Washington (CNN)Federal authorities investigating alleged sex trafficking by GOP Rep. Matt Gaetz have secured the cooperation of the congressman's ex-girlfriend, according to people familiar with the matter.The woman, a former Capitol Hill staffer, is seen as a critical witness, as she has been linked to Gaetz as far back as the summer of 2017, a period of time that has emerged as a key window of scrutiny for investigators. She can also help investigators understand the relevance of hundreds of transactions they have obtained records of, including those involving alleged payments for sex, the sources said.