Quantum state engineering using conditional measurement on a beam splitter

TL;DR

This paper explores how conditional measurements on a beam splitter can generate specific quantum states, like photon-subtracted or added Jacobi polynomial states, from various input states, with practical considerations included.

Contribution

It introduces a method to engineer quantum states via conditional measurement on a beam splitter, relating output states to input Fock states and analyzing their properties and generation probabilities.

Findings

Conditional measurement produces photon-subtracted or added Jacobi polynomial states.

Properties of generated states depend on input states like coherent and squeezed states.

Probabilities of state generation are calculated and practical effects discussed.

Abstract

State preparation via conditional output measurement on a beam splitter is studied, assuming the signal mode is mixed with a mode prepared in a Fock state and photon numbers are measured in one of the output channels. It is shown that the mode in the other output channel is prepared in either a photon-subtracted or a photon-added Jacobi polynomial state, depending upon the difference between the number of photons in the input Fock state and the number of photons in the output Fock state onto which it is projected. The properties of the conditional output states are studied for coherent and squeezed input states, and the probabilities of generating the states are calculated. Relations to other states, such as near-photon-number states and squeezed-state-excitations, are given and proposals are made for generating them by combining the scheme with others. Finally, effects of realistic photocounting and Fock-state preparation are discussed.