1. Yes, sometimes upon switching to HTTPS/SSL security on your website, you will experience a drop in rankings.
2. Yes, you absolutely, 100% should implement SSL on at least part of your site.
Your implementation just took effect. Google determines everything about a page based on the URL. The URL is the unique identifier; all other factors are associated with the URL. If you change the URL – be it a change in domain, a change in a subfolder, or what have you – Google looks at it like it’s a new page.
What this means is that when you switch to SSL, the URL changes from HTTP to HTTPS. While it’s a minor change, it IS technically a different URL, so Google defaults to thinking it’s a different page.
Almost every element of implementing SSL is concerned with telling Google that, yes, the HTTP and HTTPS versions of the page are the same. That’s why you redirect, that’s why you canonicalize, and that’s why you have to wait.
Generally, Google will get the idea sooner or later, and they will restore most or all of your rankings and traffic once they realize. The problem is that “sooner or later” aspect.
Most reports say that it takes anywhere from two weeks to two months, with an average of one month before most rankings and traffic are restored. So, if you implemented SSL and haven’t waited at least a month, it’s natural for your ranking to be a little low.
Source: SEOBlog