This dissertation covers the field of atom optics and is divided into four main chapters: In Chapter 2 we investigate the effects of light forces on the center-of-mass motion of two-level atoms. This will lead to the discussion of two regimes: the "ray optic" and the "wave optic" regime. In the first case, an atom is well localized in the field which allows a comparison to be made with classical ray optics. In the second case, the atom is strongly delocalized which leads to a wave treatment and allows a comparison with diffractive optics. We finish this chapter with an example in each regime: Doppler cooling for ray optics and an atomic Fabry-Perot for wave optics. In Chapter 3 we extend the results of the previous chapter to the diffraction of atoms by a standing light field. We cover three regimes in the near resonant Kapitza-Dirac effect: the Raman-Nath, the Bragg and the optical Stern-Gerlach regime. In the Raman-Nath and Bragg regimes, the wave-packet is strongly delocalized compared to the period of the standing wave. In contrast, the Stern-Gerlach regime has a small spatial extent. The Raman-Nath and Bragg regimes are differentiated in their treatment of the kinetic energy. Initially we only discuss coherent interactions. In the later half of this chapter we introduce spontaneous emission and show how its presence affects the diffraction pattern in each of these regimes. In Chapter 4 we cover various atomic cooling schemes: strong field Sisyphus cooling, adiabatic cooling, evaporative cooling, polarization gradient cooling and velocity selective coherent population trapping. We begin with a brief discussion of atomic temperature. We then cover two cooling schemes for two-level atoms. We eventually move to multi-level atoms and end this chapter with a two-atom multi-level system. In Chapter 5 we conclude with a brief discussion of practical uses and devices that may arise from atom optics such as lenses, mirrors, gravitational interferometry, lithography and atomic clocks.
This dissertation covers the field of atom optics and is divided into four main chapters: In Chapter 2 we investigate the effects of light forces on the center-of-mass motion of two-level atoms. This will lead to the discussion of two regimes: the "ray optic" and the "wave optic" regime. In the first case, an atom is well localized in the field which allows a comparison to be made with classical ray optics. In the second case, the atom is strongly delocalized which leads to a wave treatment and allows a comparison with diffractive optics. We finish this chapter with an example in each regime: Doppler cooling for ray optics and an atomic Fabry-Perot for wave optics. In Chapter 3 we extend the results of the previous chapter to the diffraction of atoms by a standing light field. We cover three regimes in the near resonant Kapitza-Dirac effect: the Raman-Nath, the Bragg and the optical Stern-Gerlach regime. In the Raman-Nath and Bragg regimes, the wave-packet is strongly delocalized compared to the period of the standing wave. In contrast, the Stern-Gerlach regime has a small spatial extent. The Raman-Nath and Bragg regimes are differentiated in their treatment of the kinetic energy. Initially we only discuss coherent interactions. In the later half of this chapter we introduce spontaneous emission and show how its presence affects the diffraction pattern in each of these regimes. In Chapter 4 we cover various atomic cooling schemes: strong field Sisyphus cooling, adiabatic cooling, evaporative cooling, polarization gradient cooling and velocity selective coherent population trapping. We begin with a brief discussion of atomic temperature. We then cover two cooling schemes for two-level atoms. We eventually move to multi-level atoms and end this chapter with a two-atom multi-level system. In Chapter 5 we conclude with a brief discussion of practical uses and devices that may arise from atom optics such as lenses, mirrors, gravitational interferometry, lithography and atomic clocks.
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 dissertation explores the spatial patterns that evolve dynamically in atomic clouds and beams after they interact with one or more standing wave fields, typically formed by laser beams. The main systems under study are ensembles of free atoms, but a model Bose-Einstein condensate and the harmonic oscillator are considered as well. Focused atomic patterns with features much smaller than the wave length of the light fields are possible owing to the nonlinear atom-field interaction and are emphasized. The quantitative results combine numerical simulations and analytical expressions. Computer algorithms were developed from known methods in partial differential equations to perform the numerical simulations. The analytical results relied on standard and newly contrived techniques in quantum physics. The analytical expressions were evaluated by computer in order to extract valuable quantitative information and to compare different analytical methods with one another and with the numerical simulations. The thesis is written as a self-contained piece, and as such, develops specific examples of atom-field configurations and atomic patterns of interest from a general theory of the atoms interacting with a spatially varying light field that influences the subsequent center-of-mass motion. Beyond those already published by our group and expanded upon in the thesis, significant advances are made in: the link between transient interactions in the time- and spatial-domains; an understanding of the Raman-Nath approximation, its range of validity, and its corrections; atomic focusing by pulsed adiabatic interactions between an atom and a single standing wave light field; the differences between classical and quantum free motion after periodic interactions; the distinctions between free motion after amplitude and phase gratings; harmonic oscillator ground states kicked by spatially varying pulses; and quasiperiodic echo effects. The general theoretical structure that was detailed can be applied effectively, as intended from the outset, to other problems in atom optics.
