Research Projects

In contrast to the many-body classical systems, where the dynamics is in general non-linear, the emergence of the statistical ensembles in isolated closed quantum systems is slightly tricky due to the linear unitary dynamics under a hermitian Hamiltonian. However, as shown by many [Deutsch, 1991; Rigol et al., 2008; Eisert et al., 2015], equilibration can be achieved at long times locally for a part of the system where the rest acts as a thermal bath [King et al., 2016]. Quantum entanglement plays a crucial role [D’Alessio et al., 2016] in attaining the stationary behavior from a non-equilibrium state and it is therefore of significant importance to study the entanglement dynamics. There are several interesting works, both in integrable [Essler and Fagotti, 2016] and non-integrable systems [Rigol and Srednicki, 2012], where entanglement dynamics leads to thermalization (equilibrium behavior as predicted from Gibb’s ensemble) in the long time limit. Before the steady state, the entanglement entropy (EE)—a measure of entanglement between two parts of a quantum system, generally grows linearly with time during the unitary evolution that can be quantitatively associated with the propagation of entangled quasiparticles [Calabrese, 2005]. On the other hand, when a quantum many-body system is open to the environment or attached to a measurement probe (e.g., photon detection experiment), the entanglement decreases in contrast to the closed counterpart. Due to the competing behavior from unitary dynamics and measurements (non-unitary effects), we see a transition from higher to lower entangled state as a function of measurement strength/rate [Skinner et. al., 2019; Diehl and Buchhold, 2022]—known as measurement induced phase transition (MIPT). Recent advancement in experimental techniques has realized the MIPT [Kaufman, 2016], and therefore, the control of entanglement dynamics gives us additional degrees of freedom to build quantum processors [Bluvstein, 2022]. The primary objective behind this project is to enhance theoretical understanding of dynamics of a many-body quantum system under measurements and possible ways of controlling it. Stochastic resetting [Evans and Majumdar, 2011], where a random diffusive particle is reset to its initial position at a constant rate, has been shown to have a direct connection [Gal et al., 2024] to the inherent randomness and entanglement resetting of the measurement dynamics. Starting from a many-body Hamiltonian, e.g., spatially extended Heisenberg spin models, XY models, Bose-Hubbard models, etc., we can study the dynamical signatures of EE (and their statistics) in presence of measurements and exploit the features offered by the resetting problem. Various exotic quantum phases that these models possess gives deeper understanding into different dynamical transitions that indeed help to find efficient ways of controlling a quantum evolution numerically—supported by analytics, and as well as experimentally.