1. Han Pu Rice University Collaborators: Lei Jiang (NIST/JQI) Hui Hu, Xia-Ji Liu (Swinburne) Yan Chen (Fudan U.) 2013 Hangzhou Workshop on Quantum Matter Localized Impurity in Ultracold Fermi Gas

2. Useful impurities Impurities can be used to probe physical properties of their host. Quasi-particle DOS S.H. Pan, et al., Nature, 403, 746(2000) Zn impurity in BSCCO

3. Impurities in cold atoms Cold atoms are intrinsically clean. Impurities or disorders can be engineered. Anderson localization of atomic BEC Inguscio group, nature 453, 895 (2008) Aspect group, nature 453, 891 (2008)

4. A local impurity in fermionic superfluid

5. BdG and T-Matrix method T-matrix is convenient for localized contact impurity without trap. Contact potential: T-matrix only depends on energy. BdG method gives numerical results for single impurity in harmonic trap. BdG solves self-consistently a set of coupled equations

6. Contact non-magnetic impurity BdG results with impurity without impurity LDOS at impurity site

7. Contact non-magnetic impurity Bound state occurs when T -1 (w)=0 T-matrix results T-matrix BdG LDOS xx

8. Contact magnetic impurity Bound state energy inside the gap BdG results T-Matrix results Yu-Shiba state Yu, Acta Phys. Sin. 21, 75 (1965) Shiba, Prog. Theor. Phys. 40, 435 (1968)

9. Contact magnetic impurity BdG results LDOS Superfluid gap

10. Extended magnetic impurity Spin up Spin down Impurity: Gaussian potential with width a Impurity strength A strong magnetic impurity induces local spin imbalance A controlled way of generating FFLO state Jiang et al., PRA 83, 061604(R) (2011)

11. Impurity in Fermi gas with spin-orbit coupling 2D Fermi gas with Rashba spin-orbit coupling Sau et al., PRL 104, 040502 (2010) Topological superconducting state Supports Majorana mode in the vortex excitation

12. Topological phase transition in Fermi gas with SOC Liu et al., PRA 85, 021603(R) (2012) Quasi-particle excitation spectrum in the presence of a single vortex Non-topological Topological

13. Impurity in topological and non-topological host Non-topological Topological Increasing impurity strength LDOS near a contact magnetic impurity

14. Contact impurity in topological superfluid Both magnetic and non-magnetic impurity induces mid-gap bound states. Increasing impurity strength As the impurity strength increases, the energy of the bound state approach a universal value:

15. Gap profile For sufficiently large impurity strength, the order parameter is suppressed near the impurity site. Superfluid order parameter:

16. Mid-gap state at the edge For sufficiently large impurity strength, the order parameter is suppressed near the impurity site. Topological superfluid Alicea, Rep. Prog. Phys. 75, 076501 (2012)

17. Visualizing the bound state LDOS:

18. Bound states induced by extended impurity Increasing impurity strength Hu et al., PRL 110, 020401 (2013)

19. Measuring LDOS 3 RF-spectroscopy If state 3 has a flat dispersion:

20. Conclusions and References Engineered impurities allow us to investigate a host of interesting quantum effects in ultracold atomic gases.