טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentVeksler Hagar
SubjectSimple Models for Interacting Bosons
DepartmentDepartment of Physics
Supervisor Professor Emeritus Shmuel Fishman (Deceased)
Full Thesis textFull thesis text - English Version


Abstract

While describing a gas of interacting bosons, it is very common to use approximations. In particular, one usually assumes that the range of interactions is negligible and therefore interaction between atom pairs can be written effectively as a δ -function. In modern experiments, the strength and range of interactions are controlled and situations where interactions range is not negligible (compared to the scattering length or to the wavelength of light) are accessible. This motivated us to introduce simple models which contain repulsive and attractive terms (inspired by the Van-der-Waals potential) and to take the range of interactions into account. Replacing the standard δ -function interaction by these model potentials enables to study the influence of interaction range on the spectrum of a bosonic gas. In this thesis, we calculate analytically the effect of interaction range in two specific systems: The first system is a quasi one dimensional strongly interacting Bose gas, trapped in a harmonic potential. For this system, we generalize the Gross-Pitaevskii equation in the Thomas-Fermi regime and find a correction to the ground sate energy which is proportional to the square of the trapping frequency. The second system is a dilute gas of bosons moving on a one dimensional ring. Here, we generalize the standard Lieb-Liniger model (replace the strength of interaction by an effective strength which depends on the range of interaction) and find approximate equations for the spectrum.


Another part of this thesis is about collapses and revivals of matter waves. In this part, we discuss oscillations of a Bose gas between two sites, in the framework of Bose-Hubbard model. In the Rabi regime (weakly interacting gas), these oscillations exhibit collapses and revivals which can be well described by an analytic expression that we found based on a semiclassical approximation.