You will have to do this in the update chain. Use a ScriptUpdateProcessor then write some Javascript to do this
<processor class="solr.StatelessScriptUpdateProcessorFactory">
<str name="script">updateProcessor.js</str>
</processor>
In update Processor script (in your conf directory):
function processAdd(cmd) {
doc = cmd.solrDoc; // org.apache.solr.common.SolrInputDocument
field= doc.getFieldValue("my_field");
// tokenize your string here on the & separate then put tokens into new field, which could be a multivalue
doc.setField("mySplitField", token);
}
The question is why you want to do this when you can simply tokenize on '&' when indexing then each component is searchable.
Here is some more info: https://dutchweballiance.nl/techblog/introducing-the-solr-scriptupdateprocessor/