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Two-dimensional atomic Fermi gases Michael Khl University of - - PowerPoint PPT Presentation

Dec 10, 2022 211 likes •497 views

Two-dimensional atomic Fermi gases Michael Khl University of Bonn Two-dimensional Fermi gases Two- dimensional gases: the grand challenge of condensed matter physics High-T c superconductors: After 25 years of research still

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Two-dimensional atomic Fermi gases

  • Michael Köhl
  • University of Bonn
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SLIDE 2

Two-dimensional Fermi gases

Two-dimensional gases: “the grand challenge” of condensed matter physics

High-Tc 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.

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Cold atoms meets condensed matter

  • Quasiparticle spectroscopy by momentum-resolved

photoemission (aka ARPES)

  • Spin transport and spin diffusion
  • 2D Hubbard model
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Quasi-2D geometry

Conditions for 2D:

EF , kBT < < ħwz

Strong axial harmonic confinement

) ln( 1 2

2 2 2 D F D

a k m g    

Mean-field coupling constant in 2D

(Bloom 1975)

Fermi liquid strongly interacting 2D Fermi gas non-interacting 2D Fermi gas Bose gas

  • f dimers

 

D Fa

k

2

ln

  • 1

1

  • BKT transition at TBKT ≈ 0.1 TF in the strongly interacting regime
  • TBKT 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, 105301 (2011), Inguscio, Grimm, Esslinger, Jochim, Moritz, Turlapov, Vale, Zwierlein

Spin ½ Fermi gas with contact interaction

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SLIDE 5

Quasiparticle spectroscopy

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SLIDE 6

Momentum-resolved RF spectroscopy

|↓>= |-9/2> |↑>= |-7/2> |3>= |-5/2>

ħwRF

|3> (E,k)

momentum k Energy E

final state |3> (weak interactions) initial state, e.g. BCS-like dispersion

ħwRF

 

2 2 2

2 2

) (       

m k i k

E

ħwRF

m k f k

E

2

2 2

) (

ARPES in 3D Experiment: Jin Theory: Georges, Strinati, Levin, Ohashi, Zwerger, Drummond, ...

202G Feshbach resonance

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SLIDE 7

2 2 y x

k k k  

Experimental realization

|↓> |↑> |3> RF pulse kx ky

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SLIDE 8

Fermi liquid strongly interacting 2D Fermi gas non-interacting 2D Fermi gas Bose gas

  • f dimers

 

D Fa

k

2

ln

  • 1

1

Spin-balanced Fermi liquid

Fermi liquid: EF, kBT < ħw (two-dimensional) EB < kBT (no pairing) g=1/ln(kFa2D) < 1 (weak interactions)

  • Landau-Fermi liquid

quasi-particles are fermionic

  • finite lifetime 1/t ~ (k-kF)2 (long-

lived near the Fermi surface)

  • effective mass: m*/m > 1,

depending on interaction strength

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SLIDE 9

Comparison with theory

  • B. Fröhlich et al., Phys. Rev. Lett. 109, 130403 (2012)

T/TF=0.3

Effective mass parameter

Experiment Theory

Single-particle spectral function

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SLIDE 10

Strong interactions: Pairing pseudogap

Eth

Fermi liquid strongly interacting 2D Fermi gas non-interacting 2D Fermi gas Bose gas

  • f dimers

 

D Fa

k

2

ln

  • 1

1

EF, kBT < ħw (two-dimensional) EB > kBT (pairing) g=1/ln(kFa2D) > 1 (strong interactions)

Single-particle spectral function

  • M. Feld et al., Nature 480, 75 (2011)

Observation of polaron quasiparticles: M. Koschorreck et al., Nature 485, 619 (2012)

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SLIDE 11

Spin transport

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Spin diffusion

Spin diffusion

 n v D 

m k v

F /

 

2 F

k n 

F

k 1   Fermi gas at unitarity:

m D  

Quantum limit

  • f diffusivity

Zwierlein group, Nature (2011) Weber et al., Nature (2005)

