The goal of this thesis is to study a novel approach towards all-optical continuous waveguide interferometers based on quasi-Bragg waveguide beam splitters. The Bragg beam splitter for matter waves is comprised of a periodic lattice produced by partial or full interference between two Gaussian laser beams and are used as waveguides for ultra-cold atoms. In the experimental conditions, where both waveguides have wide and deep potentials, atoms are unable to split from a single lattice. Instead, several spatially separated regions of the optical lattice are required, fulfilling the Bragg condition. This thesis will present clear evidence of the detection of discrete quantised momentum states of the atoms, created from a process of ultra-cold atoms undergoing interference in the single arms of a Michelson interferometer. A detailed investigation of the different regimes of the splitter has been completed by varying the initial atom velocity and the amplitude of the optical lattice. The findings from the study have produced optimal parameters where the splitting ratio of the atoms between the two waveguides can be finely controlled by the amplitude of the lattice within certain limits. A Michelson interferometer configuration is used to test the coherence of the atoms by decelerating them after splitting in the lattice. The return velocity of atoms is set to be equal to the initial velocity and the two clouds are recombined using the original lattice. A sinusoidal oscillation of the atomic momentum between the two output ports of the beam splitter is visible. However, only interference in single Michelson interferometer arms has been observed. The reasons are discussed in detail along with plans to move towards an all-optical design.
The goal of this thesis is to study a novel approach towards all-optical continuous waveguide interferometers based on quasi-Bragg waveguide beam splitters. The Bragg beam splitter for matter waves is comprised of a periodic lattice produced by partial or full interference between two Gaussian laser beams and are used as waveguides for ultra-cold atoms. In the experimental conditions, where both waveguides have wide and deep potentials, atoms are unable to split from a single lattice. Instead, several spatially separated regions of the optical lattice are required, fulfilling the Bragg condition. This thesis will present clear evidence of the detection of discrete quantised momentum states of the atoms, created from a process of ultra-cold atoms undergoing interference in the single arms of a Michelson interferometer. A detailed investigation of the different regimes of the splitter has been completed by varying the initial atom velocity and the amplitude of the optical lattice. The findings from the study have produced optimal parameters where the splitting ratio of the atoms between the two waveguides can be finely controlled by the amplitude of the lattice within certain limits. A Michelson interferometer configuration is used to test the coherence of the atoms by decelerating them after splitting in the lattice. The return velocity of atoms is set to be equal to the initial velocity and the two clouds are recombined using the original lattice. A sinusoidal oscillation of the atomic momentum between the two output ports of the beam splitter is visible. However, only interference in single Michelson interferometer arms has been observed. The reasons are discussed in detail along with plans to move towards an all-optical design.
We perform an experimental and theoretical study of a novel distributed quasi-Bragg splitter for cold atoms propagating in crossed optical waveguides. The atoms are guided by horizontal red-detuned laser beams which cross with an angle of roughly 90°. The lattice formed by the interference between the two waveguides is used as a quasi-Bragg splitter to continuously deflect the atomic flux from one waveguide into the other. In the limit of strong waveguide confinement and depending on the velocity of the cloud, three main regimes are observed corresponding (1) to the absence of reflection, (2) to partial reflection and (3) to full reflection into the second waveguide. In view of the application to atom interferometry, the condition to split the cloud into mainly two equally-populated fragments is only met in the highest velocity regime, where the fraction of reflected and transmitted atoms can be controlled by tuning the lattice height. A diagnostic of the momentum distribution shows that a quasi-Bragg splitter with the occupation of mainly two momentum states is achieved in this regime. This behaviour can be understood by considering the band structure associated with the potential in the crossing region and agrees with numerical simulations of the atomic dynamics.
