Two-dimensional atomic Fermi gases. Michael Köhl Universität Bonn

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1 Two-dimensional atomic Fermi gases Michael Köhl Universität Bonn

2 Ultracold Fermi gases as model systems BEC/BCS crossover Search for the perfect fluid: Cold fermions vs. Quark-gluon plasma Cao et al., Science (2012) Few particles systems, observation of Efimov states h/s > 1/4p (universal in strong coupling?) Strongly-correlated quantum phases in Optical lattices e.g. Fermi Hubbard model

3 Fermionic Pairing Bose Einstein condensate of molecules BCS superfluid

4 Fermionic Pairing BCS superfl

5 Fermionic Pairing a Magnetic field Feshbach scattering resonance 3000 Unitary interaction BCS superfl B[G]

6 Fermionic Pairing Crossover superfluid Unitary Fermi gas BCS superfl

7 Fermi pair condensates Composite bosons

8 Fermi condensates C. A. Regal, M. Greiner, and D. S. Jin, PRL 92, (2004)

9 Vortex lattices in the crossover M.W. Zwierlein et al., Nature 435, 1047 (2005)

10 BEC-BCS crossover What happens in reduced dimensions?

11 Two-dimensional Fermi gases Two-dimensional gases: the grand challenge of condensed matter physics High-T c superconductors: After 25 years of research still many open questions Material is too complicated to understand even the basic mechanism How can cold atoms help?. Cleanliness, tunability, testing models.

12 Quasi-2D geometry Strong axial harmonic confinement Conditions for 2D: E F, k B T << ħw z Spin ½ Fermi gas with contact interaction 2p Mean-field coupling constant in 2D g2d (Bloom 1975) m 2 1 ln( k a F 2D ) ln k 2D Fa Bose gas of dimers strongly interacting 2D Fermi gas Fermi liquid non-interacting 2D Fermi gas BKT transition at T BKT 0.1 T F in the strongly interacting regime T BKT decays exponentially towards weak attractive interactions (as in 3D) Theory: Bloom, P.W. Anderson, Randeria, Shlyapnikov, Devreese, Julienne, Duan, Zwerger, Giorgini, Sa de Melo,... Experiment: B. Fröhlich et al., PRL 106, (2011), Inguscio, Grimm, Esslinger, Jochim, Moritz, Turlapov, Vale, Zwierlein

13 Cold atoms meets condensed matter Quasiparticle spectroscopy by momentum-resolved photoemission (aka ARPES) Spin transport and spin diffusion

14 Quasiparticle spectroscopy

15 Momentum-resolved RF spectroscopy Energy E ħw RF 3>= -5/2> 3> (E,k) ħw RF >= -7/2> >= -9/2> 202G Feshbach resonance ħw RF final state 3> (weak interactions) 2 k E f ( k) 2m i 2 initial state, e.g. BCS-like dispersion k 2 E ( k) 2m momentum k ARPES in 3D Experiment: Jin Theory: Georges, Strinati, Levin, Ohashi, Zwerger, Drummond,...

16 Spin-balanced Fermi liquid Landau-Fermi liquid quasi-particles are fermionic finite lifetime 1/t ~ (k-k F ) 2 (longlived near the Fermi surface) effective mass: m*/m > 1, depending on interaction strength Fermi liquid: E F, k B T < ħw (two-dimensional) E B < k B T (no pairing) Bose gas of dimers strongly interacting 2D Fermi gas Fermi liquid ln k 2D Fa non-interacting 2D Fermi gas g=1/ln(k F a 2D ) < 1 (weak interactions)

17 Comparison with theory Single-particle spectral function Experiment Theory Effective mass parameter T/T F =0.3 B. Fröhlich et al., Phys. Rev. Lett. 109, (2012)

18 Strongly imbalanced Fermi gases in 2D The N+1 problem: one > impurity in a large > Fermi sea Mobile impurity interacting with a Fermi sea of atoms Tunable interactions repulsive polaron Energy ln(k F a 2D ) Polaron properties determine phase diagram of imbalanced Fermi mixtures molecule attractive polaron 3D Theory: Bruun, Bulgac, Chevy, Giorgini, Lobo, Prokofiev, Stringari, Svistunov,... 3D Experiment: Zwierlein, Salomon, Grimm, Jochim 2D Theory: Bruun, Demler, Enss, Parish, Pethick, Recati,...

