature normalized by the central density ( in units of temperatur Tf=2pi hbar^2 n0/2mk_b) Colorscale gives fraction of non gausan quasi condensate fraction. Black line position where we expect the phase transition from above analysis. Again see quasicondensate fraction non zero before transition Critical temperature on bosnic side ( as expected) realtively high and constant White line ( weakly interacting) bosonic theory phase transition : good agreement exp data little bit higher but within systematic and statstical errors agreement Bosnic theory works well until ln kf a zero also expected as in 2D there is a bound state for all interaction strengths ( on 3D reonance still 2D bosons pressent). Compare to theory: matches relatively well. Bump in the center expected as one has to match the two limiting cases. Central part significantly higher than theroy expection for true 2D but maybe due to residual influence of 3rd dimension ( biger to the BCS side for our experiment) also predicted by some theorists that in crossing to 3D critical temperature might be higher On Bcs side not cold enqough to measure significant quasi condensate fraction can not determine critical temperature there but expect to go down ( also seen from upper bound from our data) towards bcs limit bosonic fermionic M. Ries et al., PRL 114, 230401 (2015) see also viewpoint: P. Pieri, Physics 8, 53 (2015)

Investigate the phase coherence of these “condensates”

Phase correlations in 2D 𝑔 1,trap (𝑟)= ℱ𝒯 𝑛 trap (𝒌) =ℱ𝒯( ) Extract correlation function from momentum distribution Tc/TF = 0.129 BKT: 𝑔 1 𝑟 ∼ 1 𝑟 𝜂 consistent with BKT superfluid We are able to extract η(T, ln(kF a2D)) P. Murthy et al., PRL 115, 010401 (2015)

This talk: Experiments with few particles Discrete systems: Work at „T=0“

Our approach to prepare few atoms Fermi-Dirac dist. E ~100µm 1 n p0= 0.9999 2-component mixture in reservoir superimpose microtrap (~1.8 µm waist) F. Serwane et al., Science 332, 336 (2011) 8

+ magnetic field gradient in axial direction Our approach switch off reservoir p0= 0.9999 + magnetic field gradient in axial direction F. Serwane et al., Science 332, 336 (2011) 9

Spilling the atoms …. We can control the atom number with exceptional precision (including spin degree of freedom) Note aspect ratio 1:10: 1-D situation So far: Interactions tuned to zero … F. Serwane et al., Science 332, 336 (2011)

Realize multiple wells … ….. with similar fidelity and control? S. Murmann, A. Bergschneider et al., Phys. Rev. Lett. 114, 080402 (2015) See also viewpoint: Regal and Kaufman, Physics 8, 16 (2015)

The multiwell setup Light intensity distribution S. Murmann, A. Bergschneider et al., Phys. Rev. Lett. 114, 080402 (2015)

A tunable double well J $\Ket{\Psi(t=0)}=\Ket{L}_1\Ket{L}_2=\Ket{LL}$ $\Ket{\chi}=\frac{1}{\sqrt{2}}(\Ket{\uparrow}_1\Ket{\downarrow}_2-\Ket{\downarrow}_1\Ket{\uparrow}_2)= \frac{1}{\sqrt{2}}(\Ket{\uparrow\downarrow}-\Ket{\downarrow\uparrow})$

switch off left well before counting atoms A tunable double well Interactions switched off: switch off left well before counting atoms well |𝐿⟩ well |𝑅⟩ J $\Ket{\Psi(t)}=\Ket{\psi(t)}_1\Ket{\psi(t)}_2$ $\Ket{\psi(t)}_1=\frac{1}{\sqrt{2}}(\Ket{L}_1+\Ket{R}_1)+\frac{1}{\sqrt{2}}(\Ket{L}_1-\Ket{R}_1)e^{-i\Delta E t/\hbar}$

Two interacting atoms J U Interaction leads to entanglement: well |𝐿⟩ $\Ket{\Psi(t)}\neq\Ket{\psi(t)}_1\Ket{\psi(t)}_2$

Preparing the ground state If we ramp on the second well slowly enough, the system will remain in its ground state: An isolated singulett S. Murmann, A. Bergschneider et al., Phys. Rev. Lett. 114, 080402 (2015)

How to scale it up? Preparation of ground states in separated double wells Combination to larger system Can this process be done adiabatically ? Can it be extended to larger systems ? Motivated by: D. Greif et al., Science 340, 1307-1310 (2013) (ETH Zürich)

First steps towards magnetic ordering Realize a Heisenberg spin chain through strong repulsion Lots of input from theory: Dörte Blume, Ebrahim Gharashi, N. Zinner, G. Conduit, J. Levinsen, M. Parish, P. Massignan, C. Greene, F. Deuretzbacher

