Write SQL query to solve given problem: Among the Independent senators that started their term in 2011 and onwards, what are the official full names of the senators that caucused with the Democrat?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT T1.official_full_name FROM current AS T1 INNER JOIN `current-terms` AS T2 ON T1.bioguide_id = T2.bioguide WHERE T2.party = 'Independent' AND strftime('%Y', T2.start) >= '2011' AND T2.type = 'sen' AND T2.caucus = 'Democrat'