Semiconductor nanostructures 3D Fermi gases at unitarity

m D  3 . 6  m D 

2

10 

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SLIDE 13

Spin dynamics

transversely polarized Fermi gas

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SLIDE 14

Spin-spin interaction

Spin exchange / Spin-rotation Spin relaxation

e.g. spin-orbit coupling breaks symmetry underlying spin conservation

absent in cold atom systems ) ln( 1 2

2 2 2 D F D

a k m g    

Strength determined by interaction constant Many-body effects in Fermi liquid (Leggett-Rice effect)

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SLIDE 15

Longitudinal vs. transverse diffusion

Mullin & Jeon (1992)

~1/T2 longitudinal transverse Magnetisation:

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SLIDE 16

Spin-echo technique

/2 /2  time t 2t Eliminates effect of magnetic field gradient Mz(t) =

characteristic exponent Theory: Hahn, Purcell, Leggett, Mullin, Dobbs, Lhuillier, Laloe, ... Experiment in 3He: Osheroff

  • M. Koschorreck et al., Nature Physics 9, 405 (2013).
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SLIDE 17

Spin diffusion in the strongly interacting regime

Smallest spin diffusion constant ever measured: 0.07(1) ħ/m.

  • M. Koschorreck et al., Nature Physics 9, 405 (2013).
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Implications of D< ħ/m?

Spin diffusivity D < ħ/m implies lMFP< n1/D=d

Spin diffusion

MFP

l v n v D   

m k v

F /

 

2 F

k n 

Resistivity of metals (semiclassically):

MFP

Mean-free path for collisions with phonons or electrons

As function of temperature: lMFP ~ 1/T BUT: Ioffe-Regel criterion lMFP > d → Saturation of resistivity Particle separation

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Strongly correlated materials

Possible ideas for resistivity in solids:

  • Violation of quasiparticle picture [Nature 405, 1027-1030 (2000)]
  • Modification of kinetic theory by correlation effects du to stong

interactions [PRB 66, 205105 (2002)] For cold atoms → ?

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Hubbard model

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Hubbard model in two dimensions

Simplest interacting lattice model Experimental realization

a)

High-resolution imaging: Diffraction limit ~ 2 lattice sites

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With atoms: Excellent tunability

Depends on lattice depth (~ laser intensity) Inhomogeneity of the trap

  • > convenient access to

phase diagram V(x)  x

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SLIDE 23

RF spectroscopy in the lattice

  • resolve single 2D layer
  • spectroscopically separate

singly and doubly occupied lattice sites Singly

  • ccupied sites

Doubly

  • ccupied sites
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SLIDE 24

Two-dimensional Mott insulator

Singly occupied lattice sites Doubly occupied lattice sites Density vs. chemical potential T/t = 3, U/t ~ 30

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Thermodynamic quantities

Compressibility 𝜆 = 1 𝑜2 𝜖𝑜 𝜖𝜈

Theory curves: High-temperature series expansion (2nd order) T/t = 3, U/t ~ 30

Pressure 𝑄 =

−∞ 𝜈

𝑜(𝜈′) 𝑒𝜈′

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SLIDE 26

Summary

  • Quasiparticle spectroscopy of 2D Fermi gases
  • Very low spin diffusion D ~ 0.07 ħ/m in a strongly

interacting 2D Fermi gas

  • In-situ measurement of thermodynamics properties of

2D Hubbard model (-> equation of state)

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SLIDE 27

€€€: Alexander-von-Humboldt Foundation, DFG, EPSRC, ERC, ITN Comiq

Fermi gases

  • J. Bernardoff, F. Brennecke, E. Cocchi, J. Drewes, M. Koschorreck, L. Miller, D. Pertot,
  • A. Behrle, K. Gao, T. Harrison, J. Andrijauskas

Trapped ions

  • T. Ballance, L. Carcagni, M. Link, H.-M. Meyer, R. Maiwald, J. Silver

Thanks

www.quantumoptics.eu