Laser-controlled charge exchange is a promising method for producing cold antihydrogen. Caesium atoms in Rydberg states collide with positrons and create positronium. These positronium atoms then interact with antiprotons, forming antihydrogen. Laser excitation of the caesium atoms is essential to increase the cross section of the charge-exchange collisions. This method was demonstrated in 2004 by the ATRAP collaboration by using an available copper vapour laser. For a second generation of charge-exchange experiments we have designed a new semiconductor laser system that features several improvements compared to the copper vapour laser. We describe this new laser system and show the results from the excitation of caesium atoms to Rydberg states within the strong magnetic fields in the ATRAP apparatus