Research Projects

 In recent years, the study of isolated quantum systems out-of-equilibrium has emerged as an exciting field of research due to their novel properties and experimental realizations using cold atoms. The aim of this project extends from basic understanding of quantum systems out-of-equilibrium to its application in quantum simulation. We can divide our proposal broadly in two parts. In the first part, we are interested in investigating the interplay between quantum chaos, thermalization and localization due to quasi-periodic disorder and their effect on the dynamics of the system. In the second part, we implement our understanding to simulate quantum many-body systems using Floquet engineering. As an example, the concept of quantum chaos is important in building operable quantum computers. The presence of quantum chaos in a system can affect the functionality of a quantum computer. For the first case, we will consider three types of model systems and their variants. First two models, the quantum kicked rotor (QKR) and the quantum kicked top (QKT) are periodically driven quantum systems, which are also paradigmatic models of Hamiltonian chaos. The third one is the Aubry-Andre (AA) model that shows a single-particle localization transition even in one dimension in contrast to the standard Anderson localization. We will study the growth rate of OTOC for a QKR in different regimes of kick strength where the classical counterpart of the model shows localized, local chaotic or global chaotic behaviors. We will address the effect of accelerator modes, symmetry breaking terms, and the Fibonacci sequence of kick strength in the quantum chaotic behavior of a QKR. In addition, we are also interested in studying the different dynamical properties of many coupled rotors. We are interested in investigating the effect of time aperiodicities on the chaotic behavior of the QKT using various protocols like Fibonacci prescription, kicked strength drawn from a binomial distribution etc. We want to explore these effects using different measurements like entanglement entropy, Husimi distribution and OTOC. These studies are also important in the context of experiments, since missing kicks can happen during the experiments. We also want to explore the chaotic behavior of two coupled kicked tops. The Aubry-Andre model shows localization transition even in one dimension. We want to study the effect of periodic drive on localization transitions both in non-interacting and interacting limits. For the second case, our aim is to minimize trotter error in digital quantum simulation using periodic drive. Let's say if we can localize a system using periodic drive, there is a possibility of minimization of trotter error to simulate that system. In parallel, if we can extend the regular behavior of a quantum chaotic many-body system using periodic drive, we can simulate the system for an extended parametric regime without much error.