Intrinsic squeezing of mechanical motion of a harmonically trapped atom with spin-orbit coupling

In this paper we investigated one-dimensional harmonically trapped atom with Raman-induced spin-orbit coupling by mapping to quantum-like model. Using displacement Fock states in quantum optics and variational methods we found the odd-parity superposition state of left- and right-displaced oscillator state is a good approximate solution to the ground state, which captures the essential physics of the system. The ground state wave function owes nodes which is remarkably different from the conventional no-node theory in quantum mechanics. The results show the atomic motion of center of mass exhibits intrinsic squeezing properties with relation to the Raman and spin-orbit coupling strength characterized by the variance in position and momentum, information entropy, as well as the Wigner function of the ground state. The dynamics of center of mass are also studied which demonstrates intuitive Zitterbewegung oscillations in momentum space and real space. Our results could be used for observing Zitterbewegung oscillations in neutral atomic gases and engineering nonclassic states.