as soon as/ no sooner~than

From a grammar book, it sounds like 'as soon as', 'no sooner ~than'and 'hardly~when' have similar meanings. Would you check if the belows are the same meanings?

--------------------------------------------------------------

As soon as the gates were open, the crowds rushed in.

The gates had no sooner been open than the crowds rushed in.

The gates had hardly been open when the crowds rushed in.

Martin had no sooner sat down than the phone rang.

Martin had hardly sat down when the phone rang.

As soon as Martin sat down, the phone rang.

Thank you in advance!