Bose–Einstein condensation in a gas has now been achieved. Atoms are cooled to the point of condensation using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. These techniques are explained, as well as the techniques by which we observe the cold atom samples. Three different signatures of Bose–Einstein condensation are described. A number of properties of the condensate, including collective excitations, distortions of the wave function by interactions, and the fraction of atoms in the condensate versus temperature, have also been measured.
Besides the enormous opportunities offered by spectroscopy and atom interferometry, laser cooling has opened up the possibility of experimentally realizing and manipulating quantum degenerate gases: Bose–Einstein condensates and degenerate Fermionic systems. This chapter starts with an illustration of key experimental techniques, such as magnetic trapping, evaporative cooling, and Feshbach resonances. It then turns to the physics of atomic Bose–Einstein condensates, discussing their superfluid behaviour, their coherence properties, and their application to precise measurements. It also describes the experimental investigation of ultracold Fermi gases and fermionic superfluidity, as well as ongoing research into ultracold polar molecules.
This chapter presents an overview of the specific experimental tools developed in the field of ultra-cold gases to achieve and probe superfluidity in vapours of bosonic atoms. First, it describes the main cooling techniques: the magneto-optical trap, which brings an atomic vapour from room temperature down to the sub-mK range, and the evaporative cooling scheme, which bridges the gap to the superfluid regime. It then proceeds to the study of interaction effects. It shows that these play a central role in the understanding of both static and dynamic properties of trapped Bose–Einstein condensates (BECs), despite the dilute character of these gases. As a consequence, gaseous BECs and superfluid helium obey the same laws of hydrodynamics and exhibit similar dynamical properties, although their densities differ by several orders of magnitude. The third section is devoted to the coherence properties of gaseous BECs. It shows that, by contrast with liquid helium, specific features of ultra-cold gases make them suitable for a direct probing of the quantum coherence associated with Bose–Einstein condensation. Finally, the possibility of tailoring trapping potentials and realizing low-dimensional systems is discussed, where one or two directions of motion are frozen.
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.
Bose-Einstein condensation (BEC) in ultra-cold magnetically-trapped
sp7Li vapor was experimentally observed and quantitative measurements of condensate number were made. Compared to other BEC experiments, lithium is unique due to its negative s-wave scattering length, corresponding to effectively attractive interactions. Due to this attraction, condensates are expected to undergo mechanical collapse if the condensate number exceeds a critical value. In this experiment, an upper limit of about 1000 condensate atoms is found, in agreement with theoretical predictions.\nIn the experiment, the atoms are confined by a set of six permanent magnets in the Ioffe configuration. Optical forces are used to slow and guide atoms from a thermal atomic beam into the magnetic trap. With about
10sp8 atoms loaded into the trap, the vapor is laser-cooled to near 200
muK and then evaporatively cooled by application of a resonantly-tuned microwave field. Evaporative cooling produces a million-fold increase in phase-space density, reaching quantum-degenerate conditions with about 10
sp5 atoms at temperatures near 300
muK. After cooling, the trapped atom distribution is observed by in situ imaging via an optical probe. Calculated atom distributions are fit to the image data.\nIn initial data, the imaging resolution was insufficient to see the spatially-narrow condensate peak, but as phase-space densities approached the expected phase transition, the images suddenly became distorted. Initial fits to the data suggested as many as 10
sp5 condensate atoms, in strong disagreement with theoretical predictions. An imaging model, accounting for imperfections in the imaging optics, shows that the sudden appearance of the distortions is a consequence of BEC, and that these distortions led to the initial over-estimation of cloud phase-space density and condensate number.\nImproved imaging was obtained using large probe detunings, a Phase-Contrast Polarization Imaging (PCPI) technique, and near-diffraction-limited imaging optics. The PCPI method exploits the birefringence of the trapped atoms. From the resulting images, quantitative estimates of condensate number are obtained and compared with theory.
Superfluidity and Bose-Einstein condensation (BEC) in ultracold atomic gases represent macroscopic quantum phenomena arising from collective particle behavior at near-zero temperatures. Experimental realizations of BEC in alkali gases have enabled the observation of quantized vortices, matter-wave interference, and nonclassical excitations. This article reviews theoretical frameworks including Gross-Pitaevskii and Bogoliubov models, experimental techniques such as evaporative cooling and optical trapping, and computational approaches for simulating condensate dynamics. Two graphical analyses illustrate the condensate density profile and vortex lattice formation. Understanding these phenomena has implications for quantum simulation, atom interferometry, and exploration of quantum hydrodynamics.