Efimov Physics in a Many-Body Background
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October 13th 2011, Erice, Italy 1
Efimov Physics in a Many-Body Background
Nikolaj Thomas Zinner
University of Aarhus
Denmark
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Efimov Effect
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Vitaly Efimov 1970 Identical bosons in 3D have an infinite ladder of three-body bound states when there is a two-body bound state at zero energy
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Ultracold atoms
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Experimental observation – Grimm group. 133-Cesium Nature 440, 315 (2006).
Many observations have followed using different atomic species!
Florence group – 39K, Nature Phys. 5, 586 (2009).
Bar Ilan group – 7Li, PRL 103, 163202 (2009).
Rice group – 7Li, Science 326, 1683 (2009). Evidence of four-body!
Florence group – 41K-87Rb, PRL 103, 073202 (2009). Heteroatomic mixture!
Three-component 6Li fermionic systems!
Heidelberg group, PRL 101, 203202 (2008). Penn State group, PRL 102, 165302 (2009). Tokyo group, PRL 105, 023201 (2010).
New experimental technique: Radio-frequency association of 6Li trimers. Heidelberg group, Science 330, 940 (2010). Tokyo group, PRL 106, 143201 (2011).
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Background Effects?
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External confinement
Finite temperature
Non-universality
Quantum degeneracy
Condensed Bose or degenerate Fermi systems
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Outline
Effects of Fermi degeneracy on two-body physics
Implementation in the three-body problem
Spectrum and spectral flow
Realistic three-component 6Li systems
Outlook
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Reductionism
Simplify the problem – Single Fermi sea!
Top-down approach. Implement Fermi sea in one component – add two others – consider three-body bound states!
Natural to consider things in momentum space.
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kF
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Cooper pair inspiration
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D(q,E)
Dimer propagator Vacuum
Include single Fermi sea:
Critical value for bound dressed dimer:
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Three-body problem
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Momentum-space three-body equations
Skornyakov and Ter-Martirosian, Zh.Eksp. Teor. Fiz. 31, 775 (1957).
Bound states:
Needs regularization! Use method of Danilov, Zh.Eksp. Teor. Fiz. 40, 498 (1961). Nice recent discuss by Pricoupenko, Phys. Rev. A 82, 043633 (2010)
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Spectrum with Fermi sea
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Increasing kF
kF/k*=0.05
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Spectral Flow
10kF/k*=0.05
22.7 Efimov Scaling!
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The 6Li system
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k*=6.9*10-3 a0-1 kF=0.01k* n~1011 cm-3
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The 6Li system
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k*=6.9*10-3 a0-1 kF=0.03k* n~1012 cm-3
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The 6Li system
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k*=6.9*10-3 a0-1 kF=0.06k* n~1013 cm-3
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Observability?
Densities have been too small or measurements have not been around the second trimer threshold point.
Trimer moves outside threshold regime D’Incao et al. PRL 93, 123201 (2004).
Perhaps not a problem Wang and Esry New. J. Phys. 13, 035025 (2011).
Dimer regime is harder since lowest Efimov state has large binding energy.
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Outlook
Different masses and interactions.
More Fermi seas.
Normal Fermi liquid can become superfluid.
Bose gases normal and condensed.
Scattering problems in the presence of backgrounds.
Non-universal corrections.
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Take-home message
There are background effects in Efimov physics.
They are likely close to experimental regimes.
New universal physics can appear.
Efimov physics ’survives’ many-body physics!
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Acknowledgments
Nicolai Nygaard
Aksel Jensen, Dmitri Fedorov, Georg Bruun
Thomas Lompe for experimental details.
Bernhard Wunsch, Eugene Demler, Fei Zhou, Charles Wang.
Born-Oppenheimer limit and analytics – MacNeill and Zhou PRL 106, 145301 (2011).
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Thank you for your attention!
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Enjoy the dinner!