LAUSR

The ultimate achievable phase sensitivity in a Mach–Zehnder interferometer is given by the Heisenberg limit of $$1/\langle N\rangle $$ 1 / ⟨ N ⟩ , with $$\langle N \rangle $$ ⟨ N ⟩ being the number of photons in the interferometer. However, the best-known phase sensitivity as obtained through intensity measurements is $$\approx 2/\langle N \rangle $$ ≈ 2 / ⟨ N ⟩ . In this work, we provide examples of states that achieve improved phase sensitivity lesser than $$2/\langle N \rangle $$ 2 / ⟨ N ⟩ , albeit greater than $$1/\langle N \rangle $$ 1 / ⟨ N ⟩ . A modified scheme of the Mach–Zehnder interferometer that uses the first excited Fock state, single-mode squeezers, and an additional beam splitter is presented. It is shown that the modified scheme attains a phase sensitivity lesser than $$2/\langle N \rangle $$ 2 / ⟨ N ⟩ , through intensity measurements. The effect of attenuation and noise on phase sensitivity is considered. Phase sensitivity superior to the standard quantum limit is seen to persist for a finite range of attenuation and noise.