In 1924/25, Satyendranath Bose and Albert Einstein predicted that particles of integer spin (today called bosons) should undergo a statistical phase transition when cooled to temperatures very close to absolute zero (Bose, 1924; Einstein, 1925). This phenomenon, nowadays called Bose-Einstein condensation, has been experimentally observed seventy years later using (nanokelvin temperatures) of bosonic neutral atoms (Anderson et al., 1995; Bradley et al., 1995; Davis et al., 1995c). This spectacular experimental achievement was awarded the Nobel price in 1995 and has triggered a new research direction ultracold gases with more than 200 groups worldwide today. 1 Bose-Einstein condensates (BEC) of atomic represent a fascinating exotic state of matter with properties entirely determined by the laws of mechanics. Although they consisting of several thousands up to millions of atoms, the state can in most cases be described by a single collective wave function with a common phase. This wave function usually has a spatial extent ranging between 1-100 microns, allowing us to observe mechanics essentially by eye using basic magnification optics. The Bose-Einstein condensate can be described as a coherent matter wave in close analogy to the optical field emitted by (or inside) a laser. This analogy has brought about the field of quantum-atom-optics which aims to implement standard elements and experiments known from laser optics using matter waves. As heavy rest mass particles, such as atoms, are very sensitive to gravity or acceleration/rotations, matter-wave interferometers promise orders of magnitude in sensitivity gain compared to their photonic counterparts (Berman, 1996). Over the last decade, experimental tools for the creation and manipulation of matter have reached an impressive degree of sophistication. This allows the construction of tailored Hamiltonians for the system and the quantum simulation of more general physical situations, not connected to atomic physics alone. Optical lattice potentials allow to mimic solid state physics with a high degree of control over essentially all experimental parameters. Particle interactions can be tuned via Feshbach resonances, allowing the study of superconductivity, superfluidity and the formation of
In 1924/25, Satyendranath Bose and Albert Einstein predicted that particles of integer spin (today called bosons) should undergo a statistical phase transition when cooled to temperatures very close to absolute zero (Bose, 1924; Einstein, 1925). This phenomenon, nowadays called Bose-Einstein condensation, has been experimentally observed seventy years later using (nanokelvin temperatures) of bosonic neutral atoms (Anderson et al., 1995; Bradley et al., 1995; Davis et al., 1995c). This spectacular experimental achievement was awarded the Nobel price in 1995 and has triggered a new research direction ultracold gases with more than 200 groups worldwide today. 1 Bose-Einstein condensates (BEC) of atomic represent a fascinating exotic state of matter with properties entirely determined by the laws of mechanics. Although they consisting of several thousands up to millions of atoms, the state can in most cases be described by a single collective wave function with a common phase. This wave function usually has a spatial extent ranging between 1-100 microns, allowing us to observe mechanics essentially by eye using basic magnification optics. The Bose-Einstein condensate can be described as a coherent matter wave in close analogy to the optical field emitted by (or inside) a laser. This analogy has brought about the field of quantum-atom-optics which aims to implement standard elements and experiments known from laser optics using matter waves. As heavy rest mass particles, such as atoms, are very sensitive to gravity or acceleration/rotations, matter-wave interferometers promise orders of magnitude in sensitivity gain compared to their photonic counterparts (Berman, 1996). Over the last decade, experimental tools for the creation and manipulation of matter have reached an impressive degree of sophistication. This allows the construction of tailored Hamiltonians for the system and the quantum simulation of more general physical situations, not connected to atomic physics alone. Optical lattice potentials allow to mimic solid state physics with a high degree of control over essentially all experimental parameters. Particle interactions can be tuned via Feshbach resonances, allowing the study of superconductivity, superfluidity and the formation of
Bose-Einstein condensation (BEC), first predicted by Einstein in 1925, has been realized experimentally in 1995 in alkali gases. The award of the 2001 Nobel Prize in Physics to E. Cornell, C. Wieman, and W. Ketterle acknowledged the importance of the achievement. In this new state of matter, which is very dilute and at very low temperature, a macroscopic fraction of the atoms occupy the same quantum level, and behave as a coherent matter wave similar to the coherent light wave produced by a laser. In the dilute limit, the condensate is well described by a mean-field theory and a macroscopic wave function. The properties of these gaseous quantum fluids have been the focus of international interest in physics, both experimentally and theoretically, and many applications are envisioned. An important issue is the relationship between BEC and superfluidity, in particular through the existence of vortices. The focus of this book is the mathematical properties of vortices, observed in very recent experiments on rotating condensates These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
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.
The realization of Bose-Einstein Condensation (BEC) in dilute gases of ultracold atoms has revolutionized quantum physics by offering an unprecedented platform to study quantum phenomena on macroscopic scales. Ultracold atomic systems, cooled to temperatures near absolute zero, exhibit collective behaviors governed by quantum statistics, coherence, and interactions. This article discusses the theoretical and experimental frameworks underpinning the formation of BECs, focusing on the trapping, cooling, and coherence properties of ultracold bosonic gases. Further, we delve into the role of quantum phase transitions, atom-atom interactions, and external field manipulation in controlling condensate dynamics. The implications of BECs extend into precision measurements, quantum simulation, and quantum computing, positioning them as a cornerstone in modern atomic and condensed matter physics.
About seven decades ago Satyendra Nath Bose and Albert Einstein predicted that a gas of noninteracting integer-spin particles would condense into a macroscopic quantum state when cooled below a critical temperature. Of course Bose–Einstein condensation (BEC) has long since been seen in superfluid He4 and superconductors, but the condensing systems in these examples are far from being noninteracting gases; relatively strong interactions between the condensing particles greatly complicate the theoretical analysis and the experimental behavior. For more than 15 years groups have been cooling and compressing clouds of atoms on a quest to produce and observe a Bose–Einstein condensate in a nearideal gas. They pushed their devices to the limit, seeking to traverse 15 orders of magnitude of phase-space density, and as each technique proved insufficient they developed ingenious variations to create ever colder and denser states.
When the atoms in a gas are cooled to extremely low temperatures, their quantum-mechanical nature starts to dominate the properties of the whole gas. Under the appropriate conditions, the atoms will 'condense' into a single quantum state of the system-a phenomenon known as Bose-Einstein condensation (BEC). The resulting 'condensate' behaves as a single, observable quantum-mechanical object. During the last decade, this new state of matter has displayed many remarkable properties. In this paper, we review some of the most recent experimental developments in the BEC field, highlighting the role of atomic interactions and the high degree of control with which condensates may be manipulated.