This thesis describes recent experiments conducted on a Bose-Einstein condensate in an optical waveguide. This optical potential confines the atoms against gravity in the vertical dimension, guiding them to freely propagate in the horizontal. Being supported against gravity enables long expansion times of hundreds of milliseconds, facilitating techniques such as delta-kick cooling. In an ideal atom interferometer, the beamsplitters would impart a large momentum splitting between the interfering states in order to increase the signal. However, their effective use requires both an even narrower momentum width source and good vibration isolation. Three such techniques were investigated in this thesis: reflection from a repulsive light potential barrier, Bragg transitions from an optical lattice (which are effectively bouncing atoms off a moving grating), and Bloch-acceleration by loading the atoms into such an optical lattice and then accelerating the combined system. It is found that a combination of both Bragg and Bloch provides the most promising route to truly large momentum transfer in a system which is sensitive only to acceleration. Lastly, large-momentum transfer techniques can be used to effectively increase the way in which the output signal scales with time, creating interferometers which generate the same sensitivity faster (increasing the bandwidth of a sensor), or generate a much better sensitivity in the same time. We form a dual condensate of both rubidium-85 an rubidium-87 via sympathetic cooling. The collisional properties of Rubidium-85 can be modified by applying an external magnetic field, at an easy-to-experimentally-reach value of between 150-170G. It turns out that this combination of atomic isotopes is ideal for an interferometric test of the weak equivalence principle, one of the underpinnings of General Relativity. This thesis also presents the results of the first Bose-condensed version of such a dual-species interferometer. By removing any 87Rb left after condensation, we have created a pure 85Rb BEC. Using this we can now explore how the inter-atomic interactions affect the phase shift of a condensed atom interferometer, as we have complete control over the interaction strength. A condensate with no inter-particle interactions should behave like an ideal particle. With a small attractive interaction between atoms, it is possible to create a self-trapped cloud of atoms which propagates dispersionlessly. This cloud is known as a soliton, and it is predicted to have even more interesting quantum mechanical properties. For example it is predicted that by colliding two such solitons, an entangled state can be generated. Our results indicate that the dispersionless character of the soliton out-performs all other interaction strengths in an atom interferometer, including even the non-interacting cloud.
This thesis describes recent experiments conducted on a Bose-Einstein condensate in an optical waveguide. This optical potential confines the atoms against gravity in the vertical dimension, guiding them to freely propagate in the horizontal. Being supported against gravity enables long expansion times of hundreds of milliseconds, facilitating techniques such as delta-kick cooling. In an ideal atom interferometer, the beamsplitters would impart a large momentum splitting between the interfering states in order to increase the signal. However, their effective use requires both an even narrower momentum width source and good vibration isolation. Three such techniques were investigated in this thesis: reflection from a repulsive light potential barrier, Bragg transitions from an optical lattice (which are effectively bouncing atoms off a moving grating), and Bloch-acceleration by loading the atoms into such an optical lattice and then accelerating the combined system. It is found that a combination of both Bragg and Bloch provides the most promising route to truly large momentum transfer in a system which is sensitive only to acceleration. Lastly, large-momentum transfer techniques can be used to effectively increase the way in which the output signal scales with time, creating interferometers which generate the same sensitivity faster (increasing the bandwidth of a sensor), or generate a much better sensitivity in the same time. We form a dual condensate of both rubidium-85 an rubidium-87 via sympathetic cooling. The collisional properties of Rubidium-85 can be modified by applying an external magnetic field, at an easy-to-experimentally-reach value of between 150-170G. It turns out that this combination of atomic isotopes is ideal for an interferometric test of the weak equivalence principle, one of the underpinnings of General Relativity. This thesis also presents the results of the first Bose-condensed version of such a dual-species interferometer. By removing any 87Rb left after condensation, we have created a pure 85Rb BEC. Using this we can now explore how the inter-atomic interactions affect the phase shift of a condensed atom interferometer, as we have complete control over the interaction strength. A condensate with no inter-particle interactions should behave like an ideal particle. With a small attractive interaction between atoms, it is possible to create a self-trapped cloud of atoms which propagates dispersionlessly. This cloud is known as a soliton, and it is predicted to have even more interesting quantum mechanical properties. For example it is predicted that by colliding two such solitons, an entangled state can be generated. Our results indicate that the dispersionless character of the soliton out-performs all other interaction strengths in an atom interferometer, including even the non-interacting cloud.
