We classify solvable Lie groups with a free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six (here f(m, p) ...

A Bose-Einstein condensate can be well described by an order parameter called condensate wavefunction. If Bose-Einstein condensation occurs in a superposed single particle state, the condensate wavefunction is correspondingly superposed. Likewise, if two coupled distinguishable or non-overlapping Bose systems condense in an entangled single particle pair state, the condensate wavefunction is co...

The remarkable recent experiments on ensembles of magnetically trapped ultracold alkali atoms have demonstrated the transition to a highly ordered phase, that has been attributed to the process of quantum-mechanical condensation, predicted long ago (1924) by Bose and Einstein. After having presented our argument against the above attribution, we show that the known phenomenology, including a di...

We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency, ultraslow, and stored light. They have long intrinsic lifetimes and in a stationary setup, a 3D quadr...

The study of the so called “genuine” Bose-Einstein correlations (BEC) of three identical charged pions requires the subtraction of the 2nd order BEC of the pion pairs. The OPAL subtraction method used in the BEC study of the π±π±π± system, which utilised mixed charged pions triplets of the data themselves, is investigated in detail. The derivation of the subtraction formula is explained.

In this paper, we analyze phase separation of multi-component Bose-Einstein Condensates (BECs) in the presence of a strong optical lattice. This paper is in threefold. We first prove that when the inter-component scattering lengths go to infinity, phase separation of a multi-component BEC occurs. Furthermore, particles repel each other and form segregated nodal domains. Secondly, we show that t...

We propose a new method of creating solitons in elongated Bose-Einstein Condensates (BECs) by sweeping three laser beams through the BEC. If one of the beams is in the first order (TEM10) Hermite-Gaussian mode, its amplitude has a transversal π phase slip which can be transferred to the atoms creating a soliton. Using this method it is possible to circumvent the restriction set by the diffracti...

The purpose of this note is to introduce a new method for proving the existence of Sasakian-Einstein metrics on certain simply connected odd dimensional manifolds. We then apply this method to prove the existence of new Sasakian-Einstein metrics on S×S and on (S×S)#(S×S). These give the first known examples of non-regular Sasakian-Einstein 5manifolds. Our method involves describing the Sasakian...

Condensation is observed in a gas of indirect excitons confined in an electrostatic trap. Imaging and interferometric measurements detect that excitons condense at the trap bottom and exciton spontaneous coherence emerges with lowering temperature. Below a temperature of about 1 K, the direct signature of Bose−Einstein condensation, the extension of coherence over the entire cloud, is observed.

Condensation is observed in a gas of indirect excitons confined in an electrostatic trap. Imaging and interferometric measurements detect that excitons condense at the trap bottom and exciton spontaneous coherence emerges with lowering temperature. Below a temperature of about 1 K, the direct signature of Bose-Einstein condensation, the extension of coherence over the entire cloud, is observed.