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.
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.
The experimental achievement of Bose-Einstein condensation (BEC) in 1995 has aroused a large interest among the community of the physics of ultracold atomic gases.Recently new topics have attracted the attention of this very active field of research , in particular we could mention low dimensional systems, atoms in lattices, and classical and Fermi gases.As for the case of BEC, the study of the dynamical aspects of these systems provides a very valuable information.In particular time-of-flight experiments and measurements of collective excitations have been successfully realized providing a clear signature of the BEC and the regime of interaction.Following this line, in this thesis, we want to study some dynamical aspects of these new systems nowadays avaliable due to the remarkable development of the experimental techniques.In the first chapter we present the state of the art of the field, providing the historical path and the motivation for the work developed in the next chapters.In the second chapter, we discuss some general concepts in order to introduce the formalism and notation employed throughout the thesis, as well as those topics analyzed in more detail in the further chapters.In chapter three, we explain some general techniques which are useful to deal with one dimensional systems, and analyze in detail the expansion of a one dimensional Bose gas in a guide, which differs significantly from the expansion of a BEC.In particular we are able to predict the range of parameters for which the self-similarity of the expansion is violated.Chapter four is devoted to the physics of atoms in a periodic potential.We start, as in the previous chapter, introducing some general concepts and techniques employed further.First we discuss the physics of the superfluid case in a trap, showing that under certain conditions a three dimensional gas exhibits one dimensional properties.viii In particular, static properties and the lowest collective excitations differ significantly from those of a BEC.We extend the analysis to the insulating phase showing that correlation properties depend on the on-site one-dimensional regime.These correlations can be measured in current time of flight experiments.In the fifth chapter we analyze the dynamics of classical and Fermi gases.We show in detail how expansion and collective excitations depend on the interaction regime and the trap anisotropy.In particular, the expansion can be used to distinguish between a normal Fermi gas and a superfluid one.We summarize in the last chapter the new results presented in this thesis.
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.
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.
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.
Bose–Einstein condensation is a phenomenon, first proved by Einstein, in which a gas of bosons condenses into the lowest quantum state below a certain critical temperature. It occurs due to the symmetry, under particle exchange, of the boson wave function. The chapter discusses temperature, the Kelvin scale, the concept of absolute zero, and how laser cooling can reach ultralow temperatures. The property of bosons in which they often prefer to be in the same state is seen to apply to lasers, superfluid liquid helium, and to dilute nearly ideal gases. The latter are trapped in magnetic or optical potential wells where the condensation can be observed directly. These large condensate matter waves show quantum interference in a variety of possible experiments.
Research on degenerate quantum gases of dilute atomic gases has become a well established field in modern physics and revealed many astonishing phenomena. The first experiments on Bose and Fermi gases at low temperatures aimed to prove the predictions of quantum mechanics on a macroscopic scale. Since then we make use of Bose and Fermi gases and mixtures of any combination to model other many body systems. A property of Bose Einstein condensates is superfluidity which we want to investigate further in toroidal potentials with a new apparatus which can produce an all-optical BEC. This means trapping thermal atoms in an optical dipole trap and cooling the sample by evaporation into the quantum degenerate regime. This new technique was first successfully demonstrated by M.D. Barrett et al. in 2001 and promises to be faster and simpler than the well established and common way of evaporation in magnetic traps. A new apparatus was built by the author and we report on the experimental details of the trapping of 87Rb atoms from a hot vapour and cooling them in a magneto-optical trap, and further evaporation to quantum degeneracy in a crossed optical dipole trap operating at a wavelength of l = 1064nm, with accurate control of the power in both beams via a feedback loop. The evaporation of neutral atoms of 87Rb in far red detuned optical dipole traps using linearly polarised laser light is spin independent, and mixed spinor condensates of the F=1 manifold can be formed. As an empirical technique we found by applying a magnetic gradient field during the final evaporation that we can selectively populate mF spin states or prepare mixtures. This intriguing mechanism was found earlier as well by M. S. Chang, but is yet not fully understood and subject of our future research. We can now routinely prepare an almost pure condensate containing up to 7000 atoms in the condensed phase purely in the mF = 0 spin state. This thesis contains the theoretical framework of Bose-Einstein condensation with in mean-field theory, the concepts of cooling of atoms in magneto-optical traps, the trapping and evaporation in optical dipole traps and the experimental realisation. In the future this experiment will be extended by a fast scanning dipole trap to apply arbitrary time averaged potentials of more complex geometries, such as toroidal traps to study the effects of superfluidity in a periodic potential. The production of toroidal traps and cold atoms in such a trap are outlined in this thesis.