Since the discovery of superfluidity in 4He and Landau's phenomenological theory, the relationship between Bose condensation and superfluidity has been intensely debated. 4He is known by now to be both superfluid and condensed at low temperature, and more generally, in dimension D≥2, all superfluid bosonic models realized in experiments are condensed in their ground state, the most recent example being provided by ultracold bosonic atoms trapped in an optical lattice. In this Letter, it is shown that a 2D gas of bosons which is not condensed at T=0 can be achieved by populating a layer through a frustrated proximity effect from a superfluid reservoir. This condensate-free bosonic fluid is further shown to be a superfluid with incommensurate correlations.
Since the discovery of superfluidity in 4He and Landau's phenomenological theory, the relationship between Bose condensation and superfluidity has been intensely debated. 4He is known by now to be both superfluid and condensed at low temperature, and more generally, in dimension D≥2, all superfluid bosonic models realized in experiments are condensed in their ground state, the most recent example being provided by ultracold bosonic atoms trapped in an optical lattice. In this Letter, it is shown that a 2D gas of bosons which is not condensed at T=0 can be achieved by populating a layer through a frustrated proximity effect from a superfluid reservoir. This condensate-free bosonic fluid is further shown to be a superfluid with incommensurate correlations.
Motivated by recent experiments on alkali gases in atom traps, a largely pedagogical account is given of the implications of the existence of a single-particle Bose-Einstein condensate for the phenomenon of superfluidity. The first conclusion is that, for alkalis in traps at the lowest temperatures, Bose-Einstein condensation coexists with superfluidity. Both experimental evidence and basic microscopic theory are reviewed in this context, with superfluidity in finite systems, quantized vortices and the threshold for breakdown of superfluidity all being referred to. The contrast between liquid 4He below the λ point and the alkali atom gases is then emphasized. Both exhibit superfluidity, but the manifestations of a Bose-Einstein condensate are quite different. For the atomic vapours, near to 100% of the atoms are condensed at the lowest temperatures, whereas from (i) neutron scattering and (ii) computer simulations in liquid 4He present evidence is that 7% is the condensate fraction. This leads finally into a brief discussion of superfluidity without a condensate, with specific reference to the two-dimensional Bose Coulomb gas. The main conclusion is that Bose-Einstein condensation and superfluidity are distinct consequences of deeper topological properties of the many-body wavefunction.
In 1995 two different research groups observed for the first time the Bose-Einstein condensation (BEC) in ultracold gases. When the confining magnetic trap was turned off the gas was left free to expand, and the velocity of the particles showed a clear peak: most of the particles were occupying the same single particle state, the one of lowest energy. The Bose-Einstein condensation had been predicted in 1925 by Einstein, written by inspiration of a work on the statistic of the photons by Bose (1924). In this work Bose described the behavior of an ensemble of photons, treating them as massless particles, with no number conservation associated. Einstein extended this approach to particles with a mass and with fixed number, creating what is now called the Bose-Einstein distribution. The particles that follow such a description are called ``bosons'', as opposed to the ``fermions'' of the Fermi-Dirac statistics. Einstein predicted that in a gas of bosons - under a critical temperature - a finite fraction of the total number of particles would have been in the ground state, and act as a single entity. This amusing theoretical discovery found its utility a few years later. In the late thirties, new techniques allowed to cool Helium-4 at few Kelvins above the absolute zero. The properties of the resulting liquid were a puzzlement to the scientific community: among others, it could flow without experiencing friction. The liquid was called a ``superfluid''. A first explanation was given by London in 1938, which linked the superfluid behavior to the presence of a BEC among the bosonic Helium particles. The fermions cannot condense by themselves. On the other hand, they can form bound pairs and act as bosons, as it happens in a metal at low temperature. Using this approach, in 1957 Bardeen, Cooper and Schrieffer created a successful model of superconductivity by describing a superconductor as a superfluid in a charged system. During the course of these years we explored the superfluid properties of Bosons and Fermions in different settings. The original contributions of the thesis are described starting from the third chapter, where we speak about the generation and stability of solitons in a periodic optical lattices, both fixed or in motion. In the fourth chapter we study the generation of giant vortices in cold fermions, by using a generalized hydrodynamical approach. In chapter 5 we study the effect of a quasiperiodic lattice and the glassy phase it produces on a gas of bosons. Finally, we study the interaction of normal matter and superfluids with gravitational waves. While this interaction is seen to be extremely small, we believe that the resulting formalism is interesting by itself.
We present a brief overview of crucial historical stages in creation of superfluidity theory and of the current state of the microscopic theory of superfluid 4He. We pay special attention to the role of Bose-Einstein condensates (BECs) in understanding of physical mechanisms of superfluidity and identification of quantum mechanical structure of 4He superfluid component below λ-point, in particular—the possibility that at least two types of condensates may appear and coexist simultaneously in superfluid 4He. In this context we discuss the properties of the binary mixtures of BECs and types of excitations, which may appear due to intercomponent interaction in such binary mixtures of condensates. We also discuss current status of investigations of persistent currents in toroidal optical traps and present an outlook of our recent findings on this subject.
Superfluidity has become a topic of active interest in the field of atom trap Bose-Einstein condensates (BECs). We motivate this line of research by placing the BEC developments against the general backdrop of the theory of superfluidity and by highlighting the advantages offered by the atom trap technology. We review the standard description of the BEC dynamics, as well as basic concepts of superfluidity and we present theoretical arguments for expecting the BECs to exhibit superfluid behaviour. In atom traps, as in condensed and nuclear matter, superfluidity can manifest itself in a manifold of guises. Moreover, some of its manifestations can even be undesirable, as we illustrate by the poignant example of sympathetic cooling with condensates. We also review recent experimental evidence for superfluid BEC behaviour and we suggest further experiments to probe superfluidity in atom traps. The low densities of the BECs allow optical imaging and imply that the relevant physics occurs on time and length scales that are much slower and larger than in the traditional 4He superfluid. Consequently, BEC experiments can study known superfluid phenomena and structures in a different and, perhaps, more detailed manner. In addition, the flexibility offered by existing techniques in atomic, molecular and optical physics is unprecedented in the field of low-temperature physics and suggests the prospect of creating superfluids of fundamentally novel structures. Finally, it is conceivable that new applications of superfluidity may arise from these studies.
We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground-state energy, quantum depletion, and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-two-dimensional (2D) regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground-state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density nn and quantum depletion nd both exhibit a characteristic 1/ln(1/n2Da2D2) dependence. Their ratio nn/nd increases to 2 compared to the familiar 4/3 in lattice-free three-dimensional (3D) geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. The conditions for possible experimental realization of our scenario are also proposed.
After a brief introduction to the static Gross–Pitaevskii (GP) differential equation for the ground state of a Bose–Einstein condensed gas and an example of its use in describing a vortex array in a trapped condensate, a recent generalization is reviewed. By starting from the Bogoliubov–de Gennes equations for superfluid fermions, an integral equation results. This is shown to contain the static GP equation as a limiting case, by means of a low-order gradient expansion of the order parameter. The time-dependent GP approximation is then presented and illustrated by a numerical example concerning drop emission under gravity from a gaseous condensate in an optical lattice. Further selected topics of present interest relating more generally to the dynamics of trapped superfluid gases concern the effects of temperature on collective excitations in a Bose gas and the fingerprints that these excitations in a gas of paired fermions contain of the crossover from a Bardeen–Cooper–Schrieffer correlated assembly to a Bose–Einstein condensate of composite bosons. Finally, some directions are pointed in which interaction of first-principles theory with experiment should prove fruitful.