Fractality and macroscopic entanglement in two-component Bose-Einstein condensates
Tim Byrnes · Physical Review A · 2013
Spin coherent states are the matter equivalent of optical coherent states, where a large number of two component particles form a macroscopic state displaying quantum coherence. Here we give a detailed study of entanglement generated between two spin-$1/2$ Bose-Einstein condensates (BECs) due to an ${S}_{1}^{z}{S}_{2}^{z}$ interaction. The states that are generated show a remarkably rich structure showing fractal characteristics. In the limit of large particle number $N$, the entanglement shows a strong dependence upon whether the entangling gate times are a rational or irrational multiple of $\ensuremath{\pi}/4$, with a fractal dimension of $d\ensuremath{\approx}1.7$. We discuss the robustness of various states under decoherence and show that despite the large number of particles in a typical BEC, entanglement on a macroscopic scale should be observable as long as the gate times are less than $\ensuremath{\hbar}/J\sqrt{N}$, where $J$ is the effective BEC-BEC coupling energy. Such states are anticipated to be useful for various quantum information applications such as quantum teleportation and quantum algorithms.