If I may humbly assume that you are in the Software Industry the answer to your question or a solution to your problem would be to use the Enterprise Scrum Model with a solid Project Release Plan and project timeline plan.
There should be an Operations Support Scrum Team which may include a DB administrator, an Application Server administrator, Senior QA people, and Senior Production Support Analysts. This Team may look after the complete QA regression and load testing, release management, code deployment and other operations support activities for the Development Scrum Teams. The Development Scrum Teams on the other hand would just produce the releasable software and put it on the shelf for the Operations Support Team.
In this particular scenario of yours the Operations Support Team would have Backlogs on their Product Backlog list to do Regression Testing and load testing activities for the shelved product produced by the development Team - Note Regression should ideally be a part of the development process!!!
Now organizations that release every Sprint need to have the Operations Team lag a week or 2 behind the development Teams, so for example if Scrum Development Team is working on the Release 2.0 code the Operations Support Team should be deploying the Release 1.0 code which the development Team finished "shelving" 2 weeks ago.
The bottom line is that a release plan needs to be laid out with the correct timelines. There may be a misconception in Scrum that each Scrum team has its own release plan because they are self managed, and they would do their own deployment etc, which could be true to a certain extent, but the teams plan will need to be fit in with the project wide release plan as well, and the timelines will need to be fit in accordingly.
The responsibility of coordinating the timelines and organizing the backlogs as per Project timelines would mainly lie on the shoulders of the PO and offcourse the SM, who is responsible for training the PO on how to make this work most effectively. So simple answer is = 2 weeks is a good gap to have between a development team and an operations team doing QA or release activities, but time lines and gaps should be adjusted according to project needs.
If you need more details on this please ask. A conversation to discuss this would have been much easier to explain but I hope this answers your question. And By the way, releasing (to PROD) the day after the Sprint is over for the development Team is a bad idea as per me but you can always try it and inspect and adapt ;) and 1 week is a good enough gap but depends how big your application is and how big your data is, and also how many resources you have.
Thanks, Sid Telang. Certified Scrum Master