Summary form only given. Following the first observations of Bose-Einstein condensation (BEC) in dilute atomic gases, there has been considerable interest in multiple condensates as a system of interpenetrating quantum fluids. Most recently in our time averaged orbiting potential (TOP) trap, we have created coherent superpositions of condensates in the |F=1, m/sub F/=-1> and |F=2, m/sub F/=1> hyperfine ground states of Rubidium-87. A coupling field connects the states of this two level system. Following evaporative cooling to BEC in the |1,-1> state, a short coupling pulse allows us to transfer an arbitrary proportion of the atoms into the upper |2,1> state. In the first experiments with two component condensates, we have determined the ratio of the intraspecies scattering lengths for the two hyperfine states mentioned above; we have transferred half of the atoms to the upper |2,1> state to investigate the dynamics of the two components separation; and we have found that, in the regions where they overlap, the two condensates retain a well defined phase even after the damping of their relative center of mass motion. To further our studies of double condensates, we have implemented a new, state-sensitive form of nondestructive imaging, a technique first pioneered by Zernike in the field of microscopy, and more recently adapted to the imaging of condensates by the group at MIT. We exploit the state sensitivity of the technique to distinguish the two spin states inside the trap (or, more accurately, to measure their relative density across the cloud).
Summary form only given. Following the first observations of Bose-Einstein condensation (BEC) in dilute atomic gases, there has been considerable interest in multiple condensates as a system of interpenetrating quantum fluids. Most recently in our time averaged orbiting potential (TOP) trap, we have created coherent superpositions of condensates in the |F=1, m/sub F/=-1> and |F=2, m/sub F/=1> hyperfine ground states of Rubidium-87. A coupling field connects the states of this two level system. Following evaporative cooling to BEC in the |1,-1> state, a short coupling pulse allows us to transfer an arbitrary proportion of the atoms into the upper |2,1> state. In the first experiments with two component condensates, we have determined the ratio of the intraspecies scattering lengths for the two hyperfine states mentioned above; we have transferred half of the atoms to the upper |2,1> state to investigate the dynamics of the two components separation; and we have found that, in the regions where they overlap, the two condensates retain a well defined phase even after the damping of their relative center of mass motion. To further our studies of double condensates, we have implemented a new, state-sensitive form of nondestructive imaging, a technique first pioneered by Zernike in the field of microscopy, and more recently adapted to the imaging of condensates by the group at MIT. We exploit the state sensitivity of the technique to distinguish the two spin states inside the trap (or, more accurately, to measure their relative density across the cloud).
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.
Background 1 1.22This thesis 2 Chapterr 2 Theoretical background 5 2.11 Rubidium 5 2.22 Magnetic trapping 5 2.33 Bose-Einstein condensation 8 2.44 BEC formation and phase coherence 2.55 Evaporative cooling 2.5.11Evaporative cooling Lensing Chapterr 4 Broad-area diode laser system 4.11 Abstract 4.22 Introduction 4.33 Experimental setup 4.44 Characteristics 4.55 MOT application 4.66 Summary Chapterr 5 Hydrodynamic properties of dense atomic clouds Vlll l 5.11 Introduction 5.22 Density and temperature analysis 5.33 Anisotropic expansion of hydrodynamic clouds 5.44 Frequency shifts and damping of shape oscillations Chapterr 6 Condensation into non-equilibrium states and focusing of a condensate 6.11 Introduction 6.22 Preparation of degenerate samples out of equilibrium 6.33 Kinetics of the condensate growth 6.44 Formation of a non-equilibrium BEC 6.4.11Local critical temperature 6.4.22 Truncation and local temperature 6.55 Oscillation modes 6.66 Non-equilibrium phase fluctuations 6.77 Focusing of a condensate 6.7.11Focusing principle 6.7.22 Focal broadening 6.7.33 Applications of BEC focusing 6.88 High condensate fractions in non-equilibrium states Bibliographyy Summaryy Samenvattingg AcknowledgementssMostt of the theoretical groundwork on the interacting quantum gases has been developedd in the 50's and the 60's in the context of superfluidity of 4 He.However, a detailedd comparison between theory and experiment is extremely difficult in the case of liquidd helium because its density is rather high and can be varied only within a narrow range..In the 70's the observation of BEC in dilute atomic gases under equilibrium conditionss was known to be impossible.Therefore, the efforts shifted towards investigationss of metastable systems.Thee first attempts to reach BEC were done in spin-polarised atomic hydrogen.Foundationss for many techniques and methods were laid in the course of that work.Hydrogenn quantum gas was first stabilised in a cryogenic environment by Silvera and Walravenn [93] and by Cline et al. [23].Magnetic trapping was first demonstrated in sodium [79]] and in hydrogen by Hess et al. [50] and van Roijen et al. [87].Another critically importantt technique, evaporative cooling, was first experimentally demonstrated in hydrogenn [51] and further developed in [74,97, 105].Bose-Einsteinn condensation in alkali systems was achieved in magnetic traps throughh the combination of optical cooling methods with the evaporative cooling technique.iss obtained by observation of the anisotropic character of the expansion.Finally, we measuree frequency shifts and damping of shape oscillations.Inn the final part of the Thesis, Chapter 6, we describe the results produced in the experimentss on formation of condensates far from equilibrium.We compare our work with previouss experiments on condensate formation and describe how the process of formation iss triggered in our system.A brief section deals with the growth of the condensate fraction.Further,, we show how the concepts of local sample temperature and the critical temperature arisee in elongated clouds with high elastic collision rates.We present a simple model, whichh illustrates how the non-equilibrium character of the condensates leads to the quadrupolee oscillations.We also discuss non-equilibrium phase fluctuations, which manifestt themselves in the form of stripes in the time-of-flight absorption images.Condensatee focusing is introduced as a novel method for investigation of Bose-Einstein condensates..The focusing of a condensate in free flight arises from axial contraction of the expandingg cloud when the gas is released from the trap during the inward phase of a shape oscillation.. Possible applications of BEC focusing are discussed, with an estimate of the coherencee length given as an example.The last part of the chapter covers condensation into non-equilibriumm states with high condensate fractions.The situations of large and small condensatee fractions are compared.
