Search results for "Oscillator"

Synchronizing Quantum Harmonic Oscillators through Two-Level Systems

2017

Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical mechanism that forces the system to oscillate at a single frequency with a predictable and tunable phase difference. Finally, the scheme is generalized to the case of $N$ oscillators and $M(<N)$ two-level systems.

Integrated Generation of High-dimensional Entangled Photon States and Their Coherent Control

2017

Exploiting a frequency-domain approach, we demonstrate the generation of high-dimensional entangled quantum states with a Hilbert-space dimensionality larger than 100 from an on-chip nonlinear microcavity, and introduce a coherent control platform using standard telecommunications components.

Timing Control of a Heralded Single Photon Emission

2012

We experimentally demonstrate controlling the emission timing of a heralded single photon from a non-degenerate optical parametric oscillator, by placing another quickly tunable cavity at the exit as a shutter.

𝒟 $\mathcal {D}$ -Deformed Harmonic Oscillators

2015

We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint hamiltonians whose eigenvalues and eigenvectors can be found adopting the quite general framework of the so-called $\cal{D}$-pseudo bosons. In particular, we show that several models previously introduced in the literature perfectly fit into this scheme.

Riccati-Padé quantization and oscillatorsV(r)=grα

1993

We develop an alternative construction of bound states based on matching the Riccati threshold and asymptotic expansions via their two-point Pad\'e interpolation. As a form of quantization it gives highly accurate eigenvalues and eigenfunctions.

Nonstationary oscillations in gyrotrons

2001

The onset of stochastic oscillations in gyrotrons is studied by means of the self-consistent theory describing nonstationary processes. Complicated alternating sequences of regions of stationary, automodulation, and chaotic oscillations are found in the plane of the generalized gyrotron variables: cyclotron resonance mismatch and dimensionless current. The results of the investigations are important in connection with attempts to increase the output power of gyrotrons by raising the current.

From self-adjoint to non self-adjoint harmonic oscillators: physical consequences and mathematical pitfalls

2013

Using as a prototype example the harmonic oscillator we show how losing self-adjointness of the hamiltonian $H$ changes drastically the related functional structure. In particular, we show that even a small deviation from strict self-adjointness of $H$ produces two deep consequences, not well understood in the literature: first of all, the original orthonormal basis of $H$ splits into two families of biorthogonal vectors. These two families are complete but, contrarily to what often claimed for similar systems, none of them is a basis for the Hilbert space $\Hil$. Secondly, the so-called metric operator is unbounded, as well as its inverse. In the second part of the paper, after an extensio…

A simple method for limiting the quadrature oscillator amplitude

1981

The quantum relativistic harmonic oscillator: generalized Hermite polynomials

1991

A relativistic generalisation of the algebra of quantum operators for the harmonic oscillator is proposed. The wave functions are worked out explicitly in configuration space. Both the operator algebra and the wave functions have the appropriate c→∞ limit. This quantum dynamics involves an extra quantization condition mc2/ωℏ = 1, 32, 2, … of a topological character.

Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy

2012

In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory …