Robustness of Heisenberg-limited interferometry with balanced Fock states

Interferometry with Heisenberg-limited phase resolution may play an important role in the next generation of atomic clocks, gravitational wave detectors and in quantum information science. For experimental implementations the robustness of the phase resolution is crucial since any experimental realization will be subject to imperfections. In this paper, we study the robustness of phase reconstruction with two number states as input subject to fluctuations in the state preparation. We find that the phase resolution is insensitive to fluctuations in the total number of particles and robust against noise in the number difference at the input. The phase resolution depends on the uncertainty in the number difference in a universal way that has a clear physical interpretation: fundamental noise due to the Heisenberg limit and noise due to state preparation imperfection contribute essentially independently to the total uncertainty in the phase. For number difference uncertainties less than one the first noise source is dominant and the phase resolution is essentially Heisenberg limited. For number difference uncertainties greater than one the noise due to state preparation imperfection is dominant and the phase resolution deteriorates linearly with the number difference uncertainty.