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Abstract

Quantum simulation enables the experimental investigation of simplified physical models that capture the fundamental aspects of complex quantum many-body systems. In order to understand how interaction parameters impact the macroscopic properties of the system, it is essential to modify the Hamiltonian in a controlled fashion. This thesis presents novel approaches to perform tunable quantum simulations in an isolated many-body spin-1/2 system represented by dipolar interacting Rydberg atoms. These approaches are employed to study out-of-equilibrium dynamics in different regimes. The four major achievements are as follows: (i) Using various spin-encoding states within the Rydberg manifold, we realize XX, XXZ, and Ising models with spatial disorder and study magnetization relaxation dynamics. We identify a universal behavior that is independent of the microscopic properties and explained by the emergence of effective spin pairs. (ii) To introduce new effective interactions into the system, we employ a time-periodic drive to transform the natural dipolar interaction Hamiltonian into a desired target form. This method, known as Floquet engineering, is validated using both a gas of Rydberg atoms and individually trapped Rydberg atoms. We demonstrate its potential for tunable quantum simulation of Heisenberg spin models by altering symmetry and transport properties. (iii) Combining the methods developed in (i) and (ii), we devise and implement a time reversal protocol. The versatility of the approach is demonstrated by reversing quantum dynamics for a variety of many-body Hamiltonian with tunable symmetry, which we realize through Floquet engineering. (iv) Beyond experimental demonstration, we propose alternative approaches to engineer many-body systems, including a new approach to realize time-reversal operations, and an approach for introducing mobile dopants into Ryderg spin systems. The Hamiltonian engineering methods can be directly applied to further study the extend to which the emergence of effective spin pairs is the common feature of disordered quantum spin systems. In general, engineering a wide range of Hamiltonians opens up several new opportunities for investigating fields that range from spin transport and spin glasses to quantum thermalization.