Nonexistence of entanglement sudden death in dephasing of high NOON states

We study the dynamics of entanglement in continuous variable quantum systems. Specifically, we study the phenomena of entanglement sudden death (ESD) in general two-mode-N-photon states undergoing pure dephasing. We show that for these circumstances, ESD never occurs. These states are generalizations of the so-called high NOON states (i.e., a superposition of N photons in the first mode, O in the second, with O photons in the first, N in the second), shown to decrease the Rayleigh limit of lambda to lambda/N, which promises great improvement in resolution of interference patterns if states with large N are physically realized [Phys. Rev. Lett. 85, 2733 (2000)]. However, we show that in dephasing NOON states, the time to reach some critical visibility V(crit), scales inversely with N(2). On the practical level, this shows that as N increases, the visibility degrades much faster, which is likely to be a considerable drawback for any practical application of these states. (C) 2009 Optical Society of America