Quantum Signature of Analog Hawking Radiation in Momentum Space.

We consider a sonic analog of a black hole realized in the one-dimensional flow of a Bose-Einstein condensate. Our theoretical analysis demonstrates that one- and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) of the occurrence of a sonic horizon, (ii) of the associated acoustic Hawking radiation, and (iii) of the quantum nature of the Hawking process. The signature of the quantum behavior persists even at temperatures larger than the chemical potential.

Spontaneous four-wave mixing of de Broglie waves: beyond optics.

We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.

Statics and dynamics of Bose-Einstein condensates in double square well potentials.

We treat the behavior of Bose-Einstein condensates in double square well potentials of both equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schrödinger equation are known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson junction model. When the confining potential is in the form of two wells of different depth, interesting phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.

Quantum multimode model of elastic scattering from Bose-Einstein condensates.

Mean field approximation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study a semianalytic model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of incoherent scattering processes. Within the model we can treat processes of the elastic collision of atoms into the initially empty modes, and observe how, with growing occupation, the bosonic enhancement is slowly kicking in. A condition for the bosonic enhancement effect is found in terms of relevant parameters. Scattered atoms form a squeezed state. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms.