Atomic diffraction is the central concept of matter-wave interferometers, which provide the opportunity of high-precision rotation and acceleration sensing. Ultracold atoms are the ultimate quantum sensors for this purpose. Transferring photon momentum from two counterpropagating laser beams to atomic wavepackets prepares coherent superpositions in the momentum space, realising atomic beamsplitters and mirrors. Like classical optical systems, these matter-wave devices require exact specifications and ubiquitous imperfections need to be quantified. Therefore, in this thesis, the performance of (3+1)D atomic beamsplitters in the quasi-Bragg regime is studied numerically as well as analytically and is confirmed by experimental data [1]. Ideally, the incoming wavepacket can be split exactly into two parts or reflected perfectly with unit response, independent of its spatial and velocity distribution. However, the velocity selectivity of the Bragg diffraction, as well as losses into undesired diffraction orders in the quasi-Bragg regime, constitute aberrations, which cannot be neglected. The non-ideal behaviour due to spatial variations of the laser beam profiles and wavefront curvatures, regarding realistic Laguerre-Gaussian laser beams instead of ideal plane waves, reduces the diffraction efficiency and leads to rogue momentum components, just like misaligned lasers. In contrast, smooth temporal envelopes improve the beamsplitter performance. Different pulse shapes are taken into account, where some are amenable for closed analytical solutions. The realistic modelling and exhausting aberration studies characterises in detail atomic Bragg beamsplitters and demonstrate pathways for improvements, both required by challenging experiments. For hot ions in accelerator beams the atomic diffraction is used contrary to generate a velocity filter. Two counterpropagating far-detuned lasers transfer a narrow velocity class of ions from an initially broad distribution via a stimulated Raman transition between the ground states of a Λ-system. This colder subensemble prepares optimal initial conditions for precision collinear laser spectroscopy on fast ion beams. The efficiency of the filter is diminished by aberrations like the spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise. Spatial intensity variations of the ion and laser beams are considered, whereas wavefront curvature is negligible. A comprehensive master equation leads to conditions for the optimal frequency pair of lasers. The time-resolved population transfer characterises the filter performance and is evaluated numerically as well as analytically. Derived models match the numerical results, keeping the computational effort small. Taking into account the mentioned aberrations, the possible use of Raman transition as velocity filter for hot ions is demonstrated. Velocity classes with widths as low as 0.2 m/s can be transferred, achieving a significant population proportion from per mill to percent. Applying the analysis to current 40-Ca+ ion experiments, a sensitivity for measuring high ion acceleration voltages on the ppm level or below is substantiated.
Atomic diffraction is the central concept of matter-wave interferometers, which provide the opportunity of high-precision rotation and acceleration sensing. Ultracold atoms are the ultimate quantum sensors for this purpose. Transferring photon momentum from two counterpropagating laser beams to atomic wavepackets prepares coherent superpositions in the momentum space, realising atomic beamsplitters and mirrors. Like classical optical systems, these matter-wave devices require exact specifications and ubiquitous imperfections need to be quantified. Therefore, in this thesis, the performance of (3+1)D atomic beamsplitters in the quasi-Bragg regime is studied numerically as well as analytically and is confirmed by experimental data [1]. Ideally, the incoming wavepacket can be split exactly into two parts or reflected perfectly with unit response, independent of its spatial and velocity distribution. However, the velocity selectivity of the Bragg diffraction, as well as losses into undesired diffraction orders in the quasi-Bragg regime, constitute aberrations, which cannot be neglected. The non-ideal behaviour due to spatial variations of the laser beam profiles and wavefront curvatures, regarding realistic Laguerre-Gaussian laser beams instead of ideal plane waves, reduces the diffraction efficiency and leads to rogue momentum components, just like misaligned lasers. In contrast, smooth temporal envelopes improve the beamsplitter performance. Different pulse shapes are taken into account, where some are amenable for closed analytical solutions. The realistic modelling and exhausting aberration studies characterises in detail atomic Bragg beamsplitters and demonstrate pathways for improvements, both required by challenging experiments. For hot ions in accelerator beams the atomic diffraction is used contrary to generate a velocity filter. Two counterpropagating far-detuned lasers transfer a narrow velocity class of ions from an initially broad distribution via a stimulated Raman transition between the ground states of a Λ-system. This colder subensemble prepares optimal initial conditions for precision collinear laser spectroscopy on fast ion beams. The efficiency of the filter is diminished by aberrations like the spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise. Spatial intensity variations of the ion and laser beams are considered, whereas wavefront curvature is negligible. A comprehensive master equation leads to conditions for the optimal frequency pair of lasers. The time-resolved population transfer characterises the filter performance and is evaluated numerically as well as analytically. Derived models match the numerical results, keeping the computational effort small. Taking into account the mentioned aberrations, the possible use of Raman transition as velocity filter for hot ions is demonstrated. Velocity classes with widths as low as 0.2 m/s can be transferred, achieving a significant population proportion from per mill to percent. Applying the analysis to current 40-Ca+ ion experiments, a sensitivity for measuring high ion acceleration voltages on the ppm level or below is substantiated.