In recent years, atom interferometry has become established as an indispensable tool in both fundamental and applied physics. With present state-of-the-art devices based on thermal atoms reaching limits imposed by the momentum spread of the initial atomic wavepacket, it seems natural to ask whether colder sources such as Bose-Einstein condensates may prove beneficial in advancing the precision of interferometric measurements. The thesis at hand aims to inform this question, specifically by examining the role played by atomic interactions in interferometers based on Bose-condensed atoms. Interactions can have both advantageous and deleterious consequences in the context of atom interferometry. They provide a means to control the momentum width of the condensate, and facilitate the generation of nonclassical squeezed states which may enhance the phase sensitivity beyond the shot noise limit. Conversely, the condensate self-interaction causes mean-field shifts, multimode excitations and phase diffusion which can erode both the precision and the accuracy of an interferometric measurement. The question of when and in which systems the detrimental effects of interactions outweigh the advantages of using Bose-Einstein condensates is an important one, and warrants investigation. This thesis presents experimental studies into the role of interactions in both internal- and external-state atom interferometers. As a foundation for these investigations, we describe the design and construction of an apparatus for creating Bose-Einstein condensates of the two stable rubidium isotopes in an optical trap. By sympathetic cooling with a rubidium-87 reservoir, we are able to produce condensates of rubidium-85 in which the interactions may be adjusted by means of a magnetic Feshbach resonance. The tunability afforded by the Feshbach resonance is used to study inelastic losses in ultracold rubidium-85 clouds, as well as the effect of interactions on condensate stability and on the ground state of dual-species mixtures. In particular, we offer new experimental data on the dynamics of collapsing condensates with attractive interactions, over which some controversy has existed since the first experiments more than a decade ago. Good agreement is found between the measured collapse times and a simple mean-field model. Proceeding to interferometry, we present results from Ramsey interferometers operating on the clock transition of rubidium-87 Bose-Einstein condensates. In free-space operation with Raman beamsplitters, we demonstrate projection-noise-limited performance, an important prerequisite for the realisation of squeezing-enhanced sensitivity. Using large condensates of up to 10⁶ atoms and microwave coupling, we study the effect of interactions on the Ramsey fringe contrast. The dominant source of decoherence is found to be spatial dynamics driven by the difference in interparticle interaction strengths, which are analysed using the spin-echo technique and numerical simulations of the Gross-Pitaevskii equation. Finally, we turn our attention to external-state interferometry, implementing a Mach-Zehnder gravimeter using Bragg transitions in a freely falling rubidium-87 condensate. Large-momentum-transfer beamsplitters composed of higher-order Bragg diffraction and Bloch oscillations are used to increase the accumulated phase and thus the sensitivity of the interferometer. The role of interactions in this system is examined, and we canvass methods for achieving further increases in sensitivity.
Bose-Einstein condensates are coherent matter waves, produced by cooling gaseous atomic clouds to ultra-low temperatures. For applications in atom interferometry and precision measurements, Bose-condensed sources present an intriguing alternative to thermal atoms. Although the current sensitivity achievable with interferometers using coherent atoms is not comparable to thermal beam machines (mainly due to the lower flux), there are promising ways to utilise the potential of Bose-condensed sources for atom interferometry. Among those is the low momentum width of Bose-Einstein condensates, which can generally be well controlled and is advantageous for increased interferometric sensitivities by implementing large momentum transfer beam splitters. As part of this thesis, experimental and theoretical investigations are presented to investigate the potential of Bose-Einstein condensates for such applications. We shall present the quantum projection noise limited performance of a Ramsey interferometer operating on the atomic clock transition of a freely expanding cloud of Bose-condensed rubidium 87 atoms. The results include Ramsey fringes of high visibility, not measurably affected by atomic interaction-induced dephasing effects. The achievement and detection of the quantum projection noise limit rely critically on the precision and accuracy of both the imaging setup and the coupling scheme in the interferometric beam splitters. The stabilisation of the beam splitters via an optical Sagnac interferometer is the basis for the quantum projection noise limited performance of the interferometer presented. For an increase of bandwidth and flux in atom interferometric measurements, it is advantageous to use a continuous atomic beam. A truly continuous coherent atom source has not been realised to date, and we present results on a pumping mechanism in this thesis, as a decisive step towards a continuous atom laser. By the investigation of different momentum resonances, we find that the pumping scheme relies on a Raman superradiance-like process. Finally, the thesis demonstrates two interaction measurements in rubidium. The strong mean field interactions due to the high densities in Bose-Einstein condensates are used to probe the potential of a rubidium 87 condensate with an atom laser. The measurement allows a determination of the scattering length between the two atomic states involved. In addition to this two-body scattering scheme, we present a measurement of three-body loss coefficients, extracted from loss curves in rubidium 85 Bose-Einstein condensates. The measurement provides new upper bounds on the three-body loss coefficients at the scattering lengths considered.