Interacting 6Li atoms in 1D Assume zero range potential in 1D + harmonic confinement 𝑉 𝑥1−𝑥2 =𝑔1𝐷 𝛿 𝑥1−𝑥2 Tune 𝑔 1𝐷 with confinement induced resonance near Feshbach resonance: Our system: Lithium-6 atoms with 𝜔 2𝜋 ~15kHz transverse confinement M. Olshanii, PRL 81, 938941 (1998)

Energy of 2 atoms in a harmonic trap Relative energy of two contact-interacting atoms: 𝑉 𝑥 = 1 2 𝜇 𝜔 2 𝑥 2 + 𝑔 1𝐷 𝛿(𝑥) repulsive attractive B-field T. Busch et al., Foundations of Physics 28, 549 (1998)

Energy of 2 atoms in a harmonic trap Relative energy of two contact-interacting atoms: 𝑉 𝑥 = 1 2 𝜇 𝜔 2 𝑥 2 + 𝑔 1𝐷 𝛿(𝑥) repulsive attractive B-field T. Busch et al., Foundations of Physics 28, 549 (1998)

Energy of 2 atoms in a harmonic trap Relative energy of two contact-interacting atoms: 𝑉 𝑥 = 1 2 𝜇 𝜔 2 𝑥 2 + 𝑔 1𝐷 𝛿(𝑥) fermionization repulsive attractive B-field G. Zürn et al., PRL 108, 075303 (2012) T. Busch et al., Foundations of Physics 28, 549 (1998)

Energy of more than two atoms? repulsive attractive B-field

Energy of more than two atoms Fermionization Energy ℏ 𝜔 || Non-interacting S=1/2 − 1 𝑔 1𝐷 𝑎 || ℏ 𝜔 || −1 Gharashi, Blume, PRL 111, 045302 (2013) Lindgren et al., New J. Phys. 16 063003 (2014) Bugnion, Conduit, PRA 87, 060502 (2013)

Realization of a spin chain Fermionization Non-interacting S=3/2 Energy ℏ 𝜔 || S=1/2 S=1/2 − 1 𝑔 1𝐷 𝑎 || ℏ 𝜔 || −1 Gharashi, Blume, PRL 111, 045302 (2013) Lindgren et al., New J. Phys. 16 063003 (2014) Bugnion, Conduit, PRA 87, 060502 (2013)

Realization of a spin chain Antiferromagnet Ferromagnet Fermionization Non-interacting S=3/2 Energy ℏ 𝜔 || S=1 Distinguish states by: Spin densities Level occupation S=1/2 − 1 𝑔 1𝐷 𝑎 || ℏ 𝜔 || −1 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 Non-interacting system Ramp on interaction strongth Spin chain Energy ℏ 𝜔 || − 1 𝑔 1𝐷 𝑎 || ℏ 𝜔 || −1

Measurement of spin orientation Non-interacting system Ramp on interaction strength Spill of one atom Spin chain „Minority tunneling“ „Majority tunneling“ Energy ℏ 𝜔 || Remove minority atom N = 2 N = 1 − 1 𝑔 1𝐷 𝑎 || ℏ 𝜔 || −1

Measurement of spin orientation At resonance: Spin orientation of rightmost particle allows identification of state Theory by Frank Deuretzbacher et al.

Measurement of occupation probabilities Remove majority component with resonant light Spill technique to measure occupation numbers 8

We can prepare an AFM spin chain! 9

Can we scale it up?? Approach 2: Can we induce suitable correlations by spilling atoms? ? 𝐽 𝑇𝑢𝑛𝑛𝑒𝑙 𝐽 𝑆𝑝𝑖𝑙𝑙

Summary We studied the phase diagram and coherence properties of a 2-D Fermi gas and prepare and manipulate isolated mesoscopic systems with extremely good fidelity in flexible trapping geometries We prepared antiferromagnetic spin chains in 1D tubes PRL 114, 230401 (2015) PRL 115, 010401 (2015) J PRL 114, 080402 (2015) PRL 108, 075303 (2012) S. Murmann et al., arxiv:1507.01117

? Outlook Can we scale up our systems? or 𝐽 𝑇𝑢𝑛𝑛𝑒𝑙 𝐽 𝑆𝑝𝑖𝑙𝑙 See Andrea Bergschneider‘s poster

Thank you for your attention! Thomas Lompe (-> MIT) Thank you for your attention! Mathias Neidig Simon Murmann Andrea Bergschneider Luca Bayha Dhruv Kedar Martin Ries Michael Bakircioglu Vincent Klinkhamer Andre Wenz Gerhard Zürn Justin Niedermeyer Puneet Murthy Funding: