Ultracold atoms and Bose-Einstein condensates represent a burgeoning and ever exciting area of research which has produced numerous breakthroughs in the last 15 years. Ultracold atoms at nano-Kelvin temperatures, isolated in atom traps from the hot, room temperature environment, exhibit ultimate quantum properties and can serve as pure samples for testing quantum mechanics and performing precision measurements. The research described in this thesis investigates, both theoretically and experimentally, the coherence and dynamical evolution of a two-component Bose-Einstein condensate (BEC). The studies are performed on the |1 › ≡ F = 1,mF = −1 › and |2 › ≡ |F = 2,mF = +1 › hyperfine ground states of a 87Rb BEC trapped on an atom chip. Conventional understanding has been that the fringe contrast in interferometric experiments on a BEC is limited by the mean-field dephasing due to strong interatomic interactions which lead to inhomogeneous collisional shifts. We have discovered using Ramsey interferometry a mean-field driven self-rephasing effect in a trapped twocomponent BEC. When combined with a spin-echo technique, we find that the selfrephasing leads to a coherence time of 2.8 s, the longest ever recorded for an interacting BEC. Secondly, we have developed a new technique based on periodic collective oscillations for precision measurements of the interspecies and intraspecies scattering lengths and derived an analytic mean-field theory for the phase and density dynamics in the twocomponent BEC. This technique has been applied to the measurements of the scattering lengths for the two components, |1i and |2i, in 87Rb with a precision of 0.016%. Additionally, the two-body loss coefficients for these states have been measured. Thirdly, we have developed and applied a new, interferometric method for calibrating the detection system, in order to determine the total atom number precisely for Ramsey interferometric measurements. The calibration coefficient is found to be in a good agreement with that obtained using a conventional calibration technique based on the critical BEC temperature. Finally, we have detected predicted RF-induced Feshbach resonances by monitoring changes in the two-body loss coefficients in the two-component BEC. Conventional Feshbach resonances have been used in many works to tune the s-wave interactions; however, there is no achievable magnetic Feshbach resonance for magnetically trappable states of 87Rb. The RF-induced resonances which we have detected can provide a way to tune the scattering lengths which is important for interferometry and entanglement experiments. The positions of the resonances may provide useful information for predicting the atomic scattering properties of 87Rb.
Ultracold atoms and Bose-Einstein condensates represent a burgeoning and ever exciting area of research which has produced numerous breakthroughs in the last 15 years. Ultracold atoms at nano-Kelvin temperatures, isolated in atom traps from the hot, room temperature environment, exhibit ultimate quantum properties and can serve as pure samples for testing quantum mechanics and performing precision measurements. The research described in this thesis investigates, both theoretically and experimentally, the coherence and dynamical evolution of a two-component Bose-Einstein condensate (BEC). The studies are performed on the |1 › ≡ F = 1,mF = −1 › and |2 › ≡ |F = 2,mF = +1 › hyperfine ground states of a 87Rb BEC trapped on an atom chip. Conventional understanding has been that the fringe contrast in interferometric experiments on a BEC is limited by the mean-field dephasing due to strong interatomic interactions which lead to inhomogeneous collisional shifts. We have discovered using Ramsey interferometry a mean-field driven self-rephasing effect in a trapped twocomponent BEC. When combined with a spin-echo technique, we find that the selfrephasing leads to a coherence time of 2.8 s, the longest ever recorded for an interacting BEC. Secondly, we have developed a new technique based on periodic collective oscillations for precision measurements of the interspecies and intraspecies scattering lengths and derived an analytic mean-field theory for the phase and density dynamics in the twocomponent BEC. This technique has been applied to the measurements of the scattering lengths for the two components, |1i and |2i, in 87Rb with a precision of 0.016%. Additionally, the two-body loss coefficients for these states have been measured. Thirdly, we have developed and applied a new, interferometric method for calibrating the detection system, in order to determine the total atom number precisely for Ramsey interferometric measurements. The calibration coefficient is found to be in a good agreement with that obtained using a conventional calibration technique based on the critical BEC temperature. Finally, we have detected predicted RF-induced Feshbach resonances by monitoring changes in the two-body loss coefficients in the two-component BEC. Conventional Feshbach resonances have been used in many works to tune the s-wave interactions; however, there is no achievable magnetic Feshbach resonance for magnetically trappable states of 87Rb. The RF-induced resonances which we have detected can provide a way to tune the scattering lengths which is important for interferometry and entanglement experiments. The positions of the resonances may provide useful information for predicting the atomic scattering properties of 87Rb.
