Hessmo, B., 2000. Quantum optics in constrained geometries. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 574. 45 pp. Uppsala. ISBN 91-554-4830-5 When light exhibits particle properties, and when matter exhibits wave properties quantum mechanics is needed to describe physical phenomena. A two-photon source produces nonmaximally entangled photon pairs when the source is small enough to diffract light. It is shown that diffraction degrades the entanglement. Quantum states produced in this way are used to probe the complementarity between path information and interference in Young’s double slit experiment. When two photons have a nonmaximally entangled polarization it is shown that the Pancharatnam phase is dependent on the entanglement in a nontrivial way. This could be used for implementing simple quantum logical circuits. Magnetic traps are capable of holding cold neutral atoms. It is shown that magnetic traps and guides can be generated by thin wires etched on a surface using standard nanofabrication technology. These atom chips can hold and manipulate atoms located a few microns above the surface with very high accuracy. The potentials are very versatile and allows for highly complex designs, one such design implemented here is a beam splitter for neutral atoms. Interferometry with these confined de Broglie is also considered. These atom chips could be used for implementing quantum logical circuits.
Hessmo, B., 2000. Quantum optics in constrained geometries. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 574. 45 pp. Uppsala. ISBN 91-554-4830-5 When light exhibits particle properties, and when matter exhibits wave properties quantum mechanics is needed to describe physical phenomena. A two-photon source produces nonmaximally entangled photon pairs when the source is small enough to diffract light. It is shown that diffraction degrades the entanglement. Quantum states produced in this way are used to probe the complementarity between path information and interference in Young’s double slit experiment. When two photons have a nonmaximally entangled polarization it is shown that the Pancharatnam phase is dependent on the entanglement in a nontrivial way. This could be used for implementing simple quantum logical circuits. Magnetic traps are capable of holding cold neutral atoms. It is shown that magnetic traps and guides can be generated by thin wires etched on a surface using standard nanofabrication technology. These atom chips can hold and manipulate atoms located a few microns above the surface with very high accuracy. The potentials are very versatile and allows for highly complex designs, one such design implemented here is a beam splitter for neutral atoms. Interferometry with these confined de Broglie is also considered. These atom chips could be used for implementing quantum logical circuits.
When light exhibits particle properties, and when matter exhibits wave properties quantum mechanics is needed to describe physical phenomena. A two-photon source produces nonmaximally entangled photon pairs when the source is small enough to diffract light. It is shown that diffraction degrades the entanglement. Quantum states produced in this way are used to probe the complementarity between path information and interference in Young's double slit experiment. When two photons have a nonmaximally entangled polarization it is shown that the Pancharatnam phase is dependent on the entanglement in a nontrivial way. This could be used for implementing simple quantum logical circuits. Magnetic traps are capable of holding cold neutral atoms. It is shown that magnetic traps and guides can be generated by thin wires etched on a surface using standard nanofabrication technology. These atom chips can hold and manipulate atoms located a few microns above the surface with very high accuracy. The potentials are very versatile and allows for highly complex designs, one such design implemented here is a beam splitter for neutral atoms. Interferometry with these confined de Broglie is also considered. These atom chips could be used for implementing quantum logical circuits.
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.
In the case of mixed states ρAB of the composite system A ⊗ B, the previous relation generalizes to ρAB = ∑ k pkρ A k ⊗ρk , where pk are probabilities and ρk ’s (ρk ’s) are generic density matrix of the system A (B). The entanglement derives from “subtle” nonlocal correlations between the parts of a quantum system and combines three basic structural elements of quantum theory: the superposition principle, the quantum non-separability property and the exponential scaling of the state space with the number of partitions. This unique resource can be used to perform computational and cryptographic tasks otherwise impossible with classical systems. An entangled state shared by two or more separated parties is a valuable resource for fundamental quantum protocols, such as quantum teleportation [2], quantum computing [3] and quantum cryptography. By using entangled states we can deeply investigate the nonlocal properties of the quantum world. In fact, an entangled system exhibits correlations between two (or more) parties, which cannot be reproduced by a classical theory or, in general, by a Local Hidden Variables Theory (LHVT). Quantum optics represents an excellent experimental test bench for various novel concepts introduced within the framework of quantum information theory. Quantum states of photons, generally produced by a probabilistic process, namely spontaneous parametric down conversion (SPDC), may be easily and accurately manipulated using linear and nonlinear optical devices and measured by efficient single-photon detectors. Photonic qubits represent the typical carrier of quantum information and can be distributed over long distances, either in free-space or in low-loss optical fibers. Two-particle experiments correspond to operate with qubits belonging to a (2 × 2) Hilbert space. Many quantum information tasks and fundamental tests of quantum mechanics, such as the simulation of properties of quantum systems, the realization of quantum algorithms of increasing complexity and the investigation of the quantum world at a mesoscopic level, deal with a large number of qubits. In order to take full advantage of the possibilities offered by quantum mechanics, more qubits must be added to a quantum state. Two approaches may be followed to increase the number of qubits. The first one consists of increasing the number of entangled particles. In this way, multi-qubit entangled states are created by distributing the qubits between the particles so that each particle carries one qubit. A second strategy consists of encoding more than one qubit in each particle, by exploiting different degrees of freedom (DOFs) of the photon such as the polarization, the path, the emission time, the orbital angular momentum. This has been used to create two-photon fourand six-qubit states and up to five-photon ten-qubit graph states. The entanglement of two particles in different DOFs corresponds to socalled hyperentanglement. It is worth noting that multi-qubit hyperentanglement allows to achieve higher
