There are several methods to analyze chromatin fragmentation efficiency and yield after sonication. One option is to run the purified chromatin on an agarose gel to visually assess the size distribution of the DNA fragments. For a more precise measurement, one can use instruments like the TapeStation, Bioanalyzer, or Fragment Analyzer, which provide quantitative analysis of DNA fragment sizes. It's also important to ensure that sonication hasn't affected the ability of the antibody to recognize its target epitope. One can do this by carrying out immunoprecipitation followed by a western blot to confirm that the epitope in the target protein is still detectable after sonication.