acta physica slovaca, vol. 49, August 1999, no. 4

Proceedings of the 6th Central-European Workshop on Quantum Optics,   
Chudobín, April 30 - May 3, 1999

Edited by Vladimír Buzek and Gabriel Drobný

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INVITED PAPERS

 
Nonlocality of the Einstein-Podolsky-Rosen state in the phase space

Author(s):  K. Banaszek, K. Wódkiewicz

Abstract: We discuss violation of Bell inequalities by the regularized Einstein-Podolsky-Rosen (EPR) state, which can be produced in a quantum optical parametric down-conversion process. We propose an experimental photodetection scheme to probe nonlocal quantum correlations exhibited by this state. Furthermore, we show that the correlation functions measured in two versions of the experiment are given directly by the Wigner function and the Q function of the EPR state. Thus, the measurement of these two quasidistribution functions yields a novel scheme for testing quantum nonlocality.  [page 491]

 
Resonance fluorescence of a trapped four-level atom with bichromatic driving

Author(s):  J. Bergou, M. Jakob, Y. Abranyos

Abstract: The RF spectrum of a bichromatically driven four-level atom is polarization dependent. Very narrow lines occur in the incoherent parts of the spectrum for polarization directions which are different from that of the driving fields. The degree of squeezing has a maximum of $56\%$ which should make it easily observable. The second-order correlation function exhibits antibunching for zero time delay and strong superbunching for certain values of the interaction parameter and time delay. For these parameters resonant two-photon emission takes place in the form of polarization entangled photon pairs. The system can be a novel source of photons in the EPR and/or Bell states. Some experiments will be proposed which make use of this unique source.  [page 501]

 
Group theoretical quantum tomography

Author(s):  G. M. D'Ariano

Abstract: A general method is presented for estimating the ensemble average of all operators of an arbitrary quantum system from a set of measurements of a quorum of observables. The quorum--i. e. a ``complete'' set of noncommuting observables for determining the quantum state of the system--is generated from a maximal commuting set of observables--the ``seed observables''--under the action of a dynamical group of the quantum system. A method for deconvolving noise of any kind in the measurement is given in terms of the completely positive (CP) map pertaining the noise. This approach leads to a group theoretical classification of physically realizable quantum tomographic machines. These are made of two devices: 1) a measuring apparatus for the seed observables; 2) a transformation apparatus that achieves the dynamical group. Examples of applications are given in different physical contexts.  [page 513]

 
Quantum state engineering with photonic qubits

Author(s):  K. M. Gheri, P. Törmä, P. Zoller

Abstract: We outline a scheme for the generation of a train of entangled single-photon wavepackets using standard CQED-techniques. The generated photons are transferred to the continuum outside the resonator through cavity loss in the form of wavepackets each of which may be regarded as a logical qubit. We show that undesired decoherence effects can be efficiently reduced in the considered scheme.  [page 523]

 
Secret sharing via quantum entanglement

Author(s):  M. Hillery, V. Buzek

Abstract: Secret sharing is a procedure for splitting a message into several parts so that no single part is sufficient to read the message, but the entire set is. This procedure can be implemented using either GHZ states or two-particle entangled states. In the quantum case the presence of an eavesdropper will introduce errors so that her presence can be detected. We also discuss how quantum information can be split into parts so that the message can be reconstructed from a sufficiently large subset of the parts.  [page 533]

 
Decay control in dissipative quantum systems

Author(s):  A. G. Kofman, G. Kurizki

Abstract: We point out that the quantum Zeno effect, i.e., inhibition of spontaneous decay by frequent measurements, is observable only in spectrally finite reservoirs, i.e., in cavities and waveguides, using a sequence of evolution-interrupting pulses or randomly-modulated CW fields. By contrast, such measurements can only accelerate decay in free space.  [page 541]

 
Security of quantum cryptography with realistic sources

Author(s):  N. Lütkenhaus

Abstract: The interest in practical implementations of quantum key distribution (QKD) is steadily growing. However, there is still a need to give a precise security statement which adapts to realistic implementation. In this paper I give the effective key rate we can obtain in a practical setting within the scenario of security against individual attacks by an eavesdropper. It illustrates previous results that high losses together with detector dark counts can make secure QKD impossible.  [page 549]

 
Modifying the lifetime of an unstable system by an intense electromagnetic field

Author(s):  S. Pascazio, P. Facchi

Abstract: We study the temporal behavior of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. We analyze the dependence of the lifetime of the initial state on the intensity of the laser field. The phenomenon we discuss is related to both electromagnetic induced transparency and quantum Zeno effect.  [page 557]

