# Universal Relations of Ultracold Fermi Gases with Arbitrary Spin-Orbit Coupling.

We derive the universal relations for an ultracold two-component Fermi gas with spin-orbit coupling (SOC) $\sum_{\alpha,\beta=x,y,z}\lambda_{\alpha\beta}\sigma_{\alpha}p_{\beta}$, where $p_{x,y,z}$ and $\sigma_{x,y,z}$ are the single-atom momentum and Pauli operators for pseudo spin, respectively, and the SOC intensity $\lambda_{\alpha\beta}$ could take arbitrary value. We consider the system with an s-wave short-range interspecies interaction, and ignore the SOC-induced modification for the value of the scattering length. Using the first-quantized approach developed by S. Tan (Phys. Rev. Lett. \textbf{107}, 145302 (2011)), we obtain the short-range and high-momentum expansions for the one-body real-space correlation function and momentum distribution function, respectively. For our system these functions are $2\times2$ matrix in the pseudo-spin basis. We find that the leading-order ($1/k^{4}$) behavior of the diagonal elements of the momentum distribution function (i.e., $n_{\uparrow\uparrow}({\bf k})$ and $n_{\downarrow\downarrow}({\bf k})$) are not modified by the SOC. However, the SOC can significantly modify the behavior of the \textit{non-diagonal elements} of the momentum distribution function, i.e., $n_{\uparrow\downarrow}({\bf k})$ and $n_{\downarrow\uparrow}({\bf k})$, in the large-$k$ limit. In the absence of the SOC, the leading order of these elements is ${\cal O}(1/k^{6})$. When SOC appears, it can induce a term on the order of $1/k^{5}$. We further derive the adiabatic relation and the energy functional. Our results show the SOC can induce a new term in the energy functional, which simply describe the contribution from the SOC to the total energy. The form of the adiabatic relation for our system is not modified by the SOC.

Publisher URL: http://arxiv.org/abs/1801.08179

DOI: arXiv:1801.08179v2

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.