Summary form only given. The atomic hydrogen BEC is of a rather different kind from those prevalent in the now almost ubiquitous alkali-metal vapor condensates. The characteristic features of the hydrogen system are: 1. The condensate fraction is rather low, typically about 5%; 2. The number of atoms in the condensate is nevertheless very large, /spl ap/10/sup 9/, compared to /spl ap/10/sup 6/ for Na condensates and /spl ap/10/sup 5/ for Rb condensates; 3. The hydrogen condensate at MIT is a hot condensate formed with radial and axial trap frequencies; giving a trap aspect ratio of an almost one-dimensional condensate. 4. Because of the rather small scattering length of hydrogen, the condensate density is very much higher than in the alkali-metal condensates, and experimentally is measured spectroscopically using the cold-collision frequency shift for the 1S-2S two-photon transition. 5. The condensate would decay rather rapidly by two body dipolar relaxation processes, but is maintained by being fed from the very large number of noncondensate atoms. The system is thus not in thermodynamic equilibrium.
Summary form only given. The atomic hydrogen BEC is of a rather different kind from those prevalent in the now almost ubiquitous alkali-metal vapor condensates. The characteristic features of the hydrogen system are: 1. The condensate fraction is rather low, typically about 5%; 2. The number of atoms in the condensate is nevertheless very large, /spl ap/10/sup 9/, compared to /spl ap/10/sup 6/ for Na condensates and /spl ap/10/sup 5/ for Rb condensates; 3. The hydrogen condensate at MIT is a hot condensate formed with radial and axial trap frequencies; giving a trap aspect ratio of an almost one-dimensional condensate. 4. Because of the rather small scattering length of hydrogen, the condensate density is very much higher than in the alkali-metal condensates, and experimentally is measured spectroscopically using the cold-collision frequency shift for the 1S-2S two-photon transition. 5. The condensate would decay rather rapidly by two body dipolar relaxation processes, but is maintained by being fed from the very large number of noncondensate atoms. The system is thus not in thermodynamic equilibrium.
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.
We report observation of Bose-Einstein condensation (BEC) of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by two-photon spectroscopy of the 1S- 2S transition. Interactions among the atoms produce a shift of the resonance frequency proportional to density. The condensate is clearly distinguished by its large frequency shift. The peak condensate density is $4.8\ifmmode\pm\else\textpm\fi{}1.1\ifmmode\times\else\texttimes\fi{}{10}^{15}{\mathrm{cm}}^{\ensuremath{-}3}$, corresponding to a condensate population of 109 atoms. The BEC transition occurs at about $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}50\ensuremath{\mu}\mathrm{K}$ and $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\ifmmode\times\else\texttimes\fi{}{10}^{14}{\mathrm{cm}}^{\ensuremath{-}3}$.
The field of Bose-Einstein condensation (BEC) in dilute atomic gases provides a fruitful playground to test well-developed theories of quantum fluids. Research using BECs can address open questions relating to the many-body aspects of two-component quantum liquids, namely the interaction between the hydrodynamic normal and the superfluid component at finite temperatures. After the first realization of BEC some pilot experiments have been carried out, but detailed experiments are missing. This has to be compared to the case of liquid helium II, where many experiments since the 1950s have added to our understanding of novel phenomena in quantum liquids, like collective excitations, first and second sound, and others. One of the drawbacks of liquid helium is that the interactions are so strong that a clear distinction between the two components is difficult and the interpretation of the phenomena remains ambiguous. Most experimental studies of dilute Bose-Einstein condensed gases use clouds, which are in the collisionless regime. The reason for the lack of detailed experiments in BECs to study quantum liquids and in particular the hydrodynamical aspects of it, is the limited number of atoms (typically 1--10 million) in the experiments leaving the thermal atoms virtually collisionless. Efforts to decrease the mean free path by increasing the confinement limits the lifetime of the sample, since the density is limited by three-body decay. Experiments on dilute clouds of cold atoms are generally conducted in highly asymmetric traps. In these elongated, cigar-shaped geometries the mean free path of the atoms can become much shorter than the size of the cloud in the long, axial direction, but at the same time exceeds the size in the other, radial directions. In this so-called hydrodynamic-collisionless regime the system can be considered radially collisionless and axially hydrodynamic. In our setup we have created BECs containing up to 300 million sodium atoms by evaporation of atoms in an axially strongly decompressed trap with an aspect ratio of 1:65. Hot atoms created in three-body collisions are able to leave the sample in this highly asymmetric trap, before they can heat other atoms in an avalanche. The sample is axially hydrodynamic, but due to the large aspect ratio collisionless in the radial direction. Such samples are ideal for the observation of the interaction between the superfluid and normal fluid component of the cloud. In this thesis we describe the setup which is used to reach the hydrodynamic regime and we describe a novel implementation of the well-known phase contrast imaging technique. Next, we study collective excitations in the crossover from the collisionless toward the hydrodynamic regime, we determine the heat conduction in a cold, hydrodynamic thermal cloud and observe the propagation of a thermal wave in the two-fluid regime. Furthermore, we study the friction between the superfluid and normal fluid component of the cloud. In the final chapters of this thesis we study the propagation of second sound, as well as the formation and propagation of shock waves.