 
The issue of phases in quantum measurement theory

Author(s):  A. K. Pati

Abstract: The issue of phases is always very subtle in quantum world and many of the curious phenomena are due to the existence of the phase of the quantum mechanical wave function. We investigate the issue of phases in quantum measurement theory and predict a new effect of fundamental importance. We call a quantum system under goes a quantum Zeno dynamics (QZD) when the unitary evolution of a quantum system is interrupted by a sequence of measurements. In particular, We investigate the effect of repeated measurements on the geometric phase and show that the quantum Zeno dynamics can inhibit its development under a large number of measurement pulses. It is interesting to see that neither the total phase nor the dynamical phase goes to zero under large number of measurements. This new effect we call as the ``quantum Zeno Phase effect'' (QZPE) in analogous to the quantum Zeno effect (QZE) where the repeated measurements inhibit the transition probability. This ``quantum Zeno Phase effect'' can be proved within von Neumann's collapse mechanism as well as using a continuous measurement model. So the effect is really independent of any particluar measurement model considered. Since the geometric phase attributes a memory to a quantum system our results also proves that the path dependent memory of a system can be erased by a sequence of measurements. The QZPE provides a way to control and manipulate the phase of a wave function in an interference set up. Finally, we stress that the quantum Zeno Phase effect can be tested using neutron, photon and atom interference experiments with the presently available technology.  [page 567]

 
Quantum electromagnetic fields in the neighbourhood of an atom

Author(s):  E. A. Power, T. Thirunamachandran

Abstract: Non-relativistic quantum electrodynamics is used to find the Heisenberg electric and magnetic field operators when a single atom perturbs the vacuum. The expectation values of these fields for particular quantum states are found, and the differences associated with the choice between minimal and multipolar coupling are discussed. The effect of these fields on nearby atoms is shown to give Casimir potentials. Finally an extension of the theory to allow for Roentgen currents- the source of which being moving dipoles- is made.  [page 579]

 
Spontaneous decay in the presence of absorbing dielectric bodies

Author(s):  S. Scheel, L. Knöll, D.-G.Welsch

Abstract: We present a formalism for studying the influence of dispersive and absorbing dielectric bodies on a radiating atom in the framework of quantization of the phenomenological Maxwell equations for given complex permittivities of the bodies. In Markov approximation, the rate of spontaneous decay and the line shift associated with it can then be related to the complex permittivities and geometries of the bodies via the dyadic Green function of the classical boundary value problem of electrodynamics - a result which is in agreement with second-order calculations for microscopic model systems. The theory is applied to an atom near a planar interface as well as to an atom in a spherical cavity. The latter, also known as the real-cavity model for spontaneous decay of an excited atom embedded in a dielectric, is compared with the virtual-cavity model. Connections with other approaches are mentioned and the results are compared.  [page 585]

 
Atoms in a narrow-bandwidth squeezed vacuum

Author(s):  R. Tanas

Abstract: Two possible descriptions of evolution of a two-level atom driven by a strong laser field and subjected to a squeezed vacuum with finite bandwidth are discussed. One is the master equation approach in which the squeezed vacuum is treated as a Markovian reservoir to the atom, and the other is the coupled-systems (or cascaded-systems) approach in which the degenerate parametric oscillator (DPO) producing squeezed vacuum is a part of the system. Examples of optical spectra obtained using both approaches are given.  [page 595]

 
Pairing of fermions in optical lattices

Author(s):  P. Törmä, D. Jaksch

Abstract: We consider weakly interacting fermionic atoms in optical lattices. We show that the system can be described by the Hubbard model, and solve the BCS gap equations. Cooper-pairing is shown to take place for parameter values which are obtainable for alkali atoms in optical lattices.  [page 605]

 
Discrete phase-space calculus for quantum spins based on a reconstruction method using coherent states

Author(s):  S. Weigert

Abstract: To reconstruct a mixed or pure quantum state of a spin s is possible through coherent states: its density matrix is fixed by the probabilities to measure the value s along 4s(s+1) appropriately chosen directions in space. Thus, after inverting the experimental data, the statistical operator is parametrized entirely by expectation values. On this basis, a symbolic calculus for quantum spins is developed, the ``expectation-value representation.'' It resembles the Moyal representation for SU(2) but two important differences exist. On the one hand, the symbols take values on a discrete set of points in phase space only. On the other hand, no quasi-probabilities--that is, phase-space distributions with negative values--are encountered in this approach.  [page 613]

 
Entanglement swapping with PDC sources

Author(s):  M. Zukowski, D. Kaszlikowski

Abstract: We show that the possibility of distinguishing between single and two photon detection events is not a necessary requirement for the proof that recent operational realization of entanglement swapping cannot find a local realistic description. We propose a simple modification of the experiment, which gives a richer set of interesting phenomena.  [page 621]

