Optimal Quantum-Enhanced Interferometry Using a Laser Power Source

DOI: 10.1103/PhysRevLett.111.173601

Eq(17):

\[a_2=\frac{x+ip}{\sqrt{2}} \\ 2\bar{N}+1=2\left< {a_2}^{\dagger}a_2 \right> +1=2\left< \frac{x-ip}{\sqrt{2}}\frac{x+ip}{\sqrt{2}} \right> +1 \\ =\left< \left( x-ip \right) \left( x+ip \right) \right> +1 \\ =\left< x^2 \right> +\left< p^2 \right> \]