Ericsson, M., 2002. Geometric and Topological Phases with Applications to Quantum Com- putation. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 744. 53 pp. Uppsala. ISBN 91-554-5391-0. Quantum phenomena related to geometric and topological phases are investigated. The first results presented are theoretical extensions of these phases and related effects. Also experimen- tal proposals to measure some of the described effects are outlined. Thereafter, applications of geometric and topological phases in quantum computation are discussed. The notion of geometric phases is extended to cover mixed states undergoing unitary evo- lutions in interferometry. A comparison with a previously proposed definition of a mixed state geometric phase is made. In addition, an experimental test distinguishing these two phase con- cepts is proposed. Furthermore, an interferometry based geometric phase is introduced for systems undergoing evolutions described by completely positive maps. The dynamics of an Aharonov-Bohm system is investigated within the adiabatic approxima- tion. It is shown that the time-reversal symmetry for a semi-fluxon, a particle with an associated magneticflux which carries half a flux unit, is unexpectedly broken due to the Aharonov-Casher modification in the adiabatic approximation. The Aharonov-Casher Hamiltonian is used to determine the energy quantisation of neutral magnetic dipoles in electric fields. It is shown that for specific electric field configurations, one may acquire energy quantisation similar to the Landau effect for a charged particle in a homogeneous magnetic field. We furthermore show how the geometric phase can be used to implement fault tolerant quantum computations. Such computations are robust to area preserving perturbations from the environment. Topological fault-tolerant quantum computations based on the Aharonov-Casher set up are also investigated.
Atom optics has been a highly active field of research with many scientific breakthroughs over the past two decades, largely due to successful advances in laser technology, microfabrication techniques, and the development of laser cooling and trapping of neutral atoms. This dissertation details several atom optics experiments with the motivation to develop tools and techniques for precision atom wave interferometry. It provides background information about atom optics and the fundamentals behind laser cooling and trapping, including basic techniques for cold gas thermometry and absorptive detection of atoms. A brief overview of magnetic trapping and guiding in tight wire-based traps is also provided before the experimental details are presented. ❧ We developed a novel laser source of 780 nm light using frequency-doubled 1560 nm fiber amplifier. This laser system provided up to a Watt of tunable frequency stabilized light for two Rb laser cooling and trapping experiments. One system generates Bose-Einstein condensates in an optical trap while the second is based on atom chip magnetic traps. The atom chip system, detailed in this thesis, was designed and built to develop the tools necessary for transport and loading large numbers of cold atoms and explore the potential for guided atom interferometry. Techniques and results from this experiment are presented, including an efficient magnetic transport and loading method to deliver cold atom to atom chip traps. We also developed a modeling tool for the magnetic fields formed by coiled wire geometries, as well as planar wire patterns. These models helped us design traps and determine adiabatic transportation of cold atoms between macro-scale traps and micro-traps formed on atom chips. Having achieved near unity transfer efficiency, we demonstrated that this approach promises to be a consistent method for loading large numbers of atoms into micro-traps. Furthermore, we discuss an in situ imaging technique to investigate magnetic field contours of the traps and the dynamics of atoms within those confining potentials. We also controlled the propagation along the atom chip guides by accelerating atoms with longitudinal magnetic gradients, and investigated an atom focusing scheme. ❧ While the atom chip wire guides perform a role analogous to optical fibers guiding light waves, ""free space"" cold atoms offer great opportunity for precision interferometry. We describe a second on-going atom optics experiment that measures gravity gradients using a pair of atom fountain interferometers separated by one meter. We have demonstrated Gravity Gradiometer resolution down to 4x10⁻⁹ g/m using a 40 kg test mass. The atomic physics subsystem is described in detail, including the vacuum, cold atom source, optics, magnetic coils and shields, and vibration isolation and compensation. The system is designed to be a compact, robust, transportable instrument, taking strides towards future gravity gradient measurements in the field. In the realm of space applications, there has been interest for micro-gravity science experiments aboard the International Space Station, along with instrument development for gravity mapping of Earth and planetary bodies with satellite-based instruments. Furthermore, there are ground-based applications for gravity imaging of local density distributions, precision measurement of gravity, as well as proposals for redefining the kilogram, detecting gravitational waves and determining the Gravitational constant.
The rapid development of quantum technologies has driven a revolution in related research areas such as quantum computation and communication, and quantum materials. The first prototypes of functional quantum devices are beginning to appear, frequently created using ensembles of atoms, which allow the observation of sensitive, quantum effects, and have important applications in quantum simulation and matter wave interferometry. This modern text offers a self-contained introduction to the fundamentals of quantum atom optics and atomic many-body matter wave systems. Assuming a familiarity with undergraduate quantum mechanics, this book will be accessible for graduate students and early career researchers moving into this important new field. A detailed description of the underlying theory of quantum atom optics is given, before development of the key, quantum, technological applications, such as atom interferometry, quantum simulation, quantum metrology, and quantum computing.