Bootstrapping Approach for Generating Maximally Path-Entangled Photon States

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.

Figure 1

Nonlinear process to generate a high NOON state $|N0\colon\colon 0N{⟩}_{a,b}$ via a cross-Kerr nonlinearity. (a) The scheme of Ref. 7 using a single photon Fock state $|1⟩$ as a control. (b) The bootstrapping procedure employing a small NOON state $|K0\colon\colon 0K{⟩}_{c,d}$ as a control.

Figure 2

A low-NOON gun ($K\approx 100$): A scheme to transfer a GHZ state of atoms into a maximally entangled state of photons into two circular polarization modes via collective interaction of atoms with light fields. By using usual optical elements such as a quarter-wave plate (QWP), a polarizing beam splitter (PBS), and a half-wave plate (HWP), the polarization-entangled photons in the two circular polarization modes emitted by the cavity can be converted to a path-entangled NOON state. The insets show the two important steps: (1) preparation of atoms in the GHZ state and (2) transfer of entanglement from atoms to the polarization modes of the cavity.

Figure 3

Quantum Fredkin gate based on nonlinearity obtainable via cavity QED and Ramsey interferometry.