Atom interferometry allows for new precision limits in measurement and a key component of it is the beam-splitter. In this thesis we look at the properties of an all optical beam-splitter, which is created by the overlap of two Gaussian laser beams,which also function as waveguides for the Bose-Einstein condensate. For this mainly the split step Fourier method is used to model the propagation of a low density Bose-Einstein condensate of atoms. The two main areas of interest are the splitting and recombination properties. \nThe splitting is studied both in two and one dimensions. For the one-dimensional case both standing and propagating waves are used to find the ideal splitting conditions of a balanced splitting and transmission. The result of these methods are in general agreement with the exception that for the propagating wave some of the atoms can become localised inside the beam-splitter. For the propagation it was found that the splitting is not perfectly coherent as the outputs are slightly deformed. However, when looking at the two-dimensional case we see that the splitting is not even close to being coherent. This is because the beam-splitter excites the incoming wave into higher transverse modes of the waveguides. To compensate for this the depth of the waveguides was lowered and the width narrowed to reduce the potential kinetic energy that the atoms could acquire and to increase the separation between the eigenstates to lower the probability of excitation into higher modes, respectively. Nonetheless, these investigations improved the splitting balance but it is still not coherent. Another method investigated was the introduction of a third laser which acts as a filling to reduce the depth of the potential well where the lasers generate the beam-splitter. This approach does not improve the splitting. \nHence instead of recombining single mode waves we used a multimode approach. For this we found that the mirror position is crucial for certain parameters as the longitudinal momentum is not necessarily the same in the reflection and transmission waveguide. Our investigations have generated interference fringes in this model \nsystem with a fractional height up to 33%.
Abstract : Gyroscopes based on ultracold atom interferometry have the potential to exhibit an intrinsic sensitivity larger by a factor of 4 x 1010 than for light-based interferometers. One of the major technical challenges for the advancement of atom optics and development of practical guided matter wave interferometers is the realization of coherent beam splitters. The overall focus of our research program is to develop a physical understanding of the conditions needed for coherent beam splitting and transport and use this knowledge to implement atom chip based interferometers using clouds of ultracold atoms. In this report we describe our experimental apparatus in detail and discuss the current progress towards interferometric measurements with clouds of ultracold atoms in a chip-based magnetic waveguide.
Atom interferometers and gyroscopes are highly sensitive atom-optical devices which are capable to measure inertial, gravitational, electric, and magnetic fields and to sense rotations. Theoretically, the signal-to-noise ratio of atomic gyroscopes is about a hundred billion times more than that of their optical counterparts for the same particle flux and the enclosed area. Ultra cold atoms from a Bose-Einstein condensate (BEC) can easily be controlled and coherently manipulated on small chips by laser pulses. Atom-optical devices will therefore play a significant role in fundamental research, precision measurements, and navigation systems. In BEC-based atom interferometers, a BEC in a trap is split by using laser pulses, the split clouds are allowed to evolve, they are reflected, and then recombined by laser pulses to observe interference. The split clouds accumulate spatial phase because of the trap and the nonlinearity caused by atom-atom interactions. A velocity mismatch due to reflection laser pulses also introduces a phase gradient across each cloud. These factors contribute to spatial relative phase between the clouds at recombination, causing the loss of contrast of the interference fringes. The main objective of this dissertation is to study the dynamics of a split condensate in atom Michelson interferometers, investigate the effect of trap frequencies, nonlinearity, and the velocity mismatch on the contrast, and to obtain the best theoretical limit of performance in terms of the experimental parameters: trap frequencies, number of atoms, and the velocity imparted to the clouds by the splitting laser pulses.