In the years following the first Bose-Einstein condensation of dilute atomic gases in 1995, several experiments demonstrated many fundamental properties of two-component BEC. Subsequent to these pioneering experiments, almost a decade passed with little experimental activity, relative to investigations of single-component condensates. In somewhat of a renaissance, the initial observations of two-component BEC have been revisited in recent years, consolidating and clarifying results of the early works, and illuminating new and surprising behaviour of these rich quantum fluids. This thesis presents new experimental results on the relative phase evolution of two-component Bose-Einstein condensates (BECs). We approach our study of this system from the dual perspective of binary superfluidity and trapped atom interferometry. We observe nonequilibrium dynamics of the condensate that are deeply connected to the physics of interpenetrating superfluids. These dynamics have consequences for interferometers whose two paths are different internal spin states of the condensate atoms. Using trapped condensates for precision measurement draws upon the benefits of confined atom interferometry - long interrogation times, precise position control to measure near-field potentials - in addition to the unique coherence properties of BECs. Precision measurementwith trapped particles, however, is obstructed by the inherent inhomogeneities associated with the confinement itself. Spatial variation of the external potentials and atomic density can give rise to dephasing during the free evolution and imperfect splitting and recombination of the interferometric paths. In this thesis, we consider the dephasing of the two-componentmean field order parameter, which tends to diminish the interference signal attained with the condensate. The promise of fuhs for atom interferometry lies within using nonclassical many body states to reduce the fundamental noise limit imposed upon measuring the projection of atomic pseudospin. Before the many body quantum properties of two-component condensates can be used to their full potential, the ideal classical limit must be achieved and investigated. As in optical interferometry, the classical ideality of an interference measurement is contingent upon control of the spatialmodes - thematter wave fields, or single particle wave functions. Whilst much attention is currently focused on preparing nonclassical many body states for entanglement and squeezing of the condensate pseudospin, this thesis focuses on the ancillary yet important issue of spatial inhomogeneity of the condensate mean field. Reversal of the spatially inhomogeneous mean field evolution is demonstrated, employing the techniques of nuclear magnetic resonance. A new method is demonstrated to probe pseudospin -1/2 condensates involving microwave adiabatic passage. The technique permits simultaneous, spatially resolved absorption imaging of the spatial mode of each component. Controlled manipulation of the components into Zeeman states with different magnetic moments allows spatial separation using a Stern-Gerlach separation technique, providing a spatially resolved projection of the local condensate pseudospin from a single absorption image. We propose an interferometric technique which employs this imaging method to directly image the relative phase. The miscibility of the two components depends on the relative magnitude of the interactions between various collision partners. The boundary of this miscibility is found to be less pronounced than expected from the commonly applied results of homogeneous super-fluids.The effects of kinetic energy are shown to be significant at the threshold of miscibility, leading to a breakdown in the Thomas-Fermi approximation. Magnetic dipole transitions amongst alkali ground states are often used to prepare, manipulate, and interrogate pseudospin -1/2 condensates. We present a thorough investigation of the two-photonmagnetic dipole transitions between the |F = 1,mF = -1〉 and |F = 2,mF = +1〉 states, and the |F = 1,mF = +1〉 and |F = 2,mF = -1〉 states of 87Rb. Taking into account all 8 Zeeman levels of the electronic ground state reveals markedly different radiative shifts and effects beyond the rotating wave approximation, compared to the three-level formalism commonly used for these transitions.This has implications for Ramsey interferometry using the two-photon magnetic dipole transitions. The unchartered experimental territory offered by two-component condensates is vast, and future directions, supplementary to the work in this thesis, are elucidated.
