In this paper we propose a scheme for the preparation of steady entanglements in bosonic dissipative networks. We describe its implementation in a system of coupled cavities interacting with an engineered reservoir built up of three-level atoms. Emblematic bipartite ($\text{Bell}$ and $\text{NOON}$) and multipartite ($W$-class) states can be produced with high fidelity and purity.

We present a framework to engineer nonlinear selective Jaynes–Cummings interactions for one-, two- and three-photon transitions. Higher order transitions are also discussed. Numerical simulations are presented to prove the effectiveness of our scheme. We further analyse how to apply these selective interactions to deterministic step-by-step preparation of number states, even in the non-ideal situation where cavity losses and atomic spontaneous emission are considered. Finally, we present a scheme, derived from the engineered selective interactions, to delay the decoherence process of the prepared Fock state.

In this paper, we present a protocol to engineer upper bounded and sliced Jaynes–Cummings and anti-Jaynes–Cummings Hamiltonians in cavity quantum electrodynamics. In the upper bounded Hamiltonians, the atom-field interaction is confined to a subspace of Fock states ranging from $\left|0\right.〉$ up to $\left|4\right.〉$, while in the sliced interaction the Fock subspace ranges from $\left|M\right.〉$ up to $\left|M+4\right.〉$. We also show how to build upper bounded and sliced Liouvillians irrespective of engineering Hamiltonians. The upper bounded and sliced Hamiltonians and Liouvillians can be used, among other applications, to generate steady Fock states of a cavity mode and for the implementation of a quantum-scissors device for optical state truncation.

In the paper carried out by Wenjun et al. [ Phys. Rev. A 95, 032124 (2017)], a generalization of the James effective dynamics theory based on a first version of the James method was presented. However, we contend that this is not a very rigorous way of deriving the effective third-order expansion for an interaction Hamiltonian with harmonic time-dependence. In fact, here we show that the third-order Hamiltonian obtained by Wenjun et al. is not Hermitian for general situations when we consider time dependence. Its non-Hermitian nature arises from the foundation of the theory itself. In this comment paper, the most general expression of the effective Hamiltonian expanded up to third order is obtained. Our derived effective Hamiltonian is Hermitian even in situations where we have time dependence.

We prove the consistency of the different approaches for deriving the black hole radiation for the spherically symmetric case inside the theory of Massive Gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the Path Integral formulation, we find that in both cases, the presence of the extra-degrees of freedom creates the effect of extra-particles creation due to the distortions on the definitions of time defined by the different observers at large scales. This, however, does not mean extra-particle creation at the horizon level. Instead, the apparent additional particles perceived at large scales emerge from how distant observers define their time coordinate, which is distorted due to the existence of extra-degrees of freedom.