Efficient methods for generating multi-mode NOON states

Abstract

Two experimental setups to generate multi-mode NOON states are proposed. The first setup is a universal model, which can create a d-mode N-photon NOON state with an arbitrary mode number d and photon number N in principle in a lossless system with perfect optical devices, using states with non-deterministic distributions of photons as the input sources and post-selection of total N photons for detection. The second approach, on the other hand, can generate a 4-mode 4-photon NOON state using single photon sources. The core unit of both setups is the Fock state filter, which is used to filter out an arbitrary Fock state component from an incident state using a beam splitter with proper transmissivity. The intrinsic generation efficiencies of the NOON states produced by both methods, with the first setup particularly focused on using squeezed vacuum states as the inputs, are calculated. They are found to be at least two orders of magnitude larger than and scale more favorably to the previously proposed approach using coherent state inputs. We also show that the second setup has the best performance for the case with d=N=4, while the first method scales better for a larger N or d. These results manifest that multi-mode NOON states with 3 or 4 modes and 4 or 6 photons could feasibly be generated in experiments with current photonic technologies.