Localized Impurity in Ultracold Fermi Gas Han Pu

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

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

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)

A local impurity in fermionic superfluid

Bd. G and T-Matrix method Bd. G method gives numerical results for single impurity in harmonic trap. Bd. G 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.

Contact non-magnetic impurity Bd. G results with impurity without impurity LDOS at impurity site

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

Contact magnetic impurity T-Matrix results Bd. G 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

Contact magnetic impurity Bd. G results LDOS Superfluid gap

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

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

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

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

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

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

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)

Visualizing the bound state LDOS:

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

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

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