# Hermitian phase operator and quantum harmonic oscillator

I need to apply a hermitian phase operator $$\dfrac{1}{\sqrt{1+\hat{a}^\dagger\hat{a}}}\hat{a}$$ to the nth harmonic oscillator state, but I have no idea how to interpret the square root of a combination of ladder operators in a denominator. How is this operator to be interpreted and applied to a state? I would also appreciate any book references or links to information on hermitian phase operators.