19 Characterizing the attractive polaron Energy repulsive polaron ln(k F a 2D ) attractive polaron molecule free-particle dispersion subtracted Theory from: R. Schmidt, T. Enss, V. Pietilä, E. Demler, PRA 85, (2012) 0 Signal 1 M. Koschorreck et al., Nature 485, 619 (2012)

20 Coherence of the polaron Rabi oscillations between polaron and free particle E [khz] k[μm -1 ] Incoherent transfer: rate ~ amplitude M. Koschorreck et al., Nature 485, 619 (2012)

21 Spin transport

22 Spin transport: spintronics Chalmers Vision: Transport of information by spin excitations rather than charges Non-volatile Less dissipation, energy consumption

23 Spin transport: simple model n (x) n (x) x No interactions: ballistic transport Strong interactions: diffusion j = D d(n n ) dx Diffusion constant D v n Fermi velocity: Density: Cross section: v k F / 3 n k F 1 2 k F m D m Quantum limit of diffusivity for 1 2 k F

24 Spin diffusion Semiconductor nanostructures 3D Fermi gases at unitarity D 2 10 m D 6.3 m Weber et al., Nature (2005) Zwierlein group, Nature (2011) Thywissen group, Science (2014)

25 Spin dynamics transversely polarized Fermi gas

26 Longitudinal vs. transverse diffusion Magnetisation: longitudinal ~1/T 2 transverse Mullin & Jeon (1992)

27 Spin-echo technique p/2 p p/2 0 t 2t time Eliminates effect of magnetic field gradient M z (t) = characteristic exponent Theory: Hahn, Purcell, Leggett, Mullin, Dobbs, Lhuillier, Laloe,... Experiment in 3He: Osheroff M. Koschorreck et al., Nature Physics 9, 405 (2013).

28 Spin diffusion in the strongly interacting regime Smallest spin diffusion constant ever measured: 0.007(1) ħ/m. M. Koschorreck et al., Nature Physics 9, 405 (2013).

29 Implications of D< ħ/m v Reminder: diffusion constant D n vl MFP Mean free path Mean particle separation Spin diffusivity D < ħ/m l MFP < d Resistivity of metals (semiclassically): MFP Mean-free path for collisions with phonons or electrons As function of temperature: l MFP ~ 1/T BUT: Ioffe-Regel criterion l MFP > d Saturation of resistivity

30 Strongly correlated materials Possible ideas for resistivity in solids: Violation of quasiparticle picture [Nature 405, (2000)] Modification of kinetic theory by correlation effects du to stong interactions [PRB 66, (2002)] For cold atoms?

31 Weakly interacting regime r COM M. Koschorreck et al., Nature Physics 9, 405 (2013)

32 Damping and frequency shift non-interacting strongly interacting M. Koschorreck et al., Nature Physics 9, 405 (2013)

33 Damping and frequency shift Mode softening Spin-dipole mode becomes overdamped in the strongly interacting regime [Stringari et al., PRA 2000]. Measured damping rate scales as ~ 1/ln(k F a 2D ) Scattering rate ~ 1/ln(k F a 2D ) 2 Ramsey-dephasing rate: g Ramsey 1600 Hz strongly interacting non-interacting M. Koschorreck et al., Nature Physics 9, 405 (2013)

34 Summary Measurement of single-particle spectral function to observe Fermi liquid (Pseudogap) Polarons Spin diffusion with D~0.01 ħ/m

35 Thanks Fermi gases Trapped ions J. Bernardoff, F. Brennecke, E. Cocchi, J. Drewes, M. Koschorreck, L. Miller, D. Pertot, A. Behrle, K. Gao, T. Harrison, J. Andrijauskas T. Ballance, L. Carcagni, M. Link, H.-M. Meyer, R. Maiwald, J. Silver : Alexander-von-Humboldt Foundation, DFG, EPSRC, ERC, ITN Comiq