Quantum control of exciton states in clusters of resonantly interacting fluorescent particles using biharmonic laser pumping

The quantum control of dimers, trimers, and tetramers of resonantly interacting fluorescent particles using a biharmonic laser pumping is analyzed. Special emphasis is given on the preparation of all possible pure exciton states (e.g., for tetramers these are single-, two-, three-, and four-exciton states) and their maximally entangled Bell states. The general results are illustrated using as an example the pair and quartet centers of neodymium ions in calcium fluoride (M and N centers), where all necessary experimental information concerning the interactions and decoherence is available, and the experimental preparation of Bell vacuum-single exciton and vacuum-biexciton states have been recently demonstrated. These results can be easily rescaled for the cases of quantum dots and dye molecules. We show that the broad set of quantum-logic operations under such systems can be effectively performed, which again confirms their applicability as prospective quantum computer hardware. Numerical results are compared with the analytical results obtained for a particular case of the biharmonic excitation of dimers. Excellent agreement between these approaches is demonstrated.