protocol migration from http to https:// aint easy...?

i will do my best to phrase this question with detail and succinctly.

We have recently migrated from a website which was built by a third part contractor using the http:// protocol to an in house solution using https:// - this means both our sitemap and our protocol has changed significantly. The old site had built up a decent audience and was getting sufficient traffic however the user experience was awful.

When making the site move we feel we have adopted best practice however our search engine impressions within google are no-where near the level of the old site. I am wondering should we de-index the old http:// site (which currently has some 301 redirects set up) or will we lose more authority this way.

Finally its also worth mentioning the new site has been built using an ajax method, to our knowledge we are-being indexed successfully by google via push state static pages. I dont think this is our issue but have included it just in case.

Does Google see the https:// site as a completely new web property or is it possible we will regain some of our authority as google realises we are the same entity as our http:// site or are we now back to the bottom of the pile and should be fighting a different battle to start rebuilding an audience.

Any feedback would be welcome, happy to provide additional info where required.

Thanks