Research interests of Usama Al Khawaja

After my Ph. D. graduation, I have been involved actively in four main research areas, namely

1. Bose-Einstein condensation

2. Superconductivity

3. Mathematical Physics: Integrability and J-matrix method

4. Soliton molecules and their applications in optical fibers

The first is my main research topic in which I conducted my Ph.D. study and had my postdoctoral research experience. The work on the second topic was initiated in the United Arab Emirates University (UAEU) in collaboration with a small local group formed to work on this particular subject.  The third topic is the subject of my recent interest in investigating the integrability of partial differential equations that have applications in Physics and finding new exact solutions to the integrable ones. This research area includes also my work on using the J-matrix method to find resonance and bound states of atomic collisions. This was performed in collaboration with the theoretical Physics group at the Physics department of the King Fahd University for Petroleum and Minerals (KFUPM)/Saudi Arabia. The last topic is my very recent and major research activity. It focuses on the dynamics, formation, and stability of soliton molecules and their applications as data carriers in optical fibers.

Here is a detailed account of my production in each area:

• Bose-Einstein condensation: My work in this field included collective and surface modes of Bose-Einstein condensates, topological excitations, spinor condensates, low-dimensional condensates, phase fluctuations, and vortices in condensates.  I collaborated with leading groups from the Niels Bohr Institute/Copenhagen University/Denmark, Institute of Physics/Utrecht University/The Netherlands, and Rice University/USA. I have more than 16 publications in this field, two of them are single-author performed in UAEU, three are in Physical Review letters, one in Nature, and most of the rest are in Physical Review A.

• Superconductivity: We investigated numerically the critical current density of vortices in superconductors with square arrays of pinning sites. We studied the effect of various factors such as pinning strength, vortex density, pinning centers’ radius and density, and temperature. We have published more than 13 papers out of this project. We have involved two M.Sc. students and a number of undergraduate students, three of which were co-authors in our published papers. We have won two Research Project Award (UAE University, 2006, 2007) for our work in this field. One of our papers was ranked by the journal Physica C among top 25 most read papers for the first quarter of 2006 (paper 19 in my CV).     

•  Mathematical Physics (J-Matrix method): I have established a collaboration with the theoretical Physics group at the Physics department of the King Fahd University and the Saudi Center for theoretical Physics. This group includes 3 professors with whom I collaborate on calculating the resonance and bound state energies of atomic collisions. Recently, the Saudi Center for Theoretical Physics was established and I became an associate member of the Center. 

• Mathematical Physics (Integrability and exact solutions): I have been also interested in the recent years in methods of exactly solving  nonlinear partial differential equations that have applications in Physics. My major contribution in this field is the establishment of a new method to investigate the integrability of nonlinear partial differential equations and to facilitate solving them exactly, (see paper 25 in my CV).  This technique represents a key tool for researchers in different fields whenever a solution to a nonlinear partial differential equation is needed.  I have used this technique in the fields of Bose-Einstein condensation and nonlinear optics which led me to start even another new line of research, namely solitons dynamics, as described next.

• Solitons: Using the above-mentioned method of finding exact solutions, I derived new solitonic solutions to a number of nonlinear Schrödinger equations. Different external potentials were considered corresponding to different experimental situations. My major contribution in this topic is the derivation of the two-solitons solution and putting it in a novel form. From this solution, I managed to find the potential of interaction between the two solitons exactly. This is done, to the best of my knowledge, for the first time and it is expected to have implications in other topics. The appealing feature of this potential is that it is valid for long and short distances (see papers 40 and 43 in my CV). In addition, I am working currently on the stability of the bound state resulting from two solitons, namely soliton molecules. The theoretical Physics group at the King Fahd University for Petroleum and Minerals and the Saudi Center for Theoretical Physics are also interested in this research field (see papers 41 and 42 in my CV). We have also applied for a two-years project on solitons and their applications which has been accepted and started in Jan. 2011 with a budget of 236,300 Saudi Riyals. I have also oriented my research in this field to one of its applications, namely data transfer in optical fibers. Most recently, I have won the  three-years National research Foundation (NRF) grant of total budget 750,000,00 AED which is totally devoted to this application. I will be using this fund to mainly hire a postdoc, obtain the necessary equipments, and to fund my external collaborations.