Hello Aspirant,
If you want to pursue research (PhD) in astronomy or astrophysics you require a Bachelors degree in physics with mathematics. However since you have done your Bachelors in B.Tech mechanical engineering, you will have to either take up an integrated MSc with PhD in astronomy or you can do M. tech in astronomy and space engineering. Do check out the official website of Indian Institute of Astrophysics (IIAP). They provide several courses that will be right up your alley.
As for research in quantum mechanics you can apply for entrance exams in Tata institute (TIFR), IISc, International centre theoretical Sciences (ICTS). You can look into their official websites for further details.
No gap is too long to pursue your dreams, keep at it. Hope this helps and Good luck.
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