Developing theoretical and experimental tools for a hybrid quantum simulator based on trapped ions

Abstract

Quantum simulation is the process of using a highly controllable quantum system to simulate another less controllable system. Quantum simulation can provide insights into the properties and dynamics of complex many-body systems. Trapped ion platform is one of the leading candidates for a quantum simulator due to its properties such as ease of isolation, preparation and manipulation. Simulating high dimensional spin systems enables us to study the various physical phenomena in higher geometries. Previous proposals for simulating higher dimensions require experimental resources that don't scale favourably with the system. In this thesis, we propose a hybrid (digital-analog) approach to simulate an effective 2D lattice from a 1D chain of trapped ions. In the initial geometry, the ions interact with each other through a flip-flop kind of interactions generated using a global Molmer-Sorensen scheme. A series of single qubit gates are used to rescale and suppress the interactions in the initial chain to simulate the target geometry. These gates are applied using a laser field gradient which generates a site-dependent AC stark shift. I discuss the construction of this protocol in detail and the theoretical results for the case of 6, 9 and 16 ions. I also show that the number of gates and also the Stark gradient scale linearly with the system size.

Experimental implementation of an ion trap quantum simulator has various challenges, one of the which is the laser frequency stabilization within a fraction of transition linewidth. Traditionally, this is done by locking the lasers to an atomic transition. In this thesis, I discuss two alternative schemes for locking the laser frequencies used to build a 171Yb+ ion quantum simulator. One of these solutions uses a commercial wavemeter as a measuring device for the frequency and feedbacks the lasers based on this measurement. I discuss the layout of this scheme and some results. Other solution uses a Fabry Perot (FP) cavity to transfer the stability of a stable laser to an unstable laser. In this thesis, I discuss the construction, optical layout and transmission measurements of a home-built FP cavity.