Dynamics of Bose-Einstein Condensates in Optical Lattice Ratchet Potential Systems

Abstract

This thesis aims to explore intriguing phenomena observed in Bose-Einstein condensates (BEC) subjected to asymmetric optical potentials. The phenomena of interest here is directed transport, wherein the BEC is made to travel in a specific direction without applying a net force. This phenomenon becomes possible in systems out of equilibrium when certain symmetries are broken. Three different scenarios have been analyzed: (i) Bose-Einstein Condensates with time-dependent interactions subjected to a kicked ratchet potential, (ii) Non-interacting Bose-Einstein Condensates in a non-Hermitian kicked ratchet potential and (iii) Non-interacting Bose-Einstein Condensates in a kicked ratchet potential whose phase is spatially modulated.

In the first scenario, the role of atom-atom interaction on the resulting directed current is studied. A notable correlation between the kicking strength K and the interaction parameter ̃g has been uncovered. A critical boundary within the (K, g ̃) space distinguishes between quasi-periodicity and complete chaos, indicating that strong interactions lead to full chaos. Within the realm of full chaos, significant currents and current reversals, emerge, disrupting the symmetry of the current spectrum. Beyond the stability range where |g ̃|≤ 1, directed transport is no longer ensured.

In the second scenario, the impact of non-Hermitian kicking on a cold atom exposed to an asymmetric ratchet potential was explored. This non-Hermiticity stems from dissipative interactions influenced by the environment, leading to either atom-gain or loss effects on the atom. It was realized in this study that non-Hermiticity can either impede or enhance the atom’s transport. Additionally, substantial atom-gain may induce reversals in the current direction. Quantum resonance notably emerges as a pivotal factor in dictating these outcomes. Finally, we considered the effect of a spatial modulation on the transport of this system. Before illustrating the influence of this phase, we observed that within the regimes where current reversals can occur, the probability of negative current peaks is consistently lower than that of positive peaks. Furthermore, both probabilities are symmetric around the value 0.5, an intriguing observation that warrants further investigation. With the inclusion of the phase, our calculations of the transport current revealed that transport can be optimized for faster dynamics. Higher current values were achieved compared to the zero-phase scenario. Notably, starting from a zero-phase regime where current reversals are present, such as the regime of full chaos, the phase not only enhances and rectifies the transport current but also allows for its complete suppression (current blockade). From the current landscapes plotted as functions of the spatial phase θ and the potential strength P, regions of optimal currents were identified at critical values of θ and P.