Related papers: Continuous-time quantum harmonic oscillator state …
Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
We perform a detailed analysis of the behavior of coherent and squeezed states undergoing time evolution. We calculate time dependence of expectation values of position and momentum in coherent and squeezed states (which can be interpreted…
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states…
Wave packets for the Quantum Non-Linear Oscillator are considered in the Generalized Coherent State framerwork. To first order in the non-linearity parameter the Coherent State behaves very similarly to its classical counterpart. The…
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
The harmonic oscillator is one of the simplest physical systems but also one of the most fundamental. It is ubiquitous in nature, often serving as an approximation for a more complicated system or as a building block in larger models.…
We consider the relations between nonstationary quantum oscillators and their stationary counterpart in view of their applicability to study particles in electromagnetic traps. We develop a consistent model of quantum oscillators with…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
Coherently displaced harmonic oscillator number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a…
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
In this work, we have applied the integrals of motion method in a nonunitary approach and so obtained the time-dependent displacement and squeezed parameters of the coherent squeezed states (CSS). On its turn, CSS for one-dimensional…
Cooling methods and particle slowers as well as accelerators are basic tools for fundamental research and applications in different fields and systems. We put forward a generic mechanism to scale the momentum of a particle, regardless of…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
In this article, results from the previous paper (I) are applied to calculations of squeezed states for such well-known systems as the harmonic oscillator, free particle, linear potential, oscillator with a uniform driving force, and…
Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we apply the quantum singular time dependent oscillator model to describe the relative one dimensional motion of two ions in a trap. We argue that the model can be…
In this paper, we first analyze a parametric oscillator with both mass and frequency time-dependent. We show that the evolution operator can be obtained from the evolution operator of another parametric oscillator with a constant mass and…
In quantum mechanics courses, students often solve the Schr\"odinger equation for the harmonic oscillator with time-independent parameters. However, time-dependent quantum harmonic oscillators are relevant in modeling several problems as,…