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A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time…
Recent experiments on quantum behavior in microfabricated solid-state systems suggest tantalizing connections to quantum optics. Several of these experiments address the prototypical problem of cavity quantum electrodynamics: a two-level…
Hybrid quantum systems have been developed with various mechanical, optical and microwave harmonic oscillators. The coupling produces a rich library of interactions including two mode squeezing, swapping interactions, back-action evasion…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
We numerically study the quantum dynamics of a $\mathcal{PT}$-symmetric kicked harmonic oscillator. We observe that directed current of momentum and ballistic diffusion of energy coexist under the non-resonant conditions, whereas both the…
The purpose of this paper is the discussion of a pair of coupled linear oscillators that has recently been proposed as a model of a system of two optical resonators. By means of an algebraic approach we show that the frequencies of the…
In this work, we study the dynamics of quantum coherence (total coherence, global coherence and local coherence) evolving under a local PT-symmetric Hamiltonian in maximally entangled bipartite and tripartite states. Our results indicate…
Genuine quantum-mechanical effects are readily observable in modern optomechanical systems comprising bosonic ("classical") optical resonators. Here we describe unique features and advantages of optical two-level systems, or qubits, for…
The coherent states that describe the classical motion of a mechanical oscillator do not have well-defined energy, but are rather quantum superpositions of equally-spaced energy eigenstates. Revealing this quantized structure is only…
The interaction between solid-state qubits and their environmental degrees of freedom produces non-unitary effects like decoherence and dissipation. Uncontrolled decoherence is one of the main obstacles that must be overcome in quantum…
Classical Hamiltonian ratchets have been recently successfully realized using cold atoms in driven optical lattices. Here we study the current rectification of the motion of a quantum particle in a periodic potential exposed to an external…
The modes of the electromagnetic field are solutions of Maxwell's equations taking into account the material boundary conditions. The field modes of classical optics - properly normalized - are also the mode functions of quantum optics.…
In this paper we construct the coherent and trajectory-coherent states of a damped harmonic oscillator. We investigate the properties of this states.
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
We develop a general framework for the open dynamics of an ensemble of quantum particles subject to spacetime fluctuations about the flat background. An arbitrary number of interacting bosonic and fermionic particles are considered. A…
A quantum unitary evolution alternated with measurements is simulated by a bubble filled with fictitious particles called amplitude quanta that move chaotically and can be transformed by the simple rules that look like chemical reactions. A…
Mechanical resonators are gradually becoming available as new quantum systems. Quantum optics in combination with optomechanical interactions (quantum optomechanics) provides a particularly helpful toolbox for generating and controlling…
The 1-D dimension harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. In the…
We study the dynamics of a two-level quantum system interacting with an external electromagnetic field periodic and quasiperiodic in time. The quantum evolution is described exactly by the classical equations of motion of a gyromagnet in a…
Exchange of quantum states between two interacting harmonic oscillator along their evolution time is discussed. It is analyzed the conditions for such exchange starting from a generic initial state and demonstrating that the effect occurs…