This cumulative thesis consists of four publications [1-4], presented as three contributions (I) - (III), where the second one (II) consists of the joint publications [2,3]. All publications were written during the author's research activities at the Institute of Quantum Physics under the supervision of Prof. Dr. W. P. Schleich. All of the presented publications consider light-matter interactions and their potential application in atom interferometry, a comparatively young and rapidly evolving technique. Atom interferometers find application in high-precision measurements, the determination of physical constants, the testing of fundamental physics, and the provision of gravimeters and gyroscopes. The advancement of technology and science has led to significant improvements in performance and the development of ambitious mobile and space-based devices. The recent success of several experiments has led to the proposal of further experiments with the aim of opening up new frontiers. However, the construction of future devices necessitates a decision regarding the employed diffraction mechanism and geometry, depending on the specific technical and scientific requirements. Furthermore, it is necessary to enhance the sensitivity of future devices. The contributions in this dissertation address these issues. The first contribution (I) focuses on the diffraction of atoms by laser pulses which can be employed to generate atom-optical diffraction elements like beam splitters and mirrors. These diffraction elements can be combined to construct atom interferometers, which have been successfully employed for precision measurements regarding fundamental physics as well as practical applications. The article presents a numerical comparison of two distinct diffraction mechanisms (Bragg and Raman) and diffraction geometries (single and double diffraction) in microgravity. It discusses the fundamental differences between the mechanisms and geometries with respect to the diffraction efficiency, taking into account the width of the initial wave function and the duration of the light pulse. Additionally, it explores the transition between the two diffraction geometries when starting from an atom initially at rest and increasing its momentum. The results may serve as a reference for experimentalists in selecting the most suitable configuration, based on their aims and requirements in the realization of more advanced atom interferometers. The second contribution (II) is a follow-up to the previous one, but focuses exclusively on a single diffraction type in microgravity, namely the so-called double Raman diffraction. In contrast to the previous article, where we only discussed single two-photon processes, we consider in this article a six-photon process, also known as third-order diffraction, as well as three subsequent two-photon processes, which both lead to the same amount of transferred momentum and can both be used to realize large-momentum transfer (LMT). We demonstrate that third-order double Raman diffraction is a viable and advantageous method for the diffraction of small momentum distributions like Bose-Einstein condensates (BECs) compared to a sequence of three two-photon processes. Furthermore, we show that third-order Raman pulses can be successfully applied to create higher-order Raman atom interferometers. Third-order diffraction can be perfectly combined with other LMT techniques and, moreover, allows for a reduction in the overall duration of the diffraction process and the complexity of the experimental set-up, as only two distinct laser frequencies are required. Moreover, we present a third-order Mach-Zehnder interferometer with spurious paths being disregarded. As demonstrated later on in [3], this interferometer generates optimal contrast and a substantial amplitude. The third contribution (III) extends the semi-classical λ-scheme of single Raman diffraction, as discussed in detail in contribution (I), into a fully quantized multi-atom multi-λ configuration with center-of-mass motion inside a cavity. Therefore, the incorporation of an internal structure allows for a more realistic modeling of the atoms, which is relevant for multi-photon interaction or cooling processes. We use for our analysis the framework of second quantization, i.e., we take into account the field-theoretical nature of the multi-particle atomic field as well as of the diffracting light field. We reduce this model with a Hamiltonian averaging theory applied to the atomic field operators and obtain an effective Hamiltonian, which determines the time evolution of the system. We demonstrate the efficiency of our model by the application of a typical initial state. Moreover, for a specific input state, we obtain the Hong-Ou-Mandel effect simultaneously in the atomic and the optical system. Our many-body formalism is perfectly suited to theoretically describe contemporary high-precision atom interferometric experiments based on entanglement between the atoms, that aim to surpass the shot-noise limit.
