Probing bound state relaxation dynamics in systems out-of-equilibrium on quantum computers

Pump–probe spectroscopy is a powerful tool for probing the response dynamics of quantum many-body systems in and out-of-equilibrium. Quantum computers have proved useful in simulating such experiments by exciting the system, evolving, and then measuring observables to first order, all in one setting. Here, we use this approach to investigate the mixed-field Ising model, where the longitudinal field plays the role of a confining potential that prohibits the spread of the excitations, spinons, or domain walls into space. We study the discrete bound states that arise from such a setting and their evolution under different quench dynamics by initially pumping the chain out of equilibrium and then probing various non-equal time correlation functions. Finally, we study false vacuum decay, where initially one expects unhindered propagation of the ground state, or true vacuum, bubbles into the lattice, but instead sees the emergence of Bloch oscillations that are directly the reason for the long-lived oscillations in this finite-size model. Our work sets the stage for simulating systems out-of-equilibrium on classical and quantum computers using pump–probe experiments without needing ancillary qubits.