We study Kerr nonlinear resonators (KNR) driven by a continuous wave field in quantum regimes where strong Kerr interactions give rise to selective resonant excitations of oscillatory modes. We use an exact quantum theory of KNR in the framework of t
he Fokker-Planck equation without any quantum state truncation or perturbation procedure. This approach allows non-perturbative consideration of KNR for various quantum operational regimes including cascaded processes between oscillatory states. We focus on understanding of multi-photon non-resonant and selective resonant excitations of introcavity mode depending on the detuning, the amplitude of the driving field and the strength of nonlinearity. The analysis is provided on the base of photon number distributions, the photon-number correlation function and the Wigner function.
We investigate temperature reservoir effects in a lossy Kerr nonlinear resonator considering selective excitation of ooscillatory mode driven by a sequence of Gaussian pulses. In this way, we analyze time-dependent populations of photon-number states
and quantum statistics on the base of second-order photon correlation function in one-photon and two-photon transitions. The effects coming from thermal reservoirs are interesting for performing more realistic approach to generate Fock states and for study phenomena connecting quantum engineering and temperature. We also study the role of pulse-shaping effects during selective excitation.
We study the vacuum radiative corrections to energy levels of a confined electron in quantum rings. The calculations are provided for the Lamb shift of energy levels in low-momentum region of virtual photons and for both one-dimensional and two-dimen
sional quantum rings. We show that contrary to the well known case of a hydrogen atom the value of the Lamb shift increases with the magnetic momentum quantum number m. We also investigate the dependence of the Lamb shift on magnetic flux piercing the ring and demonstrate a presence of magnetic-flux-dependent oscillations. For one-dimensional ring the value of the shift strongly depends on the radius of the ring. It is extremely small for semiconductor rings but can attain measurable quantities in natural organic ring-shape molecules, such as benzene, cycloalcanes and porphyrins.
In this paper, the purity of quantum states is applied to probe chaotic dissipative dynamics. To achieve this goal, a comparative analysis of regular and chaotic regimes of nonlinear dissipative oscillator (NDO) are performed on the base of excitatio
n number and the purity of oscillatory states. While the chaotic regime is identified in our semiclassical approach by means of strange attractors in Poincare section and with the Lyapunov exponent, the state in the quantum regime is treated via the Wigner function. Specifically, interesting quantum purity effects that accompany the chaotic dynamics are elucidated in this paper for NDO system driven by either: (i) a time-modulated field, or (ii) a sequence of pulses with Gaussian time-dependent envelopes.
We study the theory of linearly chirped biphoton wave-packets produced in two basic quasi-phase-matching configurations: chirped photonic-like crystals and aperiodically poled crystals. The novelty is that these structures are considered as definite
assembles of nonlinear layers that leads to detailed description of spontaneous parametric down-conversion (SPDC) processes through the discrete Gauss sums. We demonstrate that biphoton spectra for chirped photonic crystals involving a small number of layers consist from definite well-resolved spectral lines. We also discuss the forming of broadband spectra of signal (idler) waves in SPDC for both configurations as number of layers increases as well as in dependence of chirping parameters .
In spatially structured strong laser fields, quantum electrodynamical vacuum behaves like a nonlinear Kerr medium with modulated third-order susceptibility where new coherent nonlinear effects arise due to modulation. We consider the enhancement of v
acuum polarization and magnetization via coherent spatial vacuum effects in the photon-photon interaction process during scattering of a probe laser beam on parallel focused laser beams. Both processes of elastic and inelastic four wave-mixing in structured QED vacuum accompanied with Bragg interference are investigated. The phase-matching conditions and coherent effects in the presence of Bragg grating are analyzed for photon-photon scattering.
