Gabriel Drobný

Quantum tomography via the MaxEnt principle

Abstract We show how the maximum entropy (MaxEnt) principle can be efficiently used for a reconstruction of quantum states of light from incomplete tomographic data. This MaxEnt reconstruction scheme is several orders more efficient than the standard inverse Radon transformation or the reconstruction via direct sampling using pattern functions.

Reconstruction of quantum states of spin systems via the Jaynes principle of maximum entropy

We apply the Jaynes principle of maximum entropy for the partial reconstruction of correlated spin states. We determine the minimum set of observables which is necessary for the complete reconstruction of the most correlated states of systems composed of spins 1/2 (e.g. the Bell and the Greenberger-Horne-Zeilinger states). We investigate to what extent an incomplete measurement can reveal non-classical features of correlated spin states.

The system of N two-level atoms interacting with a field mode: entanglement and parametric approximation

Abstract We study the entanglement of the cavity field mode to the ensemble of two-level atoms when their interaction is ruled by the Dicke model. Our investigation is focused mainly on initial states with fully excited atomic system and an intense cavity field mode. We give an analysis of the entanglement on the short as well as the long time scale. We derive limit expressions for the entanglement for the first moments of the evolution where the entanglement reaches constant value. We show that in the early moments of the evolution an almost pure state can be generated under suitable conditions when the intensity of the field is ∼ N. On the long time scale we point out the appearance of a clear decrease of the entanglement associated with the collapse-revival phenomenon of the mean photon number in this model. The bifurcation of initially a gaussian Q-function of the field mode into N + 1 peaks of different weight factors is shown. Finally the results known for the Jaynes-Cummings model are compared with the obtained results.

Quantum synthesis of arbitrary unitary operators

Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for realization of any unitary operator which acts on a (truncated) Hilbert space of a single bosonic mode. In particular, we consider a physical implementation of unitary transformations acting on 1-dimensional vibrational states of a trapped ion. As an example we present an algorithm which realizes the discrete Fourier transform.

QUANTUM-STATE SYNTHESIS OF MULTIMODE BOSONIC FIELDS : PREPARATION OF ARBITRARY STATES OF TWO-DIMENSIONAL VIBRATIONAL MOTION OF TRAPPED IONS

We present a universal algorithm for an efficient deterministic preparation of an arbitrary two-mode bosonic state. In particular, we discuss in detail preparation of entangled states of a two-dimensional vibrational motion of a trapped ion via a sequence of laser-stimulated Raman transitions. Our formalism can be generalized for multimode bosonic fields. We examine stability of our algorithm with respect to a technical noise.

The classical parametric approximation for three-wave interactions

We study sufficient conditions for the applicability of the classical parametric approximation in three-wave interactions when the pump intensity is very large compared to signal and idler intensity. To derive such conditions we express the exact classical solutions given by Jacobian elliptic functions in terms of hyperbolic functions. Thereby the first minimum of the pump intensity is correctly described but the periodicity is lost. We derive new approximations for the initial conditions using pump coordinate scaling and find the interval that defines complete pump depletion. We show that the classical parametric approximation with a fixed and sharp pump amplitude and phase can be used for an increasing fraction of this interval if the pump intensity is made to grow. By choosing higher and higher pump intensities the nonlinearity is shifted to the end of that interval. As an instructive example for the application of these findings the generation of two-mode squeezing is briefly considered.

Phase properties of field modes in the process of kth harmonic generation

Abstract We study the phase properties of the two field modes within the frame of the process of k th harmonic generation with a quantized fundamental mode. Using the Pegg-Barnett phase formalism the joint phase distribution is calculated numerically. It is shown that in the initial moments of the evolution the degree of the process k does not affect significantly the phase distribution.

Quantum phase properties of the process of k-photon down conversion with quantized pump

Abstract We study the phase properties of the field modes in the process of k -photon down conversion with quantized pump using the Peggy-Barnett phase formalism. The dynamics of the system is solved numerically via the diagonalization of the interaction hamiltonian. The behavior in the short and long time limit is discussed and compared to previous results related to the treated problem. In order to understand our results an exactly soluble model of the linearized k -photon down conversion is presented.

Stimulated emission via quantum interference: Scattering of one-photon packets on an atom in a ground state

Abstract Usually it is assumed that the stimulated emission appears as a consequence of the Bose—Einstein statistics of photons and that to observe this effect at least two excitations have to be initially present in the atom—field system. That is, both the atom and the electromagnetic field have to be excited. In this paper we show that stimulated emission can appear exclusively as a consequence of quantum interference in a system with just a single excitation. Specifically, we consider a single two-level atom which is initially in its lower energy state and it interacts with a single-photon multi-mode wave packet. We show that for a proper choice of the photon-wave packet the atom can exhibit stimulated emission.

Collapse-revival phenomenon in the process of k-photon down conversion with superpositions of number states

Abstract We calculate numerically the time evolution of the mean photon number in the process of k-photon down conversion process with quantized pump. The pump mode was supposed to be initially in a superposition of number states and the down converted mode in a number state. We analysed in some detail the influence of the initial field statistics of the pump mode as well as the presence of non-vacuum number states in the down converted mode on the appearance of collapses and revivals.