The temporal evolution of atomic wave packets interacting with object and reference electromagnetic waves is investigated, and an analytical solution for the off-resonant density matrix is presented. It is shown that, under certain physical conditions, the diffraction of an ultracold atomic beam by an inhomogeneous laser field can be interpreted as if the beam passes through a three-dimensional hologram. We show that high diffraction efficiencies can be realized if one restricts the extent of the atomic hologram in the time domain rather than in space. The hologram, thus, can work in a pulsed regime pumping atoms from the beam or from the initial wave packet into the reconstructed matter wave. The suggested regime is well compatible with the Raman cooling methods and the recent realization of an atom laser, which are capable of repeatedly reproducing coherent, or almost coherent, atomic wave packets necessary for the actual implementation of the reading beam. It is found that the diffraction efficiency of such a hologram may reach 100% and is determined by the duration of laser pulses. On this basis, a new method for the reconstruction of the object image with matter waves is offered. The latter may have useful practical applications, ranging from atom lithography, to the manufacturing of microstructures, and quantum microfabrication.
The temporal evolution of atomic wave packets interacting with object and reference electromagnetic waves is investigated, and an analytical solution for the off-resonant density matrix is presented. It is shown that, under certain physical conditions, the diffraction of an ultracold atomic beam by an inhomogeneous laser field can be interpreted as if the beam passes through a three-dimensional hologram. We show that high diffraction efficiencies can be realized if one restricts the extent of the atomic hologram in the time domain rather than in space. The hologram, thus, can work in a pulsed regime pumping atoms from the beam or from the initial wave packet into the reconstructed matter wave. The suggested regime is well compatible with the Raman cooling methods and the recent realization of an atom laser, which are capable of repeatedly reproducing coherent, or almost coherent, atomic wave packets necessary for the actual implementation of the reading beam. It is found that the diffraction efficiency of such a hologram may reach 100% and is determined by the duration of laser pulses. On this basis, a new method for the reconstruction of the object image with matter waves is offered. The latter may have useful practical applications, ranging from atom lithography, to the manufacturing of microstructures, and quantum microfabrication.
The temporal evolution of an atomic wave packet interacting with object and reference electromagnetic waves is investigated beyond the weak perturbation of the initial state. It is shown that the diffraction of an ultracold atomic beam by the inhomogeneous laser field can be interpreted as if the beam passes through a three-dimensional hologram, whose thickness is proportional to the interaction time. It is found that the diffraction efficiency of such a hologram may reach 100% and is determined by the duration of laser pulses. On this basis a method for reconstruction of the object image with matter waves is offered.
We study the transient dynamics that arise during the formation of an atom laser beam in a tight waveguide. The time dependent density profile develops a series of wiggles which are related to the diffraction in time phenomenon. The apodization of matter waves, which relies on the use of smooth aperture functions, allows to suppress such oscillations in a time interval, after which there is a revival of the diffraction in time. The revival time scale is directly related to the inverse of the harmonic trap frequency for the atom reservoir. PACS numbers: Atom lasers have recently been created in the laboratory and stand up for their applications in atom lithography and interferometry. Similar to their light analogues, they consist in coherent and directed (matter-) wave beams, which are extracted from a Bose-Einstein condensate (BEC). Different schemes have been proposed to out-couple the atoms from the BEC reservoir. One of the prototypes uses two-photon Raman excitation to create “output coupled ” atomic pulses with well defined mean momentum which overlap and form a quasi-continuous beam [1, 2] (For other approaches see e.g. [3] or [4]). The features of the beam profile are of outmost importance for applications [5, 6, 7], and depend on the pulse shape, duration, emission frequency, and initial phase [8]. We study the dynamics of a beam created by multiple overlapping pulses, transversely confined in a tight waveguide and with negligible interactions between the out-coupled atoms. It is found that an oscillatory pattern appears in the density profile of the beam which is closely related to the diffraction in time phenomenon. If the switching process is slow, such oscillations are suppressed on a time window after which there is a revival of the diffraction in time. The time scale in which the spatial fringes appear is related to the the spatial width of the out-coupled pulses.
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.
Atomic beam holography is a unique technique by which to fabricate a nanoscale object by using the interference of matter waves of ultracold atoms. The atomic de Broglie wave coming through a hologram interferes with and reconstructs a desired structure on a substrate. We first demonstrated holographic manipulation of metastable Ne atoms of 7 nm wavelength, where we showed the reconstruction of an “F” pattern and improvement of it. In this article, we propose and show techniques to manipulate three-dimensionally cooled Ne atoms. Atomic beam holography has the potential to make atomic-size objects, and the freedom in designing the hologram enables us to make not only a binary pattern but also an analog (gray scale) pattern. The resolution demonstrated in this experiment was about 60μ, but the minimum feature size expected is theoretically the same as the wavelength, i.e., several nanometers.
Light pulses have proven to be a powerful and versatile tool to implement beam splitters and mirrors for matter waves enabling atom interferometers. However, for high-precision measurements with such devices the specific realization is crucial and novel techniques might increase the sensitivity. To illustrate the diversity of light-pulse beam splitting and the subtle differences between the diffraction mechanisms, we study atomic Raman, Bragg, and the new method of double Bragg diffraction in a coherent way. Moreover, we introduce a versatile formalism to determine the interference signal of a Mach-Zehnder geometry and give an interpretation in terms of proper-time difference. In addition, we explore the feasibility of a specular mirror for atoms, which might lead to an interferometer testing the equivalence principle.