We present an analytical description for ultracold collisions between two spin- $\frac{1}{2}$ fermions with isotropic spin-orbit coupling (SOC) of the Rashba type. We show that regardless of how weak the SOC may be, at sufficiently low energies the collision properties are significantly modified. The ubiquitous low energy Wigner threshold behavior is changed and its modified form for ground-state neutral atoms is given. The particles are further found to scatter preferentially into the lower-energy helicity states due to the breaking of parity conservation. This latter point establishes interaction with SOC as one mechanism for the spontaneous emergence of handedness. Our theory is applicable both to elementary spin- $\frac{1}{2}$ fermions such as electrons in condensed matter and to ultracold pseudo-spin- $\frac{1}{2}$ atoms such as ${}^{6}$ Li in its ground hyperfine state.We present an analytical description for ultracold collisions between two spin-$\frac{1}{2}$ fermions with isotropic spin-orbit coupling (SOC) of the Rashba type. We show that regardless of how weak the SOC may be, at sufficiently low energies the collision properties are significantly modified. The ubiquitous low energy Wigner threshold behavior is changed and its modified form for ground-state neutral atoms is given. The particles are further found to scatter preferentially into the lower-energy helicity states due to the breaking of parity conservation. This latter point establishes interaction with SOC as one mechanism for the spontaneous emergence of handedness. Our theory is applicable both to elementary spin-$\frac{1}{2}$ fermions such as electrons in condensed matter and to ultracold pseudo-spin-$\frac{1}{2}$ atoms such as ${}^{6}$Li in its ground hyperfine state.

arXiv:1305.4750Physical Review AMay 20, 201324 citations

Advances in Ultracold Collisions: Experimentation and Theory

J. Weiner

Advances in atomic, molecular, and optical physicsJan 1, 199557 citations

Multichannel quantum-defect theory for ultracold atom–ion collisions

Zbigniew Idziaszek, Andrea Simoni, Tommaso Calarco +1 more

We develop an analytical model for ultracold atom–ion collisions using the multichannel quantum-defect formalism. The model is based on analytical solutions of the r −4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of atom–ion interaction in the ultracold domain in terms of only three parameters: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher-order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40 Ca + ion and a Na atom, and compared with numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.We develop an analytical model for ultracold atom–ion collisions using the multichannel quantum-defect formalism. The model is based on analytical solutions of the r −4 long-range potential and on the application of a frame transformation between asymptotic and molecular bases. This approach allows the description of atom–ion interaction in the ultracold domain in terms of only three parameters: the singlet and triplet scattering lengths, assumed to be independent of the relative motion angular momentum, and the lead dispersion coefficient of the asymptotic potential. We also introduce corrections to the scattering lengths that improve the accuracy of our quantum-defect model for higher-order partial waves, a particularly important result for an accurate description of shape and Feshbach resonances at finite temperature. The theory is applied to the system composed of a 40 Ca + ion and a Na atom, and compared with numerical coupled-channel calculations carried out using ab initio potentials. For this particular system, we investigate the spectrum of bound states, the rate of charge-transfer processes and the collision rates in the presence of magnetic Feshbach resonances at zero and finite temperature.

arXiv:1104.5600New Journal of PhysicsAug 8, 201181 citations

Atomic Collisions in Ultracold Atomic Gases

Paul S. Julienne, Kevin C. Jones, Paul D. Lett +4 more

Jul 1, 19970 citations

We present an analytical description for ultracold collisions between two spin-

\frac{1}{2}

fermions with isotropic spin-orbit coupling (SOC) of the Rashba type. We show that regardless of how weak the SOC may be, at sufficiently low energies the collision properties are significantly modified. The ubiquitous low energy Wigner threshold behavior is changed and its modified form for ground-state neutral atoms is given. The particles are further found to scatter preferentially into the lower-energy helicity states due to the breaking of parity conservation. This latter point establishes interaction with SOC as one mechanism for the spontaneous emergence of handedness. Our theory is applicable both to elementary spin-

\frac{1}{2}

fermions such as electrons in condensed matter and to ultracold pseudo-spin-

\frac{1}{2}

atoms such as

{}^{6}

Li in its ground hyperfine state.