1. The p-wave scattering of spin-polarized Fermi gases in low dimensions
第九届冷原子物理青年学者学术讨论会
The p-wave scattering of spin-polarized Fermi gases in low dimensions
彭世国
中科院武汉物理与数学研究所
2015年8月7日，长春
Shi-Guo Peng, Shina Tan, and Kaijun Jiang, Physical Review Letters 112, (2014)

2. Outline The p-wave scattering in cold atoms Background and motivation
The short-range boundary conditions for p-wave scattering
Calculations of scattering parameters in low dimensions
Conclusions

3. Outline The p-wave scattering in cold atoms Background and motivation
The short-range boundary conditions for p-wave scattering
Calculations of scattering parameters in low dimensions
Conclusions

4. Central forces between two cold atoms

5. The partial-wave method (Angular momentum conserved)
l-partial-wave function
Where

6. Why always s wave ? Bosons s (l=0) d (l=2) g (l=4) … … Fermions
p (l=1)
f (l=3)
h (l=5)
The contributions form high-partial waves is suppressed as energy decreases.
Polarized fermions

7. Properties of p-wave scattering ( )
s wave ( )

8. Outline The p-wave scattering in cold atoms Background and motivation
The short-range boundary conditions for p-wave scattering
Calculations of scattering parameters in low dimensions
Conclusions

9. p-wave Feshbach resonances (3D)
C. Ticknor, et al., PRA 69, (2004),
Splitting of p-wave Feshbach resonances
C. A. Regal, et al., PRL 90, (2003),
C. Ticknor, et al., PRA 69, (2004),
J. Zhang, et al., PRA 70, (2004),
C. H. Schunck, et al., PRA 71, (2005), …

10. p-wave scattering in low dimensions
K. Gunter, et al., Physical Review Letters 95, (2005).

11. Theoretical description
B. E. Granger and D. Blume, Physical Review Letters 92, (2004). (K-matrix)
L. Pricoupenko, Physical Review Letters 100, (2008). (pseudopotential)
How to describe the splitting of p-wave Feshbach resonances ?

12. Outline The p-wave scattering in cold atoms Background and motivation
The short-range boundary conditions for p-wave scattering
Calculations of scattering parameters in low dimensions
Conclusions

13. Short-range boundary conditions

14. Short-range boundary conditions

15. Outline The p-wave scattering in cold atoms Background and motivation
The short-range boundary conditions for p-wave scattering
Calculations of scattering parameters in low dimensions
Conclusions

16. Quasi-1D geometry
Idziaszek, PRA 79, (2009); Peng et al., PRA 83, (2011).

17. Quasi-1D geometry
Match the behavior of the wavefunction with the short-range boundary conditions at

18. Elastic collision
checking the behavior of the wavefunction at large separation,
i.e., , all the scattering parameters could easily be obtained.
For example,
(for isotropic interaction)
Granger&Blume (2004); Pricoupenko (2008)
S.-G. Peng, et al., PRL112, (2014).

19. Inelastic collision
S.-G. Peng, et al., PRL 112, (2014).

20. Quasi-2D geometry
After a similar procedure as that of 1D case, the scattering amplitude, phase shift, and scattering area can easily be obtained, as well as those inelastic parameters.
S.-G. Peng, et al., PRL 112, (2014).

21. vs Experiments
PRL 95, (2005).
PRL 112, (2014).

22. Conclusions
Introduce an useful short-range boundary conditions for p-wave interactions, which can describe the splitting of the p-wave resonances;
According to the short-range boundary conditions, we study the elastic scattering properties, as well as those of inelastic collision;
Our theory agrees well with the observations of the experiment.

23. Thanks for your attention !!