TY - JOUR
T1 - Pseudopotentials for two-dimensional ultracold scattering in the presence of synthetic spin-orbit coupling
AU - Hougaard, Christiaan R.
AU - Mulkerin, Brendan C.
AU - Liu, Xia Ji
AU - Hu, Hui
AU - Wang, Jia
N1 - Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/12/27
Y1 - 2019/12/27
N2 - We derive a pseudopotential in two dimensions (2D) with a 2D Rashba spin-orbit coupling (SOC), following in the same spirit of the frame transformation by Guan and Blume [Q. Guan and D. Blume, Phys. Rev. A 95, 020702(R) (2017)2469-992610.1103/PhysRevA.95.020702]. The frame transformation correctly describes the nontrivial phase accumulation and partial-wave couplings due to the presence of SOC, which modifies the original Fermi pseudopotential in free space, even when the length scale of the SOC is significantly larger than the two-body potential range. As an application, we apply our pseudopotential within the Lippmann-Schwinger equation to obtain an analytical scattering matrix. To demonstrate the validity of our approach, we compare our results with a numerical scattering calculation of the finite-range potential that shows excellent agreement over a wide range of scattering energies and SOC strengths. Our pseudopotential is applicable in the cases of a strong energy-dependent s-wave scattering length and/or non-negligible p-wave interaction, where the original free-space pseudopotential fails. It sets an ideal starting point to explore many-body physics in the presence of synthetic SOC in cold atoms.
AB - We derive a pseudopotential in two dimensions (2D) with a 2D Rashba spin-orbit coupling (SOC), following in the same spirit of the frame transformation by Guan and Blume [Q. Guan and D. Blume, Phys. Rev. A 95, 020702(R) (2017)2469-992610.1103/PhysRevA.95.020702]. The frame transformation correctly describes the nontrivial phase accumulation and partial-wave couplings due to the presence of SOC, which modifies the original Fermi pseudopotential in free space, even when the length scale of the SOC is significantly larger than the two-body potential range. As an application, we apply our pseudopotential within the Lippmann-Schwinger equation to obtain an analytical scattering matrix. To demonstrate the validity of our approach, we compare our results with a numerical scattering calculation of the finite-range potential that shows excellent agreement over a wide range of scattering energies and SOC strengths. Our pseudopotential is applicable in the cases of a strong energy-dependent s-wave scattering length and/or non-negligible p-wave interaction, where the original free-space pseudopotential fails. It sets an ideal starting point to explore many-body physics in the presence of synthetic SOC in cold atoms.
UR - http://www.scopus.com/inward/record.url?scp=85077228103&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.100.062713
DO - 10.1103/PhysRevA.100.062713
M3 - Article
AN - SCOPUS:85077228103
SN - 2469-9926
VL - 100
JO - Physical Review A
JF - Physical Review A
IS - 6
M1 - 062713
ER -