Abstract
The dilation method is a practical way to experimentally simulate non-Hermitian, especially PT-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent PT-symmetric Hamiltonian. Our system is initially set in the unbroken PT-symmetric phase and later goes across the so-called exceptional point and enters the broken PT-symmetric phase. For this system, the dilated Hamiltonian and the evolution of PT-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.