Novel quantum states in spin-orbit coupled quantum gases Han Pu (浦晗) Rice University Houston, Texas, USA 2016 Hangzhou Workshop on Quantum Degenerate Fermi Gases, Zhejiang Univ., June, 2016

Outline Introduction Itinerant ferromagnetism in trapped 2D Rashba Fermi gas Free-space soliton in attractive BEC with 3D SOC Summary SOC Single-particle dispersion Many-body properties

Spin-orbit coupling in Cold Atoms p+k atomic pseudo-spin (internal degrees of freedom) k photon atomic center-of-mass motion (external degrees of freedom) p

Itinerant ferromagnetism of Rashba Fermi Gas in 2D S.-S. Zhang, W.-M. Liu, HP, PRA 93, 043602 (2016)

Localized vs. Itinerant Magnetism in Cold Atom Itinerant ferromagnetism Stoner criterion: FM appears when the gain in exchange interaction is larger than the loss in kinetic energy

Itinerant Ferromagnetism in Cold Atom Stoner criterion: FM appears when the gain in exchange interaction is larger than the loss in kinetic energy Ketterle, Science 325, 1521 (2009)

Itinerant Ferromagnetism in Cold Atom Alternative explanation: correlation effects Gutzwiller Ansatz: Non-magnetic, correlation reduces repulsive interaction energy. Zhai, PRA 80, 051605(R) (2009) Ketterle, Science 325, 1521 (2009)

Rashba spin-orbit coupling Single-particle dispersion: Adding an isotropic harmonic trap: m For Landau-level-like structure Wu et al., CPL 28, 097102 (2011)

Trapped quantum gases with large Rashba SOC Spin textures of a Rashba BEC. Landau-level structure enhances interaction effects. Phys. Rev. Lett.108.010402 (2012), H. Hu, B. Ramachandhran, HP, and X. –J. Liu; Phys. Rev. A 87. 033627 (2013), B. Ramachandhran, H. Hu, and HP. Current work: trapped repulsive fermions with large Rashba SOC Does the system exhibit ferromagnetism?

Exact Diagonalization m Small number (N) of spin-1/2 fermions Weak repulsive interaction Lowest Landau level approximatin Fock state basis:

Ground state for N=6 Good quantum number : 3 2 1 0.1 0.2 0.3

Chiral ferromagnetism 3 2 1 0.1 0.2 0.3 Density and current distribution Spin texture

Phase diagram

Hartree-Fock treatment For weak correlated regime, Hartree-Fock approximation is valid: Solid lines: ED HF vs. ED: 1. , which is due to the neglect of correlation effect in HF. 2. Correlation effect is large near the critical point, leads to discrepancies between ED and HF.

Phase diagram: quantum vs. mean-field HF vs. ED: 1. , which is due to the neglect of correlation effect in HF. 2. Correlation effect is large near the critical point, leads to discrepancies between ED and HF. 3. At very large g, strong correlation destroys the magnetic phase, which is not captured by HF.

Itinerant ferromagnetic state without SOC? arXiv:1605.07850 (Inguscio group)

Free-space soliton in attractive BEC with 3D SOC Y.-C. Zhang, Z.-W. Zhou, B. Malomed, HP, PRL 115, 253902 (2015)

Solitons in nonlinear systems Conventional wisdom: stable solitons only exist in 1D Solitons in attractive BEC (Hulet) Balance between KE (1/L2) and attractive interaction (1/L)

Solitons in nonlinear systems In higher dimensions, solitons are unstable. Example: 2D

Solitons in nonlinear systems In higher dimensions, solitons are unstable. However, may be stabilized by adding inhomogeneous potentials. Solid lines: stable Dashed lines: unstable The trapping potential lowers the norm below the collapsing threshold, and also prevents the soliton from decaying. Mihalache et al., PRA 73, 043615 (2006)

Solitons in attractive BEC with SOC Can modified dispersion induced by SOC stabilize free-space solitons in 3D? Dimensional analysis:

Solitons in attractive BEC with SOC Focusing on m=0 (semi-vortices) Mixtures of semi-vortices (mixed mode): Full numerical method: solving the GPE. Variational method: minimizing energy w.r.t. a variational ansatz.

Solitons in attractive BEC with SOC: stability regime Stability phase diagram (shaded regime: stable soliton) MM SV semi-vortex mixed mode

Solitons in attractive BEC with SOC: collision A gentle collision A violent collision

Summary SOC in cold atoms modifies single-particle dispersion. This leads to many novel phenomena in many-body physics. S.-S. Zhang, W.-M. Liu, HP, PRA 93, 043602 (2016 Y.-C. Zhang, Z.-W. Zhou, B. Malomed, HP, PRL 115, 253902 (2015)