Jaromír Křepelka

Stimulated Raman Scattering of Squeezed Light with Pump Depletion

Abstract Using the approximation of small fluctuations around a stationary point, photon statistics and squeezing of vacuum fluctuations are derived in stimulated Raman scattering including the coupling of photon-photon and photon-phonon modes. The depletion of pump light is described and it is shown that a regime of inversion of the process is related to an increase in quantum fluctuations, which are finally reduced again, more in the anti-Stokes mode than in the Stokes mode. If the anti-Stokes coupling is stronger than the Stokes coupling, then an oscillating behaviour of the statistical characteristics occurs and substantial squeezing can be found in photon-phonon modes.

Entropy of optical fields

A systematic approach to the use of entropy as a measure of noise and order in quantum optical fields is developed. The general definition of entropy, adopting the density matrix, is expressed in terms of both the eigenvalues of this operator and the quasidistribution function related to antinormal ordering of the field operators. Special states of optical fields, such as the Fock state, the coherent state, the chaotic state, single-mode and multimode two-photon coherent states, squeezed states and the shifted gaussian state, including the time development under a particular interaction, are considered. The general conclusions reached are illustrated by numerical results.

Photon Statistics of Non-classical Fields

The photon statistics of radiation of a damped harmonic oscillator with an initial squeezed state are investigated. It is shown that a generalized model of the superposition of coherent and chaotic fields involving possibly negative noise is appropriate in this case. The influence of quantum damping can easily be recognized in this process. A relationship between sub-Poissonian statistics and squeezing is thoroughly discussed. A degenerate parametric process is related to the investigated model.

State Reduction for Correlated Photons and Eigenstates of Unitarily and Non-unitarily Displaced Number Operator

Abstract The number-quadrature minimum-uncertainty states after rotation and displacement emerge in the parametric down-conversion followed by photon number measurement in the idler mode when the coherent state inputs. Again, the state generated in the signal mode by the reduction is described by the principally measurable quantum-statistical tools.

Extended number state basis and number-phase intelligent states of light field II. The reduced number-sine intelligent and Jackiw states

The number-sine intelligent state is introduced for the extended Hilbert space and reduced to serve as an approximation to the Jackiw number-sine intelligent state. Usual and modified statistical and uncertainty characteristics of these states are determined and compared. A new technique is used for reconstructing the crescent state of Kitagawa and Yamamoto and studying the properties of the reduced number-sine intelligent state.

Quantum correlation and entanglement between an ionizing system and a neighboring atom interacting directly and via a quantized field

Quantum correlations between two neighbor atoms are studied. It is assumed that one atomic system comprises a single auto-ionizing level and the other atom does not contain any auto-ionizing level. The excitation of both atoms is achieved by the interaction with the same mode of the quantized field. It is shown that the long-time behavior of two atoms exhibits quantum correlations even when the atoms do not interact directly. This can be shown using the optical excitation of the neighbor atom. Also a measure of entanglement of two atoms can be applied after reduction of the continuum to two levels.

Photon statistics of nonclassical radiation in second harmonic generation

The Fokker-Planck equation approach to the second harmonic generation is adopted to obtain a set of moment equations for this process. This set of equations is truncated in consistence with a model of generalized superposition of coherent fields and quantum noise, which provides equations of motion for unknown quantities in the model. Numerical solution of these equations provides at once the photon number distribution and its factorial moments including fully quantum features of radiation such as its sub-Poisson behaviour and squeezing of vacuum fluctuations. Limits of this approximation are discussed and numerical results are provided.

Dynamics of nonclassical properties of two- and four-mode Bose–Einstein condensates

A two-mode Bose–Einstein condensate (BEC) prepared in a Fock state initially evolves due to the coupling of modes. The time evolution of nonclassical properties exhibits that inter-mode entanglement, single-mode and higher order antibunching are present. A four-mode BEC is considered with the initial minimum-energy Bloch states, and the nonclassical behaviour is confirmed.

Quantum statistics of stimulated Raman and hyper-Raman scattering of squeezed light with pump depletion

Abstract Using the approximation of small fluctuations around a stationary solution, photon statistics and quadrature variances are derived in stimulated Raman and hyper-Raman scattering including the coupling of pumping, Stokes, anti-Stokes and phonon modes. The depletion of pump light is included. Compared to Raman scattering, additional regimes to generate anti-bunched, sub-Poisson and squeezed light were found caused by self-interaction of the pump mode. It was possible to include effects of nonlinear dynamics, initial squeezing of radiation and phonon system, external noise and losses.

Squeezing and sub-Poisson statistics in three-mode interactions

Abstract A unique approach to the photon statistics in nonlinear optical interactions is suggested based on the use of moment equations and generalized superposition of coherent fields and quantum noise. Non-classical features such as squeezing of fluctuations and sub-Poisson statistics are derived for finite interaction times in the three-mode interaction process and limits of the model are provided.