Properties of a Bose–Einstein Condensate

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.

Jean-Louis Basdevant, Jean Dalibard

Renju Rajan, P. Ramesh Babu, Krishnamoorthy Senthilnathan

Bose–Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose–Einstein condensate (BEC) in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose–Einstein condensate. We also elaborate on the theoretical framework for atomic Bose–Einstein condensation, which includes statistical mechanics and the Gross–Pitaevskii equation. As an extension, we discuss Bose–Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck’s law in statistical mechanics. Further, a comparison is made between photon condensate and laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.

Michael J. Steel, Weiping Zhang

Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.

Rafael Navarro