Relevant Degree Programs
Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - May 2019)
In this thesis, we investigated the physics of two- and three-dimensional ultra cold Bose gases in the strongly interacting regime at zero temperature. This regime can be experimentally accessed using a Feshbach resonance. We applied a self-consistent diagrammatic approach to determine the chemical potential of three-dimensional Bose gases for a wide range of interaction values. We showed that such strongly interacting Bose gases become unstable towards the formation of molecules at a finite positive scattering length. In fact, the interaction between atoms becomes effectively attractive and the system looses its metastability before reaching the unitary limit. We also found that such systems are nearly fermionized close to the instability point. Near this critical point, the chemical potential reaches a maximum and the contribution to the system energy due to three-body forces is estimated to be only a few percent. We also studied the same system using a self-consistent renormalization group method. This approach confirms the existence of an instability point towards the formation of molecules as well as fermionization. We showed that the instability and accompanying maximum are precursors of the sign change of the effective two-body interaction strength from repulsive to attractive near resonance. In addition, we examined the physics of two-dimensional Bose gases near resonance using a similar self-consistent diagrammatic approach as the one introduced for three-dimensional Bose gases. We demonstrated that a competition between three-body attractive interactions and two-body repulsive forces results in the chemical potential of two-dimensional Bose gases to exhibit a maximum at a critical scattering length beyond which these quantum gases possess a negative compressibility. For larger scattering lengths, the increasingly prominent role played by three-body attractive interactions leads to an onset instability at a second critical value. The three-body effects studied for these systems are universal, fully characterized by the effective two-dimensional scattering length and are, in comparison to the three-dimensional case, independent of three-body ultraviolet physics.
No abstract available.
Master's Student Supervision (2010 - 2018)
In experiments with ultra-cold gases, two alkali atoms, that interact with repulsive or attractive potentials and are confined to an optical lattice, can form bound states. In order to compute the energy of such states formed by atoms in the lowest Bloch band, one needs to take into account the intra-band corrections arising from contributions by higher Bloch bands. As it is hard to implement, known calculations tend to neglect them altogether thus setting up a limit for the precision of such computations. To address the problem we apply an approach that uses renormalization-group equations for an effective potential we introduce. It allows for the expression of the bound state energy in terms of the free-space interaction scattering length and parameters of confining potentials. Expressions for bound state energies in 1D, 2D and 3D optical lattices are reported. We show that the method we use can be easily tailored to various cases of atoms confined by external fields of other geometries. A known result for atoms confined to a quasi-2D system is reproduced as an example. Universality of the approach makes it a useful tool for such class of problems.