In this paper we present a comprehensive analysis of the coherence phenomenon of two coupled dissipative oscillators. The action of a classical driving field on one of the oscillators is also analyzed. Master equations are derived for both regimes of weakly and strongly interacting oscillators from which interesting results arise concerning the coherence properties of the joint and the reduced system states. The strong coupling regime is required to achieve a large frequency shift of the oscillator normal modes, making it possible to explore the whole profile of the spectral density of the reservoirs. We show how the decoherence process may be controlled by shifting the normal mode frequencies to regions of small spectral density of the reservoirs. Different spectral densities of the reservoirs are considered and their effects on the decoherence process are analyzed. For oscillators with different damping rates, we show that the worse-quality system is improved and vice-versa, a result which could be useful for quantum state protection. State recurrence and swap dynamics are analyzed as well as their roles in delaying the decoherence process.

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In this work we present a general treatment of a bosonic dissipative network: a chain of coupled dissipative harmonic oscillators whichever its topology, i.e., whichever the way the oscillators are coupled together, the strenght of their couplings and their natural frequencies. Starting with a general more realistic scenario where each oscillator is coupled to its own reservoir, we also discuss the case where all the network oscillators are coupled to a common reservoir. We obtain the master equation governing the dynamic of the network states and the associated evolution equation of the Glauber-Sudarshan P -function. With these instruments we breafly show how to analyse the decoherence and the evolution of the linear entropy of general states of the network. We also show how to obtain the master equation for the case of distinct reservoirs from that of a common one.

We consider a network of interacting resonators and analyze the physical ingredients that enable the emergence of relaxation-free and decoherence-free subspaces. We investigate two different situations: i) when the whole network interacts with a common reservoir and ii) when each resonator, strongly coupled to each other, interacts with its own reservoir. Our main result is that both subspaces are generated when all the resonators couple with the same group of reservoir modes, thus building up a correlation (among these modes), which has the potential to shield particular network states against relaxation and/or decoherence.The search for mechanisms to bypass decoherence, a subject of major concern for quantum information processing, has deepened our understanding of open quantum systems and led to ingenious schemes for coherence control, which go far beyond the quest for conditions that weaken the system-reservoir coupling [1,2]. The myriad contributions to this subject started, inspired by classical error-correcting codes, with quantum coding schemes for information stored in a quantum memory [3]. On the assumption that the decoherence process acts independently on each of the qubits stored in a memory, a particular qubit encoded in a block of ancillary qubits is able to withstand a substantial degree of interaction with the reservoir without degradation of its information. Another strategy, the so-called engineering reservoirs [4], compels the system of interest, whose state is to be protected against decoherence, to engage in additional interactions besides that with the reservoir. This program, based on the indirect control of system-reservoir dynamics, has been developed for trapped ions [5,6] and atomic two-level systems [7,8] as well. Finally, the process of collective decoherence, where a composite system interacts with a common reservoir, has also instigated several interesting results related to what has been called a decoherence-free subspace (DFS) [9,10,11]. It is noteworthy that while quantum error-correcting codes presuppose quantum systems that decohere independently, DFS -as it has been understood until the present study -is generated by distinct quantum systems coupled to a common reservoir.In this contribution we are concerned with collective dissipation and decoherence in a network of N coupled resonators. We analyze the physical ingredients ruling the emergence of a DFS and, in particular, a relaxationfree subspace (RFS) composed of states protected against both dissipation and decoherence, demonstrating that a DFS contains a RFS. We first analyze the situation, treated in the literature to date, where all the resonators are coupled to a common reservoir. However, as the scenario of a common reservoir is in practice rather unusual, we next analyze the situation where each resonator interacts with its own reservoir, which seems to be more appropriate for most physical systems. In the domain of cavity quantum electrodynamics, distinct reservoirs must be considered for distinguishable cavities,...

Here we present an strategy for the derivation of a time-dependent Dyson map which ensures simultaneously the unitarity of the time evolution and the observability of a quasi-Hermitian Hamiltonian. The time-dependent Dyson map is derived through a constructed Schrödinger-like equation governed by the non-Hermitian Hamiltonian itself; despite its time-dependence our scheme ensures the time-independence of the metric operator, a necessary condition for the observability of the quasi-Hermitian Hamiltonian. As an illustrative example we consider a driven Harmonic oscillator described by a time-dependent non-Hermitian Hamiltonian. After computing the Dyson map and demonstrating the time-independence of the associated metric operator, we successfully derive an eigenvalue equation for this time-dependent Hamiltonian which enable us to analyze the PT -symmetry breaking process.