Wave mechanics and interference have always been at the heart of quantum mechanics. Many ofthe most striking quantum effects, at their heart, arise from the wave nature that quantum particles exhibit. In this thesis, I describe two experiments which showcase two different interference effects using a rubidium Bose-Einstein condensate. The first experiment examines the ways geometric phases enter into two-dimensional spin systems by studying their effect on an atomic Ramsey interferometer. The addition of an off-resonantly coupled level causes the location of interference minima to shift on frequency scales comparable to relevant Rabi frequencies of the system, as well as potentially creating locations with increased or decreased sensitivity to magnetic noise. The second experiment is a weak Stern-Gerlach experiment, showing how the components of a superposition state, with different magnetic moments, can interfere to show a greatly increased shift due to a magnetic gradient. The effect is observed using the second-order magnetic sensitivity of the clock states of 87Rb, with a greater than fivefold amplification of the momentum shift created by the magnetic gradient.
Wave mechanics and interference have always been at the heart of quantum mechanics. Many ofthe most striking quantum effects, at their heart, arise from the wave nature that quantum particles exhibit. In this thesis, I describe two experiments which showcase two different interference effects using a rubidium Bose-Einstein condensate. The first experiment examines the ways geometric phases enter into two-dimensional spin systems by studying their effect on an atomic Ramsey interferometer. The addition of an off-resonantly coupled level causes the location of interference minima to shift on frequency scales comparable to relevant Rabi frequencies of the system, as well as potentially creating locations with increased or decreased sensitivity to magnetic noise. The second experiment is a weak Stern-Gerlach experiment, showing how the components of a superposition state, with different magnetic moments, can interfere to show a greatly increased shift due to a magnetic gradient. The effect is observed using the second-order magnetic sensitivity of the clock states of 87Rb, with a greater than fivefold amplification of the momentum shift created by the magnetic gradient.
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.
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.
We describe effects of matter-wave interference of spinor states in the 87Rb Bose-Einstein condensate. The components of the F=2 manifold are populated by forced Majorana transitions and then fall freely due to gravity in an applied magnetic field. Weak inhomogeneities of the magnetic field, present in the experiment, impose relative velocities onto different mF components, which show up as interference patterns upon measurement of atomic density distributions with a Stern-Gerlach imaging method. We show that interference effects may appear in experiments even if gradients of the magnetic field components are eliminated but higher-order inhomogeneity is present and the duration of the interaction is long enough. In particular, we show that the resulting matter-wave interference patterns can mimic spontaneous pattern formation in the quantum gas.
In the frame of quantum mechanics, we consider an ensemble of spin-½ neutral particles passing through a Stern–Gerlach apparatus and explore how their motions depend on the initial phase difference between two internal spin states. Assuming the particles moving along y-axis, due to the initial phase difference between spin states, they not only split along the longitudinal direction (z-axis) but also separate along the lateral direction (x-axis). The dependence of the lateral displacement on the initial phase difference reminds one of the picture of a quantum interference. This generalized interference provides an alternative approach to measuring the initial phase difference. The experimental realization with ultracold atoms or Bose–Einstein condensates is also discussed.
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.
In this paper, a quantum Stern-Gerlach thought experiment is introduced where, in addition to the intrinsic angular momentum of an atom, the magnetic field is considered to be a quantum mechanical field. A free falling spin polarized Bose-Einstein condensate passes close to a flux qubit and interacts with the quantum superimposed magnetic field of the flux qubit. Such an interaction results a macroscopic quantum entanglement of the path of a Bose-Einstein condensate with the magnetic flux quantum state of the flux qubit. In this paper, three regimes of coupling between the flux qubit and a free falling Bose-Einstein condensate are discussed. This paper also explains how to produce a path entangled Bose-Einstein condensate where the condensate can be located at physically distinct locations simultaneously. This paper highlights new insights about the foundations of the quantum Stern-Gerlach experiment.