Quantum Zeno Dynamics of two interacting particles

According to quantum Zeno dynamics (QZD), the evolution of a quantum system can be restricted to a subspace of its Hilbert space by frequent measurements. A crucial question in QZD of a particle's position is: how short the time interval between successive measurements should be, in order to confine the particle in its initial spatial region? To address this question, we consider a toy model with two ions initially known to be, for simplicity, in a one-dimensional spatial region. By simulating the evolution of this two-body quantum system, we estimate the measurement frequency needed to keep the ions within their initial confined region at a desired confidence level. Two key parameters we employ in our calculations are the Zeno time and the leakage probability of the quantum system. The measurement frequencies are calculated and compared when ions are located initially at different spatial regions. For our simulation, we introduce the Python code 2IonQZD.