Despite the many advances and achievements in the fields of atom optics and atom cooling, there remains a wealth of dynamical detail to be filled in. While the main features of the important phenomena of atomic cooling, trapping and manipulation by electromagnetic fields are well understood, there are interesting subsidiary effects that are worth our attention. An example, which we discuss in Ch. 5 is the discovery that atomic diffusion in optical lattices may not follow the normal diffusion equation. The work reported in this dissertation represents an investigation into possible few-body effects in some atom optical configurations of interest. The effects of indistinguishability, through the exchange force, on atomic diffraction by standing wave light fields is considered in Ch. 2. In Ch. 3, after a brief overview of atomic collisions in light fields, we look at the role that the dipole-dipole interaction might play, again in atomic diffraction. Chapters 4 and 5 are concerned with optical lattices, and lay the ground work for a study of the effect of the dipole-dipole interaction on the dynamics of atoms confined in such lattices.
Two of the major classes of atom optical elements are microfabricated structures and light beams. For instance, a standing light wave can act as a phase grating for atoms, as each absorption and emission process is accompanied by a coherent atomic recoil. After a simple discussion of the mechanical effects of light on atoms, we use a band-theoretical approach to categorize the main resonances (Bragg and Doppleron) that can be exploited to operate such a grating effectively. We discuss the incoherent effects of spontaneous emission, showing when and how they lead from a diffractive to a diffusive regime of atom–field interactions. We turn next to the diffraction of atoms by quantized fields and show the sensitivity of the resulting atomic diffraction pattern to the field photon statistics. In this quantized regime, the atom–field interaction leaves the system in an entangled state. We conclude by reviewing some proposals that exploit this property to perform measurements on the field (atom) to prepare and/or monitor specific atomic (field) states.
Matter–wave interferometry dates from the inception of quantum mechanics, i.e., the early electron diffraction experiments. More recent neutron interferometry experiments have yielded new insights into many fundamental aspects of quantum mechanics. Presently, atom interferometry has been demonstrated and holds promise as a new field of optics – matter–wave optics. This field is particularly interesting since the potential sensitivity of matter–wave interferometers far exceeds that of their light-wave or ‘photon’ antecedents. In this chapter we consider the physics of light-induced forces on the center-of-mass motion of atoms and their application to atom optics (Fig. 17.1). The most obvious being the recoil associated with the emission and absorption of light. This ‘radiation pressure’ is the basis for laser induced cooling. Another very important mechanical effect is the gradient force due to, e.g., transverse variation in the laser beam. These, essentially semiclassical, forces are useful in guiding and trapping neutral atoms. After considering the basic forces which allow us to cool, guide, and trap atoms, we turn to the optics of atomic center-of-mass de Broglie waves, i.e., atom optics. In keeping with the spirit of the present text, we will focus on the quantum limits to matter–wave interferometry. An analysis of a matter–wave gyro in an obvious extension of the laser gyro and the similarity and relative merits of the two will be compared and contrasted. Finally we derive the “recoil limit” to laser cooling; and show that it is possible to supersede this limit via atomic coherence effects.
The diffraction of a coherent, stationary, beam of atoms from a standing wave of light is considered. Particular attention is paid to long interaction times for which the motion of the atoms inside the light field must be taken into account. This is the regime of dynamical diffraction, and is treated within the framework of a set of differential difference equations due to Raman and Nath. The popular Raman-Nath approximation, in which the kinetic energy imparted to the atoms by the light wave is ignored, is no longer valid and the full equations must be solved. When the interaction between the atoms and the light is very weak then few beams are produced. To describe spontaneous emission from the atom one can invoke a complex potential as a model for dissipation. If the atom beam is obliquely incident one finds anomalously high transmission close to the Bragg angles which is the physical manifestation of degeneracies in non-Hermitian matrices. The classical limit is approached when the atom-light interaction is strong, producing many beams. The classical dynamics (geometrical rays) reveal that the farfield intensity pattern is dominated by caustics. These proliferate with increasing interaction distance. Two methods are presented for analytically treating the semiclassical limit of the wave mechanics. The first begins with W.K.B. solutions to the continuised Raman-Nath equations. Mapping onto parabolic cylinder functions removes the spurious divergences of the W.K.B. solutions, giving eigenvectors which are uniformly valid for all scattering angles and may be summed to give the wavefunction. The second method transforms the original W.K.B. eigensum, using the Poisson summation formula, giving a new sum, each term of which has classical significance. This method shows that wave theory decorates the classical caustics with an Airy function intensity profile, as predicted by catastrophe theory.