Join two tables without unique column (DAX)

You can create a calculated column in the first table with something like this:

= CALCULATE( COUNTROWS(Table2), FILTER(Table2, Table2[experiment_id] = Table1[experiment_id]) )

That will count all rows in Table2, where the current row's experiment_id equals the experiment_id in Table2.  If you want to sum the def_id, then change COUNTROWS() to SUM().

You could try with a calculation like this. I first create a table returning the distinct values of def_id where experiment_id exists in Table1 and then count the rows of the new table.

Measure = 
VAR DefTable = CALCULATETABLE(
					VALUES( Table2[def_id] );
					FILTER( 
						ALL ( Table2[experiment_id] );
						CONTAINS(
							VALUES( Table1[experiment_id] ); 
							Table1[experiment_id];
							Table2[experiment_id]
						)
					)
				)
RETURN
	COUNTROWS( DefTable )

If you instead need to could all rows in Table2 instead of the distinct values of def_id you will only have to make a small change to the code where instead of returning the distinct values of def_id you return the distinct rows of all the table instead. If you will have multiple rows in Table2 with the same value in all columns then you will have to add an Index Column to the table to make sure that all rows have unique values.

Measure = 
VAR DefTable = CALCULATETABLE(
					VALUES( Table2 );
					FILTER( 
						ALL ( Table2[experiment_id] );
						CONTAINS(
							VALUES( Table1[experiment_id] ); 
							Table1[experiment_id];
							Table2[experiment_id]
						)
					)
				)
RETURN
	COUNTROWS( DefTable )

Depending on there you live you might have to replace the ';' in the code with ','