1. 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

2. 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

3. 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

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

5. 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

6. 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)

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

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

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

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

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

12. Chiral ferromagnetism3 2 1
0.1
0.2
0.3
Density and current distribution
Spin texture

13. Phase diagram

14. Hartree-Fock treatment
For weak correlated regime, Hartree-Fock approximation is valid:
Solid lines: ED
HF vs. ED:
, 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.

15. Phase diagram: quantum vs. mean-field
HF vs. ED:
, 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.

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

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

18. 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)

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

20. 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, (2006)

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

22. 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.

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

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

25. 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, (2016
Y.-C. Zhang, Z.-W. Zhou, B. Malomed, HP, PRL 115, (2015)