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We give an operator solution to an advanced-retarded differential equation. The application of the operators involved produces a solution in terms of Bessel functions.

Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which exotic modern technologies are founded. In general, the most prominent adversary of quantum coherence is noise arising from the interaction of the associated dynamical system with its environment. Under certain conditions, however, the existence of noise may drive quantum and classical systems to endure intriguing nontrivial effects. Along these lines, here we demonstrate, both theoretically and experimentally, that when two indistinguishable particles co-propagate through quantum networks affected by noise, the system always evolves into a steady state in which coherences between certain separable states perpetually prevail. Furthermore, we show that the same steady state with surviving quantum coherences is reached irrespectively of the configuration in which the particles are prepared.

We demonstrate that superpositions of coherent and displaced Fock states, also referred to as generalized Schr��dinger cats cats, can be created by application of a nonlinear displacement operator which is a deformed version of the Glauber displacement operator. Consequently, such generalized cat states can be formally considered as nonlinear coherent states. We then show that Glauber-Fock photonic lattices endowed with alternating positive and negative coupling coefficients give rise to classical analogs of such cat states. In addition, it is pointed out that the analytic propagator of these deformed Glauber-Fock arrays explicitly contains the Wigner operator opening the possibility to observe Wigner functions of the quantum harmonic oscillator in the classical domain., 17 pages, 5 figures

Quantum superposition is the quantum-mechanical property of a particle whereby it inhabits several of its possible quantum states simultaneously. Ideally, this permissible coexistence of quantum states, as defined on any degree of freedom, whether spin, frequency or spatial, can be used to fully exploit the information capacity of the associated physical system. In quantum optics, single photons are the quanta of light, and their coherence properties allow them to establish entangled superpositions between a large number of channels, making them favourable for realizations of quantum information processing schemes. In particular, single-photon W-states (that is, states exhibiting a uniform distribution of the photons across multiple modes) represent a class of multipartite maximally-entangled quantum states that are highly robust to dissipation. Here, we report on the generation and verification of single-photon W-states involving up to 16 spatial modes, and exploit their underlying multi-mode superposition for the on-chip generation of genuine random numbers.

We establish an approximate equivalence between a generalised quantum Rabi model and its nth order counterparts, where spinboson interactions are nonlinear as they comprise a simultaneous exchange of n bosonic excitations. Although there exists no unitary transformation between these models, we demonstrate their equivalence to a good approximation in a wide range of parameters. This shows that nonlinear spin-boson couplings, i.e., nth order quantum Rabi models, are accessible to quantum systems with only linear coupling between boson and spin modes by simply adding spin rotations and after an appropriate transformation. Furthermore, our result prompts novel approximate analytical solutions to the dynamics of the quantum Rabi model in the ultrastrong coupling regime improving previous approaches., publishedVersion