Entanglement Dynamics of Second Quantized Quantum Fields

We study the entanglement dynamics in the system of coupled boson fields. We demonstrate that there are different natural notions of locality in this context leading to inequivalent notions of entanglement. We concentrate on the particle picture, when entanglement of one particle is determined by one-particle density matrix. We study, in detail, the effect of interaction preserving populations of individual one-particle states. We show that if the system is initially in a disentangled state with the definite total number of particles and the dimension of the one-particle Hilbert space is more than two, then only potentials of the special form admit complete entanglement, which is shown to be reached at NOON states. If the system is initially in Glauber’s coherent state, complete entanglement is not reached despite the presence of two entangling channels in this case. We conclude with studying the time evolution of entanglement of photons in a cavity with multiple quantum dots in the limit of large number of photons. We show that in a relatively short time scale the completely entangled states belong to the class of graph states and are formed due to the interaction with dots in resonance with the cavity modes. 1. Introduction Entanglement [1] is a quintessentially quantum feature. It signifies that different parts of a compound system may form a new entity, a complex; for example, when neither of two particles can be characterized by a definite state so that instead of two particles one has to consider a pair and so on. If one would attempt to access a particular part of the complex by performing a local measurement, this would unavoidably modify the state of other parts even if the direct interaction between the parts is absent or negligible. Such departure from the classical properties makes entanglement the central object in various contexts, from the perspective of application in quantum informatics [2] to understanding the physics of quantum phase transitions [3]. As a problem of special interest, therefore, the problem of preparation of a system in an entangled state stands out. Among different appearances of this problem, entangled states of quantized electromagnetic field, as perhaps the most accessible and the most flexible object, presents a significant importance on its own. Nowadays, the most developed and widely used method of generating entangled photons is the parametric down conversion [4–6], which is based on the two-photon radiative decay of material excited states. This method, however, suffers from well recognized intrinsic