Matter-wave interferometers show great a potential for improving inertial sensing. The absence of drifts recommends them for a variety of applications in geodesy, navigation, or fundamental physics. Here, ultracold atomic ensembles, featuring a velocity distribution well below the photon recoil velocity, open up new perspectives. In contrast to standard laser cooling methods, they allow to reach better beam-splitting efficiencies and, hence, a higher contrast as well as to reduce systematic uncertainties and biases. Presently, Bose-Einstein condensates (BECs) provide the means to achieve the lowest expansion energies of few picokelvin. Indeed, the momentum distribution of a BEC can be further narrowed after reaching the regime of ballistic expansion, where all mean field energy is converted to kinetic energy, by the application of the delta-kick collimation technique. With such ensembles, Bragg processes can be driven with an efficiency of above 95% as well as Bloch oscillations performed without large atomic losses or dephasing. Both enable efficient large momentum transfer in interferometers to enhance their sensitivity for inertial effects. In a so-called twin-lattice atom interferometers more than thousand photon recoils are used to form compact but sensitive atom interferometers. These methods not only bring in reach extremely accurate gravimeters and accelerometers but also gyroscopes. Like the Sagnac effect in ring laser or fiber gyroscopes, the sensitivity of atom interferometers to rotations increases with the space-time area enclosed by the interferometer. In the case of light interferometers, the latter can be enlarged by forming multiple fiber loops. However, the equivalent for matter-wave interferometers remains an experimental challenge. An atom interferometer with scalable area may be formed in a twin lattice combined with a relaunch mechanism to obtain multi loops as well. Due to this scalability, it offers the perspective of reaching unprecedented sensitivities for rotations in comparably compact sensor head setups. Moreover, atom-chip technologies offer the possibility to generate a BEC and perform delta-kick collimation in a fast and reliable away, paving the way for field-deployable miniaturized atomic devices. Last but not least, the extremely low expansion energies of BECs open up to extend the time atoms spend in the interferometer to tens of seconds. This brings in reach unprecedented sensitivities in space-borne applications such as satellite geodesy.
This thesis contributes to the debate over the viability of using Bose-condensed sources to improve the sensitivity of atom interferometers. Specifically, we present theoretical investigations into (1) the effect of source momentum width on large momentum transfer (LMT) atom interferometry with Bragg pulses, and (2) the prospect of stabilising a high flux, narrow linewidth, continuously pumped atom laser via measurement-based feedback control of the BEC that forms the lasing mode of the atom laser. To begin, this thesis considers the effect of the atomic source's momentum width on the phase sensitivity of Bragg pulse atom interferometers in the Mach-Zehnder configuration. We show that an atomic cloud's momentum width places a fundamental upper bound on the maximum transfer efficiency of a Bragg mirror pulse, and furthermore limits the phase sensitivity of a Bragg pulse atom interferometer. We quantify these momentum width effects and precisely compute how mirror efficiencies and interferometer phase sensitivities vary as functions of Bragg order and source type. In particular, we show that narrow momentum width Bose-condensed sources give comparable sensitivities to broad momentum width thermal sources, even after incorporating the lower atom flux of Bose-condensed sources. Coupled with other favourable properties of Bose-condensed sources, such as their high tolerance to classical noise due to optical wavefront aberrations and the Coriolis effect, this suggests that LMT Bragg atom interferometry with Bose-condensed sources should yield improved sensitivities over current inertial sensors. Furthermore, our results and methodology allow for the efficient optimisation of Bragg pulses, which will help in the design of LMT Bragg mirrors and beamsplitters for atom-interferometer-based inertial sensors, irrespective of source type. In the second part of this thesis, we investigate the prospect of measurement-based feedback control of a BEC, with the aim of reducing density fluctuations by cooling the condensate to a stable spatial mode. Firstly, we consider the effects of experimental imperfections on the estimation-based feedback control of a weakly-interacting BEC undergoing continuous position measurement. These limitations violate the assumption that the estimator (i.e., filter) accurately models the underlying system, thus requiring a separate analysis of the system and filter dynamics. We show that the control scheme is robust to detector inefficiency, time delay, technical noise and miscalibrated parameters. These results imply that reasonable experimental imperfections do not limit the feasibility of cooling a BEC by continuous measurement and feedback. Secondly, we designed a feedback-control scheme for a trapped condensate, with interatomic interactions of any strength, based on a phase-contrast imaging setup. We derive the filtering equation for the system, and show that it gives a continuous measurement of the condensate's density. A semiclassical analysis of this control scheme shows that feedback-cooling of an interacting BEC is also possible, and that the interatomic interactions actually increase the effectiveness of the control. Therefore, measurement-based feedback control can stabilise the spatial mode of a BEC, which is a requirement for the high flux, narrow linewidth, continuously pumped atom laser sources that could potentially give inertial measurement sensitivities orders of magnitude beyond current state-of-the-art devices.