Summary form only given. Bose-Einstein condensation (BEC) of trapped atomic vapor has been realized in several atomic species. The static and dynamical properties of BEC crucially depend on the sign of the interatomic interaction. When the interaction is attractive, BEC in a spatially uniform 3D system is unstable to collapse into a denser phase. In a spatially confined system, however, the zero-point energy serves as a kinetic obstacle against collapse, allowing metastable BEC to be formed if the number of BEC atoms is below a certain critical number. Above the critical number of atoms, BEC collapses. The BEC with attractive interactions, therefore, has been restricted to a small number of atoms (/spl sim/1000) and the number has not been controllable.
Atomic hydrogen has been loaded into a 1-K deep magnetic trap through the use of a dilution refrigerator. Evaporative cooling has been used to cool the trapped hydrogen into the submillikelvin temperature regime. These techniques have produced a sample with density of 8 × 1013 cm-3 at a temperature of 100 μK. At this density a transition to a Bose-Einstein condensate is predicted to occur at a temperature of 30 μK. These results have been obtained with a magnetic trap that has been constructed to accommodate upcoming experiments based on laser spectroscopy of the 1S-2S two photon transition in the trapped hydrogen. A frequency doubled narrow linewidth cw dye laser system has been constructed to excite the 1S-2S transition. The excitation will be detected by the observation of electric field-induced Lyman-alpha fluorescence. The optical detection system should yield improved sample density and temperature diagnostic capabilities that will facilitate a closer approach to the quantum degenerate regime. Additionally the cold, confined hydrogen gas offers the possibility of improving the level of resolution of Doppler-free hydrogen 1S-2S laser spectroscopy by several orders of magnitude.
Experimental efforts to produce a Bose Einstein condensed (BEC) gas of spin-polarized atomic hydrogen have been intensely pursued since 1980. Initial efforts studied hydrogen in contact with superfluid helium surfaces. In order to avoid the limiting wall recombination a static magnetic trap was developed which utilizes magnetic barriers to isolate atoms from the van der Wals walls. In this approach traps can be filled to about 10{sup 14} atoms/cm{sup 3} for which the critical temperature is in the region of 20-30 {mu}K. However, approaching BEC conditions, a new instability dominates the behavior. The authors have developed a new type of electromagnetic trap, a microwave (mw) trap in which the trapped atoms are in the ground spin-state so that at low temperature relaxation to a barrier state is strongly suppressed and BEC should be attainable. The shallow mw trap has recently been demonstrated experimentally for the cesium atom. Because the mw trap is so shallow it is necessary to precool the atoms for loading. The authors are constructing a hybrid trap in which the atoms are cooled in a static trap and then transferred to a mw trap where they can be further evaporatively cooled in an effort to achieve BEC.more » This trap should have density limits in the region of 10{sup 16} to 10{sup 17}/cm{sup 3} due to three-body recombination. A second, promising approach is in a 2-D geometry for which in finite sized systems BEC is allowed. Hydrogen atoms are confined to a superfluid helium surface by the absorption potential to form a 2-D gas. Although recombination is an important process on helium surfaces, recently the authors have shown that only a very small fraction of the recombination energy is coupled into the surface. With an appropriate geometry the recombination energy can be removed from the sample region to suppress heating to a negligible level. Furthermore in 2-D a magnetic field can have a maximum so that atoms can be confined to a very small area.« less