This thesis presents theoretical principles on laser cooling and trapping as well as magnetic trapping and evaporative cooling, methods necessary for Bose-Einstein condensation.It presents the construction of a very dependable BEC machine.We demonstrate a novel class of trapping potentials, time-averaged adiabatic potentials (TAAP) which allows the generation of a large variety of traps and waveguides for ultracold atoms.The ring-geometry is of particular interest for guided matter-wave interferometry as it provides a perfectly smooth waveguide of controllable diameter, and thus a tunable sensitivity of the interferometer.In addition we report the experimental realization of double-well traps based on TAAP traps.Quantum degenerate Fermi gases and Bose-Einstein condensates give access to a vast new class of quantum states.The resulting multi-particle correlations places extreme demands on the detection schemes.Here we introduce diffractive darkground imaging as a novel ultra-sensitive imaging technique.We detect clouds with less than 30 atoms with near atom shot-noise limited signal to noise ratio.This presents an improvement of about one order of magnitude when compared to our standard absorption imaging.We also examine the optimal conditions for absorption imaging including saturation and fluorescence contributions.
Summary form only given.We have established an experimental and theoretical program focused on understanding photon atom interactions in condensates with the aim of probing the properties of condensates as well as testing our models of the interactions themselves. With a combination of laser and evaporative cooling, we are routinely creating million atom Bose-Einstein condensates of sodium atoms in the newly designed 4D magnet. Our experimental setup incorporates a candlestick atomic beam source, which provides for recirculation of uncollimated sodium atoms, The laser cooling step involves a zero-crossing Zeeman slower, magneto-optic trap, and polarization gradient cooling. The laser-cooled atom cloud is loaded into the 4D magnetic trap and adiabatically compressed to high density and an evaporative cooling process is initiated. Using a RF magnetic resonance technique, hot atoms are ejected through magnetic spin flips. After formation of the condensate in the tightly confining trap, we manipulate the condensate by adiabatically changing the trapping potential and through interaction with photons. We have developed a technique for probing the condensates directly inside the trap using near-resonant absorption imaging. This imaging technique gives high sensitivity to details of the condensate wavefunction and to its surface structure. Images of pure condensates are compared to calculations of the condensate wavefunction based on a Hartree mean field description of the two-body interaction between condensate atoms.
Optical trapping as a viable means of exploring the physics of ultracold dilute atomic gases has revealed a new spectrum of physical phenomena. In particular, macroscopic and sudden occupation of the ground state below a critical temperature—-a phenomenon known as Bose-Einstein condensation—-has become an even richer system for the study of quantum mechanics, ultracold collisions, and many-body physics in general. Optical trapping liberates the spin degree of the BEC, making the order parameter vectorial (‘spinor BEC’), as opposed to the scalar order of traditional magnetically trapped condensates. The work described within is divided into two main efforts. The first encompasses the all-optical creation of a Bose-Einstein condensate in rubidium vapor. An all-optical path to spinor BEC (as opposed to transfer to an optical trap from a magnetic-trap condensate) was desired both for the simplicity of the experimental setup and also for the potential gains in speed of creation; evaporative cooling, the only known path to dilute-gas condensation, works only as efficiently as the rate of elastic collisions in the gas, a rate that starts out much higher in optical traps. The first all-optical BEC was formed elsewhere in 2001; the years following saw many groups worldwide seeking to create their own version. Our own all-optical spinor BEC, made with a single-beam dipole trap formed by a focused CO₂ laser, is described here, with particular attention paid to trap loading, measurement of trap parameters, and the use of a novel 780 nm high-power laser system. The second part describes initial experiments performed with the nascent condensate. The spinor properties of the condensate are documented, and a measurement is made of the density-dependent rate of spin mixing in the condensate. In addition, we demonstrate a novel dual-beam atom laser formed by outcoupling oppositely polarized components of the condensate, whose populations have been coherently evolved through spin dynamics. We drive coherent spin-mixing evolution through adiabatic compression of the initially weak trap. Such dual beams, nominally number-correlated through the angular momentum-conserving collision m=0 + m=0 ⇌ m=+1 + m=-1 have been proposed as tools to explore entanglement and squeezing in Bose-Einstein condensates.
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.