Many works have stated that nonlinear interactions can improve phase sensitivity beyond the Heisenberg limit scaling of $1/N$ with $N$ being the mean photon number. This raises some open questions---among them the conclusive sensitivity limits with respect to single-mode inputs. Namely, when one of two inputs is vacuum, is there a shot-noise-style sensitivity bound on a nonlinear Mach-Zehnder interferometer? Within the reach of second-order nonlinear phase shifts, we make an attempt to provide an answer to this question. Based upon phase-averaging approach, this puzzle is partially resolved with careful calculations of the quantum Fisher information regarding three kinds of common inputs: Gaussian states, squeezed number states, and Schrödinger cat states. The results suggest that shot-noise-style sensitivity limit is no longer available, and the ideal candidate is squeezed vacuum.Many works have stated that nonlinear interactions can improve phase sensitivity beyond the Heisenberg limit scaling of $1/N$ with $N$ being the mean photon number. This raises some open questions---among them the conclusive sensitivity limits with respect to single-mode inputs. Namely, when one of two inputs is vacuum, is there a shot-noise-style sensitivity bound on a nonlinear Mach-Zehnder interferometer? Within the reach of second-order nonlinear phase shifts, we make an attempt to provide an answer to this question. Based upon phase-averaging approach, this puzzle is partially resolved with careful calculations of the quantum Fisher information regarding three kinds of common inputs: Gaussian states, squeezed number states, and Schrödinger cat states. The results suggest that shot-noise-style sensitivity limit is no longer available, and the ideal candidate is squeezed vacuum.

arXiv:1906.10867Jun 26, 20191 citation

Phase-controlled nonlinear interferometry

G. L�pke, Gerd Marowsky, Robert Steinhoff

Applied Physics BSep 1, 198922 citations

The phase sensitivity of a fully quantum three-mode nonlinear interferometer

Jefferson Flórez, Enno Giese, Davor Curic +3 more

We study a nonlinear interferometer consisting of two consecutive parametric amplifiers, where all three optical fields (pump, signal and idler) are treated quantum mechanically, allowing for pump depletion and other quantum phenomena. The interaction of all three fields in the final amplifier leads to an interference pattern from which we extract the phase uncertainty. We find that the phase uncertainty oscillates around a saturation level that decreases as the mean number N of input pump photons increases. For optimal interaction strengths, we also find a phase uncertainty below the shot-noise level and obtain a Heisenberg scaling . This is in contrast to the conventional treatment within the parametric approximation, where the Heisenberg scaling is observed as a function of the number of down-converted photons inside the interferometer.We study a nonlinear interferometer consisting of two consecutive parametric amplifiers, where all three optical fields (pump, signal and idler) are treated quantum mechanically, allowing for pump depletion and other quantum phenomena. The interaction of all three fields in the final amplifier leads to an interference pattern from which we extract the phase uncertainty. We find that the phase uncertainty oscillates around a saturation level that decreases as the mean number N of input pump photons increases. For optimal interaction strengths, we also find a phase uncertainty below the shot-noise level and obtain a Heisenberg scaling . This is in contrast to the conventional treatment within the parametric approximation, where the Heisenberg scaling is observed as a function of the number of down-converted photons inside the interferometer.

arXiv:1808.06136New Journal of PhysicsDec 21, 20189 citations

Many works have stated that nonlinear interactions can improve phase sensitivity beyond the Heisenberg limit scaling of

1/N

with

N

being the mean photon number. This raises some open questions---among them the conclusive sensitivity limits with respect to single-mode inputs. Namely, when one of two inputs is vacuum, is there a shot-noise-style sensitivity bound on a nonlinear Mach-Zehnder interferometer? Within the reach of second-order nonlinear phase shifts, we make an attempt to provide an answer to this question. Based upon phase-averaging approach, this puzzle is partially resolved with careful calculations of the quantum Fisher information regarding three kinds of common inputs: Gaussian states, squeezed number states, and Schrödinger cat states. The results suggest that shot-noise-style sensitivity limit is no longer available, and the ideal candidate is squeezed vacuum.