Theory of atom interferometry based on bragg diffraction and bloch oscillations
Creators: name: Fitzek, Florian
Publisher: name: Hannover : Institutionelles Repositorium der Leibniz Universität Hannover
Year: 2024
Subjects: subject: Atom interferometry
subject: Bragg diffraction
subject: Large momentum transfer
subject: Bloch oscillations
subject: Wannier-Stark states
subject: Adiabatic theorem
subject: Atominterferometer
subject: Bragg-Streuung
subject: Großimpulsübertragung
subject: Bloch-Oszillationen
subject: Wannier-Stark Zustände
subject: Adiabatisches Theorem
subject: Dewey Decimal Classification::500 | Naturwissenschaften::530 | Physik

description: Atom interferometers are versatile quantum sensors that enable a wide range of high-precision and high-accuracy measurements ranging from fundamental physics to real-world applications. Large momentum transfer (LMT) techniques offer an excellent tool to increase the sensitivity of state-of-the-art atom interferometers by orders of magnitude. In this thesis, we develop two theoretical frameworks to investigate the current sensitivity limits of state-of-the-art LMT atom interferometers based on Bragg diffraction (BD) and Bloch oscillations (BOs). In the first part, we develop a unified numerical framework that enables us to accurately model atom interferometers based on elastic scattering processes, i.e., when the internal state of the atoms remains unchanged. Departing from the widely-used approach of solving a system of coupled ordinary differential equations (ODEs), we base our treatment on the split-step Fourier method. This method demonstrates superior scalability and efficiency in the case of complex spatial dependencies of the light potential and trapped atom interferometers with interacting atomic ensembles. To demonstrate the capabilities of our numerical framework, we examine a wide range of scenarios relevant for the field of precision atom interferometry. We show that an accurate understanding of the interference process requires a careful analysis that goes beyond often-used approximations and effective theories in the treatment of atom-optical systems. Moreover, we provide a comprehensive numerical error and convergence analysis, demonstrating that our numerical framework allows to efficiently study the relative phase beyond the microradian level. The flexibility, numerical scalability and accuracy of our numerical framework make it an excellent tool to design, understand and quantitatively analyze precision atom interferometers. In the second part, we investigate sequences of Bloch oscillations of atoms with optical lattices, which offer a powerful technique to realize LMT atom interferometers. To unlock the full potential of this method, an accurate theoretical description of losses and phases beyond the capabilities of existing treatments is required. We develop a comprehensive theoretical treatment of BO-enhanced atom interferometers and validate its accuracy against an exact numerical solution of the Schrödinger equation. Our approach enables us to define the fundamental efficiency and accuracy limits of BO-enhanced atom interferometers and to formulate design criteria for their saturation. We compare these efficiency and accuracy limits to several state-of-the-art experiments and formulate requirements to achieve the next level of ultra-sensitive measurements using BO-enhanced atom interferometers.