The efficiency of an atomic interferometer in proximity of a surface is discussed. We first study which is the best choice of frequency for a pulse acting on internal atomic transitions in the same well. Then, considering the modification of atomic energy levels in vicinity of the surface, we propose the application of two simultaneous Raman lasers and numerically study the associated interference fringes. We show that the efficiency of the interferometric scheme is limited by the existence of a residual phase depending on the atomic path. We propose a symmetric scheme in order to avoid these contributions. We finally show that the suggested modifications make the contrast of the interference fringes close to 1 in any configuration, both close and far from the surface, and with one or more initially populated wells.
The efficiency of an atomic interferometer in proximity of a surface is discussed. We first study which is the best choice of frequency for a pulse acting on internal atomic transitions in the same well. Then, considering the modification of atomic energy levels in vicinity of the surface, we propose the application of two simultaneous Raman lasers and numerically study the associated interference fringes. We show that the efficiency of the interferometric scheme is limited by the existence of a residual phase depending on the atomic path. We propose a symmetric scheme in order to avoid these contributions. We finally show that the suggested modifications make the contrast of the interference fringes close to 1 in any configuration, both close and far from the surface, and with one or more initially populated wells.
Imperfect Raman pulses can lead to the formation of multiple interfering paths and affect the output of an atom interferometer in high-precision measurement.We study the effect of the imperfect Raman pulses on the interferometric fringe contrast and the phase shift in the three-pulse atom interferometer by using the evolution operator method.Analytical expressions expanded to the second-order fluctuation of imperfect pulses are derived, in which the effect of coupling the imperfect pulses with laser detuning and pulse duration is also considered.The result indicates that the second-order fluctuation of imperfect pulses is dominant, however, it can be nearly ignored in the current requirements of atomic experiments.Even so, theoretical analysis is very necessary as it may be helpful in proposing some schemes to improve the interference efficiency for future high-precision measurements with atomic interferometry.
In this paper we present a mathematical procedure to analytically calculate the output signal of a pulsed atom interferometer in an inertial field. Using the well-known ABCD ξ method we take into account the full wave dynamics of the atoms with a first order treatment of the wavefront distortion by the laser pulses. Using a numerical example we study the effect of both the length of the beam splitting laser pulses and of the width of the initial spatial distribution of the atoms. First, we find that in a general inertial field the interferometer only has a limited window in terms of the initial width (centered around 100 μm in the example calculation) in which interference fringes are visible at all. This effect is caused by the inevitable statistical spread in atomic parameters, such as initial position and momentum, and the dependence of the interferometer phase on these. In the optimum case, the useful range of the initial width is formed by the range in which both the spatial distribution and the diffraction limited momentum spread are small enough to avoid large phase differences over the atomic wavefunction. As a second result we find that the interferometer phase depends strongly on the length of the laser pulses and, to a smaller extent, on the initial width of the atomic cloud. This spatial dependency is relatively small (∼10 −5 rad) and justifies semiclassical approximations, as used in other calculations, for most experiments. New high-accuracy experiments, however, will come in the range where this effect is no longer negligible.
The authors propose a novel experiment based on atoms trapped close to a macroscopic surface, to study the interactions between the atoms and the surface at very small separations (0.6 to 10 mum). In this range the dominant potential is the QED interaction (Casimir-Polder and Van der Waals) between the surface and the atom. Additionally, several theoretical models suggest the possibility of Yukawa type potentials with sub-mm range, arising from new physics related to gravity. The paper proposes a set-up very similar to neutral atom optical lattice clocks, but with the atoms trapped in lattice sites close to the reflecting mirror. A sequence of pulses of the probe laser at different frequencies is then used to create an interferometer with a coherent superposition between atomic states at different distances from the mirror (in different lattice sites). Assuming atom interferometry state of the art measurement of the phase difference and a duration of the superposition of about 0.1s we expect to be able to measure the potential difference between separated states with an uncertainty of about 10-4Hz. A preliminary analysis of systematic effects for different atoms (Sr, Yb, Rb, Cs) indicates no fundamentally limiting effect at the same level of uncertainty, but does influence the choice of atom and isotope. Based on those estimates, we expect that such an experiment would improve the best existing measurements of the atom-wall QED interaction by <2 orders of magnitude, whilst gaining up to 4 orders of magnitude on the best present limits on new interactions in the range between 100 nm and 100mum
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.
The coherent control of atomic wave packets in multiple momentum dimensions is a central challenge in Raman atom optics and a key requirement for multidimensional atom interferometry. In this paper, a momentum-basis theoretical framework is developed for two-dimensional Raman interactions. We formulate the atom-laser interaction for two-dimensional Raman beams and obtain the effective two-level ground-state Hamiltonian after adiabatic elimination of the excited states. The resulted Hamiltonian is constructed on the reachable momentum-state lattice and includes AC Stark shifts, intra-dimensional Raman couplings, and cross-dimensional Raman coupling terms, thereby describing multidimensional Raman dynamics beyond a simple superposition of independent single-dimensional models. The framework is used to analyze the principles and operating conditions of two-dimensional atom interferometry. Cross-dimensional Raman coupling and sequential reverse Raman transitions are identified as the main mechanisms that redistribute atoms into non-target momentum states and reduce the contrast of atomic interferometer fringe. Experimentally, Ramsey fringes are observed in a cold-atom fountain interferometer, with a contrast of 14.8% at an interrogation time of T=10ms, in good agreement with the theoretical calculation. The conditions required for velocity-sensitive multidimensional atom interferometry are further clarified, including detuning control, velocity-class selection, and suppression of undesired inter-dimensional transitions. This work provides a theoretical and experimental basis for multidimensional Raman atom interferometry.
We describe an experiment based on atoms trapped close to a macroscopic surface, to study the interactions between the atoms and the surface at very small separations $(0.6--10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m})$. In this range the dominant potential is the QED interaction (Casimir-Polder and van der Waals) between the surface and the atom. Additionally, several theoretical models suggest the possibility of Yukawa-type potentials with sub-millimeter range, arising from new physics related to gravity. The proposed setup is very similar to neutral atom optical lattice clocks, but with the atoms trapped in lattice sites close to the reflecting mirror. A sequence of pulses of the probe laser at different frequencies is then used to create an interferometer with a coherent superposition between atomic states at different distances from the mirror (in different lattice sites). Assuming atom interferometry state-of-the-art measurement of the phase difference and a duration of the superposition of about 0.1s, we expect to be able to measure the potential difference between separated states with an uncertainty of $\ensuremath{\approx}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$. An analysis of systematic effects for different atoms and surfaces indicates no fundamentally limiting effect at the same level of uncertainty, but does influence the choice of atom and surface material. Based on those estimates, we expect that such an experiment would improve the best existing measurements of the atom-wall QED interaction by \ensuremath{\geqslant} 2 orders of magnitude, while gaining up to four orders of magnitude on the best present limits on new interactions in the range between 100nm and $100\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$.