Interferometry with atoms is a young discipline of physics. The ¯rst interfer- ometers were realised in the early 1990s, using light pulses as beamsplitters in momentum space. Recent developments in atom optics have led to new proposals for interferometers, where the splitting takes place spatially. Mag- netic and optical traps are both suited for this kind of interferometer if a well de¯ned and highly controllable trap is realised. In this thesis results from two experiments that in principle allow the creation of such traps are presented. After reviewing the principles and techniques of atom optics necessary for the understanding of this thesis, a theoretical discussion about the spatial single atom interferometer in a double well potential follows. It is shown that within reasonable limits the system can be reduced to two levels and solved by the Bloch equations. Using the realistic case of a not perfectly symmetric double well potential allows an understanding of the physics behind such an interferometer: how phase is accumulated and how localisation of the atoms leads to the loss of the interferometric signal. Then two experiments are presented. One experiment was newly built up as part of this thesis: it uses a novel hybrid atom chip' with a combination of a magneto-optical ¯lm and current-carrying structures to produce the magnetic trapping potentials. This experiment allowed 5¢108 87Rb atoms to be captured in a magneto-optical trap, where the atom-chip's surface acts as a mirror. The atoms were then transferred into a purely magnetic trap which was created by current carrying structures on the chip. From there on, RF radiation enforced evaporative cooling, so that a quantum degenerate Bose-Einstein condensate of up to 105 atoms was created. It was also shown that the magneto-optical ¯lm is able to hold and trap the atoms. In the second experiment atoms are trapped in the spatially varying inten- sity of light of 1.03 ¹m wavelength. This experiment used an existing set-up as a basis and was modi¯ed and improved for this new project. This experiment starts with 109 87Rb atoms in a 6-beam magneto-optical trap. After examining and optimising the loading process, 1:5 ¢ 105 atoms could be loaded directly from the Magneto-optical trap into the optical dipole potential of two crossed laser beams at 1.03 ¹m. Evaporative cooling was demonstrated though the phase transition to quantum degeneracy was not reached.
The subject of this thesis is the use of BECs for atom interferometry. The standard way atom interferometry is today performed is by interrogating free falling samples of atoms. The employed samples are cold (but not condensed) to have high coherence, and dilute, not to interact significantly with each other. This technique represents nowadays an almost mature field of research in which the achievable interferometric sensitivity is bounded by the atomic shot noise. Until a few years ago the employment of BECs in such devices was strongly limited by the effect of the interactions between the condensed atoms. This obstacle is today removable exploiting interaction tuning techniques. The use of BECs would be advantageous for atom interferometry inasmuch they represents the matter analogue of the optical laser providing the maximum coherence allowed by quantum mechanics. Moreover, non-linear dynamic can be exploited in order to prepare entangled states of the system. The realization of entangled samples can lead to sub-shot noise sensitivity of the interferometers. At today very nice proof-of-principle experiments have been realized in this direction but a competitive device is still missing. This thesis work is inserted in a long term project whose goal is the realization of such a device. The basic operational idea of the project starts with the preparation of a BEC in a double well potential. By the effect of strong interactions the atomic system can be driven into an entangled state. Once the entangled state is prepared, interactions can be †switched off†and the interferometric sequence performed. This thesis begins with the description of the apparatus for the production of tunable BECs to be used in the interferometer. We chose to work with 39K atoms because this atomic species presents many convenient Feshabch resonances at easily accessible magnetic field values. The cooling of this particular atomic species presents many difficulties, both for the laser and evaporative cooling processes. For this reason, this was the last alkaline atom to be condensed. Its condensation up to now was only possible by employing sympathetic cooling with another species. In this thesis our solutions to the various cooling issues is reported. In particular we realized sub-Doppler cooling for the first time for this species and we achieved condensation via evaporation in an optical dipole trap taking advantage of a Feshbach resonance. In the last part of this work, are presented original calculations for the effects of thermal fluctuations on the coherence of a BEC in a double well, discussing the interplay between thermal fluctuations and interactions in this system. Estimations and feasibility studies regarding the double well trap to be realized are also reported.