This thesis develops a general theoretical and numerical framework for achieving high-contrast atom interferometry based on double Bragg diffraction (DBD). While DBD offers intrinsic symmetry, reduced sensitivity to internal-state systematics, and suitability for microgravity experiments, its performance has long been limited by imperfect diffraction and contrast loss. This work overcomes these limitations by constructing an analytic Hamiltonian description of DBD -- including Doppler effects and polarization imperfections -- and by deriving reduced two- and five-level models via a truncated Magnus-expansion approach. These models clarify the origin of AC-Stark shifts, polarization-induced errors, and Doppler selectivity, and they provide accurate predictions for realistic input momentum distributions.
Building on this theoretical foundation, the thesis introduces a tri-frequency laser scheme with dynamically tunable detuning and evaluates different detuning-control strategies using a five-level S-matrix formalism. Linear detuning sweeps and optimal-control pulses are shown to provide near-ideal beam-splitter and mirror performance, respectively, ensuring robust contrast across a wide range of experimental imperfections. Complementary full three-dimensional simulations using the GPU-accelerated Universal Atom Interferometer Simulator (UATIS) incorporate interacting Bose-Einstein condensates and realistic optical potentials, revealing transverse effects and polarization-induced distortions that extend the predictions of the one-dimensional non-interacting models. Taken together, this thesis establishes a coherent theoretical and numerical framework demonstrating that, with appropriate detuning control, double-Bragg atom interferometers can achieve the robustness required for precision inertial sensing and future space-based quantum tests of fundamental physics.
The use of retroreflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called ``method of averaging,'' which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.
We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Laguerre-Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Laguerre-Gaussian laser beam envelope, studied with (3+1)-dimensional numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular, Gaussian, Blackman, and hyperbolic secant pulses. For the last, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the $\ensuremath{\pi}$-pulse time is explained from a renormalization of the simple Pendell\"osung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)-dimensional numerical simulations for pulsed Laguerre-Gaussian laser beams, as well as experimental data, and find very good agreement considering a mixture of Bose-Einstein condensate and thermal cloud.
The goal of this thesis is to study a novel approach towards all-optical continuous waveguide interferometers based on quasi-Bragg waveguide beam splitters. The Bragg beam splitter for matter waves is comprised of a periodic lattice produced by partial or full interference between two Gaussian laser beams and are used as waveguides for ultra-cold atoms. In the experimental conditions, where both waveguides have wide and deep potentials, atoms are unable to split from a single lattice. Instead, several spatially separated regions of the optical lattice are required, fulfilling the Bragg condition. This thesis will present clear evidence of the detection of discrete quantised momentum states of the atoms, created from a process of ultra-cold atoms undergoing interference in the single arms of a Michelson interferometer. A detailed investigation of the different regimes of the splitter has been completed by varying the initial atom velocity and the amplitude of the optical lattice. The findings from the study have produced optimal parameters where the splitting ratio of the atoms between the two waveguides can be finely controlled by the amplitude of the lattice within certain limits. A Michelson interferometer configuration is used to test the coherence of the atoms by decelerating them after splitting in the lattice. The return velocity of atoms is set to be equal to the initial velocity and the two clouds are recombined using the original lattice. A sinusoidal oscillation of the atomic momentum between the two output ports of the beam splitter is visible. However, only interference in single Michelson interferometer arms has been observed. The reasons are discussed in detail along with plans to move towards an all-optical design.
Summary form only given. Atom interferometry based on cold atoms and light beamsplitters is a mature technique, which allows for the realization of highly sensitive inertial sensors. In the most advanced inertial sensors based on atom interferometry, atomic wavepackets are manipulated by light beamsplitters using two-photon Raman transitions. The interferometer phase shift, which depends on the acceleration and the rotation of the experimental setup with respect to the inertial reference frame defined by the atoms in free fall, is derived from the relative displacement of the atoms with respect to the beamsplitter laser's equiphases. Wavefront aberrations thus induce parasitic phase shifts, which bias the measurement, and which are linked to the residual ballistic motion of the atoms across the laser beam profile during their free fall and cancels out at zero atomic temperature. The wavefront distortions of the lasers beamsplitters is an important limit in the accuracy of atom interferometers and in particular, the dominating contribution in best cold atom gravimeters (CAG) uncertainty budget. This work clears the way towards unprecedented accuracies for absolute gravimetry, below the 1 μGal level. The method proposed can be applied to any atomic sensor based on light beamsplitters, which are inevitably affected by distortions of the lasers wavefronts. The improved control of systematics it provides will have significant impact in high precision measurements with atom interferometry, with important applications to geodesy, fundamental physics tests and to the development of highest grade inertial sensors.