QUROPE Quantum Information Processing and Communication in Europe

We use the exact diagonalization method to analyze the possibility of generating strongly correlated states in two-dimensional clouds of ultracold bosonic atoms that are subjected to a geometric gauge field that was created by coupling two internal atomic states to a laser beam. On tuning the gauge field strength, the system undergoes stepwise transitions between different ground states (GSs), which we describe by using analytical trial wave functions, including the Pfaffian (Pf), the Laughlin and a Laughlin quasiparticle many-body state. Whereas for an infinitely strong laser field, the internal degree of freedom of the atoms can adiabatically follow their center-of-mass movement, a finite laser intensity gives rise to non-adiabatic transitions between the internal states, which are shown to break the cylindrical symmetry of the Hamiltonian.We study the influence of the asymmetry on the GS properties of the system. The main effect is to reduce the overlap of the numerical solutions with the analytical trial expressions by occupying states with higher angular momentum. Thus, we propose generalized wave functions arising from the Laughlin and Pf wave functions by including components where extra Jastrow factors appear while preserving important features of these states. We analyze quasihole excitations over the Laughlin and generalized Laughlin states and show that they possess effective fractional charge and obey anyonic statistics. Finally, we discuss the observability of the Laughlin state for increasing numbers of particles  

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