Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently this effect has been analyzed and observed in a number of physical systems close to the quantum mechanical regime. In this work we propose the mutual information as a useful order parameter which can capture the emergence of synchronization in very different contexts, ranging from semi-classical to intrinsically quantum mechanical systems. Specifically we first study the synchronization of two coupled Van der Pol oscillators in both classical and quantum regimes and later we consider the synchronization of two qubits inside two coupled optical cavities. In all these contexts, we find that mutual information can be used as an appropriate figure of merit for determining the synchronization phases, independently of the specific details of the system.

By modeling a linear polarizable and magnetizable medium (magnetodielectric) with two quantum fields, namely E and M, electromagnetic field is quantized in such a medium consistently and systematically. A Hamiltonian is proposed from which, using the Heisenberg equations, Maxwell and constitutive equations of the medium are obtained. For a homogeneous medium, the equation of motion of the quantum vector potential, A, is derived and solved analytically. Two coupling functions which describe the electromagnetic properties of the medium are introduced. Four examples are considered showing the features and the applicability of the model to both absorptive and nonabsorptive magneto-dielectrics.

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The performance of quantum technologies that use entanglement and coherence as a resource is highly limited by the effects of decoherence due to their interaction with some environment. In particular, it is important to take into account situations where such devices unavoidably interact with surrounding. Here, we study memory effects on energy and ergotropy of quantum batteries in the framework of open system dynamics, where the battery and charger are individually allowed to access a bosonic environment. Our investigation shows that the battery can be fully charged as well as its energy can be preserved for long times in non-Markovian dynamics compared with Markovian dynamics. Moreover, the non-Markovianity increase makes it possible to extract the total stored energy as work and the discharge time becomes longer. Our results indicate that memory effects can play a significant role in improving the performance of quantum batteries.

The Huttner$-$Barnett model is extended to a magnetodielectric medium by adding a new matter field to this model. The eigenoperators for the coupled system are calculated and electromagnetic field is written in terms of these operators. The electric and magnetic susceptibility of the medium are explicitly derived and shown to satisfy the Kramers$-$Kronig relations. It is shown that the results obtained in this model are equivalent to the results obtained from the phenomenological methods.Comment: 25 page