Localized Impurity in Ultracold Fermi Gas

1. Localized Impurity in Ultracold Fermi Gas 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

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

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

4. A local impurity in fermionic superfluid

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

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

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

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

9. Contact magnetic impurity BdG results Superfluid gap LDOS

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 Topological superconducting state Supports Majorana mode in the vortex excitation Sau et al., PRL 104, 040502 (2010)

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

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

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 Huet al., PRL 110, 020401 (2013)

19. Measuring LDOS RF-spectroscopy 3 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.