  Zitterbewegung (ZB) is a phenomenon in relativistic quantum systems where the
electron wave packet exhibits a trembling or oscillating behavior during its
motion, caused by its interaction or coupling with the negative energy state.
To directly observe ZB in electronic systems is difficult, due to the
challenges associated with the atomic scale wavelength of the electron.
Photonic systems offer an alternative paradigm. We exploit the concept of
pseudo parity-time (pseudo PT ) symmetry to study ZB in non-Hermitian quantum
systems implemented as an experimentally feasible optical waveguide array. In
particular, the non-Hermitian Hamiltonian is realized through evanescent
coupling among the waveguides to form a one-dimensional lattice with periodic
modulations in gain and loss along the guiding direction. As the modulation
frequency is changed, we obtain a number of phenomena including periodically
suppressed ZB trembling, spatial energy localization, and Hermitian-like ZB
oscillations. We calculate phase diagrams indicating the emergence of different
types of dynamical behaviors of the relativistic non-Hermitian quantum system
in an experimentally justified parameter space. We provide numerical results
and a physical analysis to explain the distinct dynamical behaviors revealed by
the phase diagrams. Our findings provide a deeper understanding of both the
relativistic ZB phenomenon and non-Hermitian pseudo-PT systems, with potential
applications in controlling/harnessing light propagation in waveguide-based
optical systems.
