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**Creating new states of matter:**

Experiments with ultra-cold Fermi gases Selim Jochim MPI für Kernphysik and Universität Heidelberg Henning Moritz ETH Zürich

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**Today The molecular BEC – what can we do with it?**

Crossover to a gas of (weakly bound) Cooper pairs Fundamental excitations, gap Fermi Superfluidity With tunable interactions: Model system for High-TC superconductors, Neutron stars, Quark-Gluon Plasma and more ….

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**The molecular condensate:**

What makes it special? Why does it work? What can we do with it? How cold is it?

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**Change the magnetic field!**

molecular BEC na3 = 0.04

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**exploring the crossover**

na3 = 0.28 molecular BEC na3 = 0.04

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**exploring the crossover**

Bosons Fermions na3,kF|a| = na3 = 0.28 molecular BEC na3 = 0.04

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**exploring the crossover**

Bosons Fermions na3,kF|a| = na3 = 0.28 kF|a| = 6 molecular BEC na3 = 0.04

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**exploring the crossover**

Bosons Fermions na3,kF|a| = na3 = 0.28 kF|a| = 6 molecular BEC degenerate Fermi gas na3 = 0.04 kF|a| = 1 Bartenstein et al, PRL 92, (2004)

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**crossover reversible and lossless !**

reversibility BEC 1s Fermi gas 1s BEC BEC after 2s crossover reversible and lossless ! T/TF 0.03 in Fermi gas limit Carr et al.,PRL 92, (2004) for 90% condensate fraction in BEC limit

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**BEC – BCS crossover 1980 crossover molecules Cooper pairs**

strong coupling Cooper pairs weak coupling crossover 1980

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**A tunable BEC-BCS gas! 6Li2 BEC critical temperature**

We can freely change the interaction without increasing the entropy B-field kBTF: Fermi energy Epair : pairing energy M. Holland et al., PRL (2001)

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**What determines the shape of a BEC?**

Noninteracting atoms: ground state of the trap

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**Shape of a BEC Interacting atoms: mean field**

V n = N/V N ri r Valid for na3<<1 !!!

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**Gross-Pitaevskii equation**

Describe system as single particle wave function external potential interaction chemical potential kinetic term Ignore kinetic term: Thomas-Fermi approx.

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**Size of a Fermi gas Ignoring interactions:**

With interactions: no analytic expression, even difficult to calculate numerically RF Fermi energy EF=kBTF

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Interacting Fermi gas Description difficult: kinetic energy is dominant (Fermi momentum), or of similar magnitude as interaction, simple mean field interaction only works for a<< 1/kF More general: scattering cross section is limited:

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Unitary interaction For unitary interaction (k>>1/a), the mean field energy scales just as the kinetic energy: This results in a rescaling of the Fermi energy by a constant factor (1+b) EF,unitary=(1+b)EF,ideal

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**Universal behavior on resonance!**

EF,unitary=(1+b)EF,ideal is supposed to be a universal parameter independent of the physical system: In neutron stars, nuclei, quark-gluon plasma Hard to determine quantitatively Now measured experimentally Also quantum Monte Carlo and other methods are now in good agreement, best precision caclulation so far: b=-0.58(1) Astrakharchik et al. PRL (2004)

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**How to measure b ? Simply measure cloud size!**

shape should be the same as for noninteracting gas … Unfortunately: Precision very poor!

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**More precise measurements**

Which quantities can be measured with the highest accuracy?

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**collective modes cigar-shaped trap nr = 755(10) Hz, nz 22 Hz axial**

radial

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**collective modes two kinds of radial modes: „breathing“ compression**

„quadrupole“ surface mode

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**axial coll. excitation on resonance: frequency (normalized to sloshing**

mode) 600 800 1000 1200 magnetic field (G) on resonance:

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axial coll. excitation frequency (normalized to sloshing mode)

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**axial coll. excitation frequency (normalized to sloshing mode) 600 800**

1000 1200

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**radial coll. excitation**

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**What kind of mode was excited?**

surface mode? compression mode? need to have a closer look! Lee, Huang, Yang prediction

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**More frequency measurements …**

Radio frequency spectroscopy rf ~80MHz breaking molecules costs energy → molecular signal up-shifted breaking pairs costs energy → pair signal up-shifted mI= -1 |3> |2> 1 |1> high B-field

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**rf spectra in BEC limit atoms only atom-molecule mixture**

no evaporation T >> Tc atoms only atom-molecule mixture evaporation to T Tc P = 300 mW molecular signal: two-body physics !! evaporation to T < 0.4 Tc P = 35 mW pure molecular sample (BEC) rf offset (kHz) 100kHz 4.8mK 0.4neV

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**rf spectra in BEC limit T ≈ 0.2 TF double-peak structure:**

very large pos. sc. length T ≈ 0.2 TF double-peak structure: atoms and pairs T = 0.0? TF pairs only ! pair signal shifts with EF ! many-body physics rf offset

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**rf spectra in crossover regime**

very large neg. scatt. length rf offset (kHz)

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**rf spectra in crossover regime**

large neg. sc. length rf offset (kHz) 100kHz 4.8mK 0.4neV 1kHz 48nK 4peV!

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**gap vs. interaction strength**

Fermi energy at two different levels of trap power 1.1µK (23 35mW 3.3µK (68 1 W

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**gap vs. interaction strength**

comparison with radial trap frequency

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**universal lineshape data taken on resonance,**

frequency scale normalized to Fermi energy 0.16 EF

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**Where’s superfluidity?**

We’ve seen the gap: But is there superfluidity?? Is there a “condensate”??? Yes, there it is!! Condensate above resonance, 900G Zwierlein et al., MIT First observation: JILA Observe bimodal distributions, with both condensed pairs and thermal cloud

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**Condensate Fraction Data: MIT (2004)**

Temperature measurement difficult: Alternative: measure condensate fraction

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Superfluidity??? Bimodal distributions are a strong indication for a phase transition, but is there a superfluid phase? To date best method: Rotating superfluid needs to develop a vortex lattice Challenge: The visibility of the vortices might be very small: condensate fraction is rather tiny in BCS regime

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**Observation of vortices!**

MIT experiment (2005) Vortices on BEC side of resonance!

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**Vortices in the cross over**

792G 740G 766G 812G 833G 843G 853G 863G Now a tool to check superfluidity!!!

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Polarized gases What happens if you change the balance between the two different spin states in the experiment? What would that correspond to in a superconductor? …..

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**Many different answers ….**

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**Superfluidity in an imbalanced gas**

MIT

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Condensate fraction …. MIT

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**Polarization detection scheme**

MIT experiment

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Phase separation MIT experiment

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**Condensate fraction vs. P**

MIT experiment

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**Phase separation (elongated trap)**

Rice University

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**A matter of temperature??**

This trap is very elongated!!

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**tomorrow Condensed Matter Physics with atoms?**

Periodic potentials, bosonic Case: Mott isolator Fermions: The Fermi Surface Interactions of Fermions in optical lattices Low dimensional systems Future directions with optical lattices Final discussion Slides available at

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