Having an issue that my girlfriend has brought to my attention and it is really affecting her.

So appare fly I have been talking in my sleep on and off for the 3 months we have been together. Some of it gibberish but apparently a fair amount of it is regarding my ex, her name, saying I love her.
Now my ex and I had a messy breakup (she lied cheated on my, broke up with me on my birthday, strung me along). I want nothing to do with her. I don't think of her consciously at all during the day. I don't want to be with her and do not love her.

My current girlfriend I love and adore and makes me so happy. This has become an issue though because it is recurring and while she knows that I have no control over it due to being asleep, she cannot trust that what i am saying in my sleep isn't actually how I feel. And doesn't believe me when I tell her I love her when I an concious and awake.

I don't know what to do or where to begin. I want to fix this but I have no control over what I say when I am asleep and it's my subconcious acting on past experiences and does not reflect how I actually feel now. Please any advice would be helpful.