Database

db={"datasets":[{"colorDescription":"braun, rose gold","stateHistory":[{"state":"scanning","date":"2022-02-22T13:06:13.493+00:00"},{"state":"scanned","date":"2022-02-18T13:06:13.493+00:00"},{"state":"reconstructing","date":"2022-02-16T13:06:13.493+00:00"}]},{"colorDescription":"beige, silber","stateHistory":[{"state":"scanning","date":"2022-03-22T13:06:13.493+00:00"},{"state":"scanned","date":"2022-03-18T13:06:13.493+00:00"},{"state":"reconstructing","date":"2022-03-16T13:06:13.493+00:00"}]}],"users":[{"name":"Aravinth","prices":[{"date":"2022-02-16T13:06:13.493+00:00","price":45},{"date":"2022-03-22T13:06:13.493+00:00","price":55}]},{"name":"Raja","prices":[{"date":"2022-02-24T13:06:13.493+00:00","price":75},{"date":"2022-03-23T13:06:13.493+00:00","price":85}]}]}

Query

db.datasets.aggregate([{"$lookup":{"from":"users","as":"details","localField":"stateHistory.date","foreignField":"prices.date"}},{"$project":{color:"$details.colorDescription",prices:"$details"}}])

Result