1 / 31

Bogoliubov-de Gennes Study of Trapped Fermi Gases

Bogoliubov-de Gennes Study of Trapped Fermi Gases. Han Pu Rice University (INT, Seattle, 4/14/2011). Leslie Baksmaty Hong Lu Lei Jiang. Randy Hulet Carlos Bolech. Imbalanced Fermi mixtures. Fulde-Ferrel-Larkin-Ovchinnikov instability. BCS Cooper pairs have zero momentum

shirin
Download Presentation

Bogoliubov-de Gennes Study of Trapped Fermi Gases

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Bogoliubov-de Gennes Study of Trapped Fermi Gases Han Pu Rice University (INT, Seattle, 4/14/2011) Leslie Baksmaty Hong Lu Lei Jiang Randy Hulet Carlos Bolech

  2. Imbalanced Fermi mixtures

  3. Fulde-Ferrel-Larkin-Ovchinnikov instability • BCS Cooper pairs have zero momentum • Population imbalance leads to finite-momentum pairs • FFLO instability results in textured states

  4. Experiments on spin-imbalanced Fermi gas • Rice (Hulet Group) • Science 311, 503 (2006) • PRL 97, 190407 (2006) • Nuclear Phys. A 790, 88c (2007) • J. Low. Temp. Phys. 148, 323 (2007) • Nature 467, 567 (2010) • MIT (Ketterle Group) • Science 311, 492 (2006) • Nature 442, 54 (2006) • PRL 97, 030401 (2006) • Science 316, 867 (2007) • Nature 451, 689 (2008) • ENS (Salomon Group) • PRL 103, 170402 (2009)

  5. Observation: Phase separation MW. Zwierlein, A. Schirotzek, C.H. Schunck, and W, Ketterle: Science 311, 492-496 (2006) Superfluid core with polarized halo

  6. Experimental results Hulet n↑ n↓ n↑ - n↓ High T Low T Ketterle Salomon MIT/Paris data are consistent with Local Density Approximation (LDA) Rice data (low T) strongly violates LDA.

  7. Surface Tension 60 mm • Phase Coexistence -> Surface Tension 1 mm Aspect Ratio of Cloud: 50:1 Aspect Ratio of Superfluid: 5:1 Data: Hulet Surface tension causes density distortion Effects of surface tension more important in smaller sample.

  8. Breakdown of LDA P=0.14 LDA LDA + surface tension P=0.53 P=0.72 De Silva, Mueller, PRL 97, 070402 (2006) Data points from Rice experiment.

  9. Surface tension Optimal value that fits data: However, from microscopic theoretical calculation: PRA 79, 063628 (2009)

  10. Solving BdG equations Choose T and

  11. Effect of trap anisotropy: N=200, P=0.4 Density along z-axis Density along r-axis Gap along z-axis AR=1 AR=5 AR=50

  12. Quasi-1D system: N=200, AR=50 Density along z-axis Density along r-axis Gap along z-axis P=0.2 P=0.4 P=0.7

  13. BdG vs. LDA: N=200, AR=50, P=0.6 Gap along z-axis Gap along r-axis LDA BdG n↑ - n↓ N~200,000 n↑ n↓

  14. Going to higher N BdG equation is very nonlinear, it may support many stationary states. Complicated energy landscape For large N, starting from different initial configurations, the BdG solver may converge to different final states.

  15. 3 classes of states SF NN LO

  16. Density profiles (N=50,000) NN SF LO Increasing energy

  17. Upclose on the LO state n↑ n↓

  18. Robustness of the density oscillation Bulgac and Forbes, PRL 101, 215301 (2008) Pei, Dukelsky and Nazarewicz, PRA 82, 021603 (2010)

  19. FFLO in 1D homogeneous trapped Orso, PRL (2007); Hu et al., PRL (2007)

  20. Experiment in 1D (Hulet group) Liao et al., Nature 467, 567 (2010)

  21. … Dimensional crossover: 3D – 1D t t X 1D … ? 3D ? 3D 1D

  22. Model for single impurity in Fermi superfluidity H0 is BCS mean field Hamiltonian

  23. BdG and T matrix methods BdG method givesnumerical results for single impurity in harmonic trap. BdG solves self-consistently a set of coupled equations T-matrix gives exact solutions for localized contact impurity without trap. Contact potential: T matrix only depends on energy.

  24. Localized non-magnetic impurity in 1D trap BdG results with impurity without impurity T matrix results Bound state occurs when T-1(w)=0

  25. Localized magnetic impurity BdG results T matrix results Bound state energy inside the gap This bound state is below the bottom of quasiparticle band.

  26. Spin up Spin down Density and gap profiles for localized magnetic impurity What if we increase impurity width and strength ?

  27. Spin up Spin down Magnetic impurity induced FFLO state Impurity: Gaussian potential Impurity strength

  28. Magnetic impurity induced FFLO state (3D)

  29. Conclusion • Two component Fermi gas offers very rich physics. • Effects of trapping confinement. • Flexibility of atomic system provides opportunities of studying exotic pairing mechanisms.

  30. References • “Concomitant modulated superfluidity in polarized Fermi gases”,Phys. Rev. A 83 023604 (2011) • “Single impurity in ultracold Fermi superfluids”,arXiv:1010.3222 • “Bogoliuvob-de Gennes study of trapped spin-imbalanced unitary Fermi gases”,arXiv:1104.2006

More Related