Sleep deprivation

I’m a FTM, my baby is currently 4 days old. My mum is in town to help me out for a little bit. After being in the hospital and dealing with baby I’m quite sleep deprived as expected. However my mum has alerted me that during times when she’d let me get a nap I sleep completely like a zombie throughout my baby’s crying and any other noise. She’s gonna be leaving soon and although I might have someone else who can help for a bit it’s still bad that I can’t come to my baby’s rescue when I need to. What can I do? I know getting rest obviously 🤷🏽‍♀️ I’m usually not a deep sleeper