A semi-classical analysis of the coupling strength γ between motional quantum states of spatially distant trapped ions interacting via a conducting wire
Interfacing ion qubits in separate traps is among the challenges towards scaling up trapped ion quantum computing. This theoretical study focuses on using a conducting wire to couple the motional quantum states of ions in separate planar traps. The approach of interfacing ion traps provides an alternative to coupling distant qubits with lasers or via ion shuttling. We develop a detailed model for the coupling strength γ, which in turn allows us to calculate the time required to exchange motional quantum states between two ions, tex.. To maximize the coupling strength γ, a rule of thumb is developed to relate the distance deq. between a trapped ion and a nearby pickup disk, to the optimal radius ropt. of the disk, deq./2≤ropt.≤deq.. We include a coefficient ζ which describes three self-capacitances connected in series, relating the capacitances of each part of the coupling system, which corrects an oversight common to several previous works. Our analytical model for the coupling strength is then compared with other existing analytical models in the literature. This requires a standardization of the coupling systems and mapping them to a common set of parameter values. Similarities, differences and limitations of the various models are discussed. This study's focus on the coupling strength γ and tex. provides a foundational pillar for exchanging quantum information between trapped ions via a wire. In addition, many insights are general and apply broadly to hybrid systems interfacing trapped ions with nearby conductors.
The time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.
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. \n \nExperimental 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.