We observe the coherence of an interacting two-component Bose-Einstein condensate (BEC) surviving for seconds in a trapped Ramsey interferometer. Mean-field-driven collective oscillations of two components lead to periodic dephasing and rephasing of condensate wave functions with a slow decay of the interference fringe visibility. We apply spin echo synchronous with the self-rephasing of the condensate to reduce the influence of state-dependent atom losses, significantly enhancing the visibility up to 0.75 at the evolution time of 1.5 s. Mean-field theory consistently predicts higher visibility than experimentally observed values. We quantify the effects of classical and quantum noise and infer a coherence time of 2.8 s for a trapped condensate of $5.5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ interacting atoms.
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 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.
The three experiments described in this thesis investigate fundamental properties of ultracold atoms. Using laser cooling and evaporative cooling, a dilute gas of sodium atoms is cooled to ~100 nK. Under these circumstances a Bose-Einstein condensate (BEC) forms, where millions of atoms collapse into the lowest energy state of the system and share a macroscopic wavefunction. The experiments are done in an ultrahigh vacuum and the atoms are manipulated remotely using laser beams, magnetic fields, and RF-fields. Using ultracold atoms allows unprecedented control over the internal and external degrees of freedom of the system, making it very suitable for precision measurements. Ultracold atoms also serve as a model system for more complicated or remote fields such as solid-state physics and cosmology. In the first experiment the refractive index of an ultracold bosonic gas is studied. The atomic clouds are analyzed for temperature and number of particles using nearly non-destructive phase-contrast imaging. After each pulse of probe light a small fraction of the atoms is lost, while the cloud is simultaneously slightly heated. This makes it possible to study the scattering rate as a function of temperature using only a single sample. It is observed that the scattering rate increases below the critical temperature for BEC by more than a factor of 3 compared to the classical value. This enhancement is in good agreement with the predictions by theoretical work that takes two-body correlation and the Lorentz-Lorenz correction into account. The method is also used to perform calorimetry on the Bose gas and directly measure the heat capacity of the BEC. The second chapter deals with magnetism in ultracold gases. When cooling an ultracold gas containing different spin components below the critical temperature for BEC, stable magnetic domains form. The appearance of these domains and the dynamics of the domain walls are studied. The spin mixture is prepared by performing an RF-sweep on ground state atoms in the presence of a magnetic field. Spin dynamics are induced by applying magnetic gradients. Spin drag, which is the transport coefficient responsible for damping spin currents, was measured in a two-component system. Furthermore a new method for spin resolved phase contrast imaging is presented, which is used to study time evolution in situ non-destructively. The last experiment focuses on spontaneous symmetry breaking. When passing a continuous phase transition, spontaneous symmetry breaking causes the development of domains with an independently chosen order parameter. The domains are separated by boundary defects. In this experiment the spontaneous creation of solitons was observed, which are boundary defects in the phase of the condensate, as well as magnetic domain walls, which are the boundary defects in the magnetization. Through the Kibble-Zurek mechanism it is possible to determine the critical exponents that characterize the phase transition. The critical exponents are predicted to be universal, i.e. do not depend on the microphysics of the system, so the results from our ultracold atoms lab can help answer universal questions for example from cosmology and from the early universe.
We experimentally and theoretically study phase coherence in two-component Bose-Einstein condensates of ^{87}Rb atoms on an atom chip. Using Ramsey interferometry we determine the temporal decay of coherence between the |F=1,m_{F}=-1⟩ and |F=2,m_{F}=+1⟩ hyperfine ground states. We observe that the coherence is limited by random collisional phase shifts due to the stochastic nature of atom loss. The mechanism is confirmed quantitatively by a quantum trajectory method based on a master equation which takes into account collisional interactions, atom number fluctuations, and losses in the system. This decoherence process can be slowed down by reducing the density of the condensate. Our findings are relevant for experiments on quantum metrology and many-particle entanglement with Bose-Einstein condensates and the development of chip-based atomic clocks.