Bose Condensation

John Edward Gough, Pulé, J.V.

In 1968 Gunton and Buckingham pointed out that there is a close relationship between the critical behaviour of the spherical model and that of the ideal Bose gas. In this paper we concentrate on this similarity between the two systems. We show that in the spherical model there is in fact Bose-Einstein condensation into the spin modes with low energy. As in the Bose gas we distinguish between generalised Bose-Einstein condensation and Bose-Einstein condensation. We find that the spherical model in certain cases has two critical temperatures: one temperature T c corresponding to the onset of generalised Bose-Einstein condensation (and of spontaneous magnetisation) and a lower temperature T m at which generalised condensation becomes condensation into the spin mode with the lowest energy

Isaac F. Silvera

Anatolii N Oraevsky

The dynamic analogy between the Bose condensate of photons (laser), Bose condensate of atoms, and Bose condensate of Cooper pairs in a superconductor is discussed. It is pointed out that the coherent state of Bose condensates of different types can appear only due to stimulated transitions.The equations are discussed that combine into a unified dynamic system the order parameter of the Bose condensate and the concentration of atoms beyond the condensate for an ensemble of atoms captured by a trap, as well as the order parameter of Cooper pairs, the concentration of free quasi-particles, and the densities of phonons and photons in a semiconductor.

S. K. Giri

Ultracold atoms in the atomic Bose-Einstein condensate (ABEC) state can form molecular Bose-Einstein condensate (MBEC) through photoassociation.In the atom-molecule Bose-Einstein condensates (BECs), two or more atoms in the ABEC can combine to form a molecule in the MBEC and again a molecule from a MBEC can decompose to atoms in the ABEC.The Bose-stimulated Raman adiabatic passage is an efficient mechanism for conversion of an atomic BEC to a molecular BEC.A three-mode atom-molecule Bose-Einstein condensates system can be prepared through the photoassociative Bose-stimulated Raman adiabatic passage.In our system, three modes are one ABEC, one excited MBEC, and one stable MBEC.The intramodal interactions due to the  (3) nonlinearity is present in all three BEC modes along with ABEC-excited MBEC and excited MBEC-stable MBEC intermodal couplings.The quantum mechanical Hamiltonian of the system is constructed considering all three intraspecies interactions and intermodal couplings among the modes.The Hamiltonian of the system is solved analytically using a special intuitive approach which is more general and gives more accurate result than the well-known short time approximation method.The correctness of the solution is verified through the equal time commutation relation.Staring from a three-mode composite coherent state we compute the time evolution of the field annihilation operators of all three modes in presence of all possible interactions and couplings.Using these solutions, we investigate the quantum entanglement properties of the system for all three two-mode combinations.Entanglement is found for two combinations of modes, where as one combination is always separable.Also, we study the dependence of the entanglement properties of the system with the interaction and coupling constants.

Allan Griffin, David W. Snoke, S. Stringari +1 more