The observation of Bose-Einstein condensation (BEC) in dilute atomic gases was the realization of many long-standing goals: (1) to cool neutral atoms into the ground state of the system, thus exerting ultimate control over the motion and position of atoms limited only by Heisenberg's uncertainty relation; (2) to generate a coherent sample of atoms all occupying the same quantum state (this was subsequently used to realize an atom laser, a device which generates coherent matter waves); and (3) to create a quantum fluid with properties quite different from the quantum liquids He-3 and He-4. This provides a test-ground for many-body theories of the dilute Bose gas which were developed many decades ago, but never tested experimentally.
The observation of Bose-Einstein condensation (BEC) in dilute atomic gases was the realization of many long-standing goals: (1) to cool neutral atoms into the ground state of the system, thus exerting ultimate control over the motion and position of atoms limited only by Heisenberg's uncertainty relation; (2) to generate a coherent sample of atoms all occupying the same quantum state (this was subsequently used to realize an atom laser, a device which generates coherent matter waves); and (3) to create a quantum fluid with properties quite different from the quantum liquids He-3 and He-4. This provides a test-ground for many-body theories of the dilute Bose gas which were developed many decades ago, but never tested experimentally.
The experimental realization in 1995 of Bose–Einstein condensation in dilute atomic gases marked the beginning of a very rapid development in the study of quantum gases. The initial experiments were performed on vapours of rubidium, sodium, and lithium. So far, the atoms 1 H, 7 Li, 23 Na, 39 K, 41 K, 52 Cr, 85 Rb, 87 Rb, 133 Cs, 170 Yb, 174 Yb and 4 He * (the helium atom in an excited state) have been demonstrated to undergo Bose–Einstein condensation. In related developments, atomic Fermi gases have been cooled to well below the degeneracy temperature, and a superfluid state with correlated pairs of fermions has been observed. Also molecules consisting of pairs of fermionic atoms such as 6 Li or 40 K have been observed to undergo Bose–Einstein condensation. Atoms have been put into optical lattices, thereby allowing the study of many-body systems that are realizations of models used in condensed matter physics. Although the gases are very dilute, the atoms can be made to interact strongly, thus providing new challenges for the description of strongly correlated many-body systems. In a period of less than ten years the study of dilute quantum gases has changed from an esoteric topic to an integral part of contemporary physics, with strong ties to molecular, atomic, subatomic and condensed matter physics. The dilute quantum gases differ from ordinary gases, liquids and solids in a number of ways, as we shall now illustrate by giving values of physical quantities.
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.
For sufficiently low temperatures, a Bose gas experiences a transition into a Bose-Einstein condensate, characterized by a macroscopic occupation of the ground state of the system. The development of efficient cooling and trapping techniques for neutral atoms led in 1995, to the first observation of BEC in dilute alkali gases in 87Rb [1]. This remarkable achievement has been followed by BEC experiments in various other elements. The BEC has become during the last years, one of the most active and fruitful research areas of modern atomic physics, constituting an interdisciplinary field, which links atomic physics with various other research areas, like quantum optics, condensed-matter physics, and very especially nonlinear 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.
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.