Digital quantum simulation of Dirac equation with a trapped ion
POSTER
Abstract
Recently there has been growing interest in simulating relativistic effects in controllable physical system [1,2]. We digitally simulate the Dirac equation in 3$+$1 dimensions with a single trapped ion. We map four internal levels of ${ }^{171}\mbox{Yb}^{+}$ ion to the Dirac bispinor. The time evolution of the Dirac equation is implemented by trotter expansion. In the 3$+$1 dimension, we can observe a helicoidal motion of a free Dirac particle which reduces to Zitterbewegung in 1$+$1 dimension. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00301, the National Natural Science Foundation of China Grant 61033001, 61061130540. KK acknowledge the support from the recruitment program of global youth experts.\\[4pt] [1] L. Lamata, et al., Phys. Rev. Lett. 98, 253005 (2007).\\[0pt] [2] R. Gerritsma, et al., Nature 463, 68 (2009).