We propose a bootstrapping approach to the generation of maximally path-entangled states of photons, so-called "NOON states." The strong atom-light interaction of cavity QED can be employed to generate NOON states with about 100 photons. These can then be used to boost the existing experimental Kerr nonlinearities based on quantum coherence effects, to facilitate NOON generation with an arbitrarily large number of photons. We also offer an alternative scheme that uses an atom-cavity dispersive interaction to obtain a sufficiently high Kerr nonlinearity necessary for arbitrary NOON generation.
We propose a bootstrapping approach to generation of maximally path-entangled states of photons, so called ``NOON states'', achievable within the current experimental technology. Strong atom-light interaction of cavity QED can be employed to generate NOON states with about 100 photons; which can then be used to boost the existing experimental Kerr nonlinearities based on quantum coherence effects to facilitate NOON generation with arbitrarily large number of photons. We also offer an alternative scheme that uses an atom-cavity dispersive interaction to obtain sufficiently high Kerr-nonlinearity necessary for arbitrary NOON generation.
To generate a NOON state with a large photon number
N, the number of operational steps could be large and the fidelity will decrease rapidly with
N. Here we propose a method to generate a type of quantum entangled states, $(|NN00\ensuremath{\rangle}+|00NN\ensuremath{\rangle})/\sqrt{2}$, called ``double NOON'' states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the ``double'' NOON state creation needs only
N+2 operational steps. One application of double NOON states is to get a phase error of
1/(2N) in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\ensuremath{\rangle}+|0,2N\ensuremath{\rangle})/\sqrt{2}$ is needed, which requires at least
2N operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\ensuremath{\le}10$ even for imperfect devices is feasible with the present circuit QED technique.