We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schrödinger equation, which goes beyond the standard semiclassical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semiclassical model. In particular, for atoms at low velocity and close to the material surface, the semiclassical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g., for metrological applications. Published by the American Physical Society 2024
We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schrödinger equation, which goes beyond the standard semiclassical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semiclassical model. In particular, for atoms at low velocity and close to the material surface, the semiclassical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g., for metrological applications. Published by the American Physical Society 2024
We present a theoretical model of matter-wave diffraction through a material nanostructure. This model is based on the numerical solution of the time-dependent Schr{ö}dinger equation, which goes beyond the standard semi-classical approach. In particular, we consider the dispersion force interaction between the atoms and the material, which is responsible for high energy variations. The effect of such forces on the quantum model is investigated, along with a comparison with the semi-classical model. In particular, for atoms at low velocity and close to the material surface, the semi-classical approach fails, while the quantum model accurately describes the expected diffraction pattern. This description is thus relevant for slow and cold atom experiments where increased precision is required, e.g. for metrological applications.
Abstract The diffraction of atoms and molecules through tiny, sub-nanometre holes in atomically thin membranes is a promising approach for advancing atom interferometry sensing and atomic holography. However, dispersion interactions, such as the Casimir-Polder force, pose a significant challenge by attracting diffracting particles to the membrane, limiting the minimum hole size. This paper presents a numerical simulation of helium matter-wave diffraction through sub-nanometre holes in hexagonal boron nitride by solving the time-dependent Schrödinger equation. Our results show that the transmission rates in the quantum approach are significantly higher than those predicted by the commonly used semi-classical approach. This suggests that significantly smaller holes can be used in the design of diffractive masks, provided that fabrication techniques can meet the atomic-level precision to realise such holes. Furthermore, we observe notable differences in diffraction patterns, even for atom velocities that are much greater than the expected convergence threshold between semi-classical and quantum computational models.
In recent years, matter-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and the study of fundamental aspects of quantum theory. Diffraction and interference of matter waves can be observed not only at a spatial aperture (such as a screen edge, slit, or grating), but also at a time-domain aperture (such as an absorbing barrier, or ``shutter,'' that is being periodically switched on and off). The wave phenomenon of the latter type is commonly referred to as ``diffraction in time.'' Here, we introduce a versatile, exactly solvable model of diffraction in time. It describes time evolution of an arbitrary initial quantum state in the presence of a time-dependent absorbing barrier, governed by an arbitrary aperture function. Our results enable a quantitative description of diffraction and interference patterns in a large variety of setups, and may be used to devise new diffraction and interference experiments with atoms and molecules.
Bloch oscillations of atoms in optical lattices are a powerful technique that can dramatically boost the sensitivity of atom interferometers to a wide range of signals by large momentum transfer. To leverage this method to its full potential, an accurate theoretical description of losses and phases is required, going beyond existing treatments. Here, we present a comprehensive theoretical framework for Bloch-oscillation-enhanced atom interferometry and verify its accuracy through comparison with a numerical solution of the Schrödinger equation. Our approach establishes design criteria to reach the fundamental efficiency and accuracy limits of large momentum transfer using Bloch oscillations and allows us, in a broader context, to define the fundamental efficiency limit of the transport of neutral atoms using optical lattices. We compare these limits to the capabilities of current state-of-the-art experiments and make projections for the next generation of quantum sensors. Published by the American Physical Society 2024
This work considers the semi-classical description of two applications involving cold atoms. This is, on one hand, the behavior of a BOSE-EINSTEIN condensate in hybrid systems, i.e. in contact with a microscopic object (carbon nanotubes, fullerenes, etc.). On the other, the evolution of phase space distributions in matter wave interferometers utilizing ray tracing methods was discussed. For describing condensates in hybrid systems, one can map the GROSS-PITAEVSKII equation, a differential equation in the complex-valued macroscopic wave function, onto a system of two differential equations in density and phase. Neglecting quantum dispersion, one obtains a semiclassical description which is easily modified to incorporate interactions between condensate and microscopical object. In our model, these interactions comprise attractive forces (CASIMIR-POLDER forces) and loss of condensed atoms due to inelastic collisions at the surface of the object. Our model exhibited the excitation of sound waves that are triggered by the object’s rapid immersion, and spread across the condensate thereafter. Moreover, local particle loss leads to a shrinking of the bulk condensate. We showed that the total number of condensed particles is decreasing potentially in the beginning (large condensate, strong mean field interaction), while it decays exponentially in the long-time limit (small condensate, mean field inetraction negligible). For representing the physics of matter wave interferometers in phase space, we utilized the WIGNER function. In semi-classical approximation, which again consists in ignoring the quantum dispersion, this representation is subject to the same equation of motion as classical phase space distributions, i.e. the LIOUVILLE equation. This implies that time evolution of theWIGNER function follows a phase space flow that consists of classical trajectories (classical transport). This means, for calculating a time-evolved distribution, one has know the initial distribution and one has to solve the classical equations of motion. Concerning the initial distribution, we have studied a stationary solution of the nonlinear LIOUVILLE equation, the LAMBERT density. We saw that it agrees very well with results from singleparticle quantum mechanics as well as the MAXWELL-BOLTZMANN distribution in the weakly interacting limit. Likewise, in the strongly interacting limit, familiar results of the THOMAS-FERMI approximation are recovered. A distribution that is first prepared in a trap and then released can be described quite conveniently in terms of WIGNER functions. However, propagation in optical potentials associated to the interferometer elements (beam splitter, Pi-half-pulse) do not satisfy the condition of the semiclassical approximation. Nevertheless, one finds discrete before-after mappings that describe the effect of these elements on incident distributions. This leads to several channels of phase space propagation which relate to the interferometer paths and interferences between them. The formalism for WIGNER functions in an interferometer can be translated straightforwardly into a ray tracing algorithm. As mentioned above, this algorithm solves the classical equations of motion and computes time-evolved distributions, using values of the initial distribution. This procedure, in contrast to most analytical solutions, does not require the HAMILTON function to be quadratic (e.g. free propagation, const. acceleration, harmonic oscillator). We compared simulation results to analytic expressions in case of freely propagating GAUSS distribution. They showed perfect agreement, especially for the functional dependence of wave length and contrast of interference fringes on the laser pulse timings.
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.