Complex sentence: The excited state then decays to both states depending on the values of\\ Gamma_1 and\\ Gamma_2, however, the population that decays to the first state is repumped back to the excited state but the population that decays to the second state is trapped.
Split into simpler sentences: The excited state then decays to both states, depending on the values of\\ Gamma_1 and\\ Gamma_2. However, the population that decays to the first state is repumped to the excited state but the population that decays to the second state is trapped.