J. Křepelka

Multimode description of spontaneous parametric down-conversion

We derive the multimode generating function, joint photon-number distribution and joint integrated-intensity distribution for spontaneous parametric down-conversion in relation to measured experimental data.

Quantum-phase properties of the Kerr couplers

We use the concept of phase space and Husimi quasidistribution to derive joint-phase probability distribution and quantum-phase properties for the Kerr couplers. The exact numerical as well as approximate analytical solutions of the Schrodinger equation are found. The spatial development of the single-mode phase distributions and phase-difference distribution is demonstrated. The Fourier coefficients of the phase distributions are introduced and employed to describe quantum-phase behaviour. It is shown that the phase-difference evolution is closely connected to an energy exchange between two waveguides, which form the coupler. The collapses and revivals of the mean photon number oscillations are due to the bifurcation of the phase-difference probability distribution, which has a two-fold symmetry in the interval of collapse.

Effect of Kerr-like medium on a two-level atom in interaction with bimodal oscillators

In this article we study the effect of the Kerr-like medium on a system consisting of two-level atom and two fields injected simultaneously within perfect cavity. We assume that in the presence of the nonlinear Kerr coupler, the atom interacts with each field separately. The present system can be regarded as a co-directional nonlinear coupler composed of two Kerr nonlinear waveguides, where the atom–field interaction plays the role of the energy exchange between the waveguides. The system includes two effective different coupling parameters λ1 and λ2, such that each coupling connects the atom with one of the field mode. Moreover, it includes two different susceptibility factors, one represents self-coupling while the other is responsible for cross-action processes. Under certain conditions, the exact solution of the wavefunction in the Schrodinger picture is obtained and the Husimi quasidistribution is derived. A consideration of some physical phenomena, such as collapses and revivals is given, and the degree of entanglement is also discussed. The system is found to be sensitive to the variation of both mean photon numbers as well as to the Kerr-like medium.

Experimental joint signal-idler quasidistributions and photon-number statistics for mesoscopic twin beams

Joint signal-idler photoelectron distributions of twin beams containing several tens of photons per mode have been measured recently. Exploiting a microscopic quantum theory for joint quasidistributions in parametric down-conversion developed earlier we characterize properties of twin beams in terms of quasidistributions using experimental data. Negative values as well as oscillating behavior in the quantum region are characteristic for the subsequently determined joint signal-idler quasidistributions of integrated intensities. Also the conditional and difference photon-number distributions are shown to be sub-Poissonian and sub-shot-noise, respectively.

Joint distributions of multimode stimulated parametric down-conversion and controllable nonclassical effects

Based on recent results (Peřina and Křepelka 2006 Opt. Commun. 265 632) we derive and illustrate multimode joint photon-number distributions, integrated-intensity distributions, sum and difference distributions and conditional distributions for stimulated parametric down-conversion in the approximation of large degrees of freedom. The stimulated process can increase or decrease nonclassical effects from spontaneous processes and it can be used to control them.

Linear coupling, loss and gain of counterpropagating beams

We investigate counterpropagation of the two-mode input state in a corrugated waveguide, which reproduces a photonic band-gap structure. First assuming a gain medium, we model a distributed feedback laser as an amplifier. From this case we pass to the attenuator, which corresponds to a lossy medium. We determine the transmission and fidelity spectra for the waveguide in the dependence on a mismatch coefficient and a measure of losses.

Linear entropy and squeezing of the interaction between two quantum system described by su (1, 1) and su(2) Lie group in presence of two external terms

A Hamiltonian, that describes the interaction between a two-level atom (su(2) algebra) and a system governed by su(1,1) Lie algebra besides two external interaction, is considered. Two canonical transformations are used, which results into removing the external terms and changing the frequencies of the interacting systems. The solution of the equations of motion of the operators is obtained and used to discuss the atomic inversion, entanglement, squeezing and correlation functions of the present system. Initially the atom is considered to be in the excited state while the other systems is in the Perelomov coherent state. Effects of the variations in the coupling parameters to the external systems are considered. They are found to be sensitive to changing entanglement, variance and entropy squeezing.

A beam splitter with second-order nonlinearity modelled as a nonlinear coupler

We provide two quantum descriptions of a beam splitter with second-order nonlinearity. Models of nonlinear couplers could be the same. For simplicity, a symmetry of the device is assumed, which does not exclude various reflectivities. The models differ in taking into account the co-propagation of beams and replacing it by their counter-propagation. The unitary operators that evolve the input states into the output ones are calculated by using a momentum operator and the effective distance of presumed co-propagation and counter-propagation, respectively.

Quantum statistics and entanglement in a Raman process

A simple trilinear Hamiltonian is utilized for a description of the Raman effect. The method of invariant subspaces, which is suitable for numerical calculations in the Schrodinger picture, is analyzed. As an example of the numerical calculation, the time dependence of an entanglement measure, the so-called negativity, is found for the initial few-photon states. Most of the analysis is devoted to the Heisenberg picture, in which the perturbation expansions are known.