Atomic diffraction is the central concept of matter-wave interferometers, which provide the opportunity of high-precision rotation and acceleration sensing. Ultracold atoms are the ultimate quantum sensors for this purpose. Transferring photon momentum from two counterpropagating laser beams to atomic wavepackets prepares coherent superpositions in the momentum space, realising atomic beamsplitters and mirrors. Like classical optical systems, these matter-wave devices require exact specifications and ubiquitous imperfections need to be quantified. Therefore, in this thesis, the performance of (3+1)D atomic beamsplitters in the quasi-Bragg regime is studied numerically as well as analytically and is confirmed by experimental data [1]. Ideally, the incoming wavepacket can be split exactly into two parts or reflected perfectly with unit response, independent of its spatial and velocity distribution. However, the velocity selectivity of the Bragg diffraction, as well as losses into undesired diffraction orders in the quasi-Bragg regime, constitute aberrations, which cannot be neglected. The non-ideal behaviour due to spatial variations of the laser beam profiles and wavefront curvatures, regarding realistic Laguerre-Gaussian laser beams instead of ideal plane waves, reduces the diffraction efficiency and leads to rogue momentum components, just like misaligned lasers. In contrast, smooth temporal envelopes improve the beamsplitter performance. Different pulse shapes are taken into account, where some are amenable for closed analytical solutions. The realistic modelling and exhausting aberration studies characterises in detail atomic Bragg beamsplitters and demonstrate pathways for improvements, both required by challenging experiments. For hot ions in accelerator beams the atomic diffraction is used contrary to generate a velocity filter. Two counterpropagating far-detuned lasers transfer a narrow velocity class of ions from an initially broad distribution via a stimulated Raman transition between the ground states of a Λ-system. This colder subensemble prepares optimal initial conditions for precision collinear laser spectroscopy on fast ion beams. The efficiency of the filter is diminished by aberrations like the spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise. Spatial intensity variations of the ion and laser beams are considered, whereas wavefront curvature is negligible. A comprehensive master equation leads to conditions for the optimal frequency pair of lasers. The time-resolved population transfer characterises the filter performance and is evaluated numerically as well as analytically. Derived models match the numerical results, keeping the computational effort small. Taking into account the mentioned aberrations, the possible use of Raman transition as velocity filter for hot ions is demonstrated. Velocity classes with widths as low as 0.2 m/s can be transferred, achieving a significant population proportion from per mill to percent. Applying the analysis to current 40-Ca+ ion experiments, a sensitivity for measuring high ion acceleration voltages on the ppm level or below is substantiated.
Matter wave interferometry offers a novel approach for high precision measurements, such as the determination of physical constants like the local gravity constant g or the fine-structure constant. Since its early demonstration, it has become an important tool in the fields of fundamental and applied physics. The present work covers the implementation of matter wave interferometers as well as the creation of novel guiding potentials for ultra-cold ensembles of atoms and Bose-Einstein condensates for this purpose. In addition, novel techniques for the manipulation of atoms with Bragg lattices are presented, serving as elements for interferometry. The measurements in this work are performed with a Bose-Einstein condensate of 25000 87 rubidium atoms created in a crossed optical dipole trap. The crossed optical dipole trap is loaded from a magneto-optical trap and allows a measurement every 25 s. This work introduces the novel technique of double Bragg diffraction as a tool for atom optics for the first time experimentally. The creation of beamsplitters and mirrors for advanced interferometric measurements is characterized. An in depth discussion on the momentum distribution of atomic clouds and its influence on double Bragg diffraction is given. Additionally experimental results for higher-order Bragg diffraction are explained and double Bragg diffraction is used to implement a full Ramsey-type interferometer. A second central result of this work is the implementation of novel guiding structures for ultra-cold atoms. These structures are created with conical refraction, an effect that occurs when light is guided along one of the optical axis of a bi-axial crystal. The conical refraction crystal used to operate the novel trapping geometries is a KGd(WO4)2 crystal that has been specifically cut orthogonal to one of the optical axis. Two regimes are discussed in detail: the creation of a toroidal matter wave guide and the implementation of a three-dimensional dark focus. Additional geometries accessible with conical refraction are introduced and possible applications are shown. The first regime characterized in detail is the creation of a toroidal wave guide for ultra-cold atoms and Bose-Einstein condensates. With the aid of a lightsheet potential atoms are trapped in a quasi two-dimensional ring geometry. Inside of the geometry atoms are accelerated, decelerated and held for extended storage times of up to two seconds. First attempts for the implementation of a Mach-Zehnder-type interferometer in a toroidal trap are presented. The second regime shown is the creation of a three-dimensional dark focus that is used to trap atoms in a repulsive confinement of light. The parameters of the dark focus are investigated in detail. Future application of a two-dimensional array of dark foci is shown by demonstrating the respective light field.