CONTRIBUTED PAPERS

 
Two-mode correlated states in cavity with injected atoms

Author(s):  G. Ariunbold, J. Perina, Ts. Gantsog, F. A. A. El-Orany

Abstract: We study a model of a lossless micromaser with two-level atoms interacting with a two-mode cavity field via two-photon transitions. We show that when the atoms are initially prepared in a superposition state then there is an operation regime of the micromaser when the cavity field evolves into a two-mode squeezed vacuum.  [page 627]

 
Maximum-likelihood algorithm for quantum tomography

Author(s):  K. Banaszek

Abstract: Optical homodyne tomography is discussed in the context of classical image processing. Analogies between these two fields are traced and used to formulate an iterative numerical algorithm for reconstructing the Wigner function from homodyne statistics.  [page 633]

 
Reconstruction of the density matrix as a constrained optimization problem

Author(s):  K. Banaszek, G. M. D'Ariano, M.G. A. Paris, M. F. Sacchi

Abstract: We present a numerical algorithm for the maximum-likelihood estimation of the density matrix, and apply it to the homodyne tomography of a single-mode radiation field. The algorithm is based on a specific form of the Gauss decomposition for positive definite Hermitian matrices. Results from Monte Carlo simulated experiments are presented.  [page 639]

 
Determination of the Wigner function from photon statistics

Author(s):  K. Banaszek, C. Radzewicz, K. Wódkiewicz, J. S. Krasinski

Abstract: We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator for the phase space displaced quantum state.  [page 643]

 
Malus' law and quantum information

Author(s):  C. Brukner, A. Zeilinger

Abstract: The information content of the most elementary quantum system is represented by one single proposition. Therefore such an elementary system can only give a definite result in one specific experimental arrangement. A change of experimental parameters then necessarily implies probabilistic measurement results in the new experimental arrangement. Assumption of the invariance of the information content of a system upon change of the representation of our knowledge of the system together with homogeneity of the experimental parametric axis leads to the Malus' law in quantum mechanics, the familiar sinusoidal relation between the probabilities and the laboratory parameters.  [page 647]

 
Conditional quantum state engineering at beam splitter arrays

Author(s):  J. Clausen , M. Dakna, L. Knöll, D.-G. Welsch

Abstract: The generation of arbitrary single-mode quantum states from the vacuum by alternate coherent displacement and photon adding as well as the measurement of the overlap of a signal with an arbitrarily chosen quantum state are studied. With regard to implementations, the transformation of the quantum state of a traveling optical field at an array of beam splitters is considered, using conditional measurement. Allowing for arbitrary quantum states of both the input reference modes and the output reference modes on which the measurements are performed, the setup is described within the concept of two-port non-unitary transformation, and the overall non-unitary transformation operator is derived. It is shown to be a product of operators, where each operator is assigned to one of the beam splitters and can be expressed in terms of an s-ordered operator product, with s being determined by the beam splitter transmittance or reflectance. As an example we discuss the generation of and overlap measurement with Schrödinger-cat-like states.  [page 653]

 
Generation and measurement of nonclassical states by quantum Fock filter

Author(s):  G. M. D'Ariano, L. Maccone, M. G. A. Paris, M. F. Sacchi

Abstract: We study a novel optical setup which selects a specific Fock component from a generic input state. The device allows to synthesize number states and superpositions of few number states, and to measure the photon distribution and the density matrix of a generic signal.  [page 659]

 
Synthesis of operators: universal quantum gates for a trapped ion

Author(s):  G. Drobný, B. Hladký, V. Buzek

Abstract: We investigate physical implementations of universal quantum gates which perform arbitrary unitary transformations of unknown inputs. In particular, two approaches for synthesis of arbitrary unitary operators acting on vibrational states of a trapped ion are considered.  [page 665]

 
Wigner function and coherence properties of cold and thermal neutrons

Author(s):  P. Facchi, A. Mariano, S. Pascazio

Abstract: We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek et al., in which a polarized neutron crosses a magnetic field that is orthogonal to its spin, producing highly non-classical states. The quantal coherence is extremely sensitive to the field fluctuation at high neutron momenta. A ``decoherence parameter" is introduced in order to get quantitative estimates of the losses of coherence.  [page 671]

 
Berry phase due to quantum measurements

Author(s):  P. Facchi, S. Pascazio

Abstract: The usual, ``static'' version of the quantum Zeno effect consists in the hindrance of the evolution of a quantum systems due to repeated measurements. There is however a ``dynamic'' version of the same phenomenon, first discussed by von Neumann in 1932 and subsequently explored by Aharonov and Anandan, in which a system is forced to follow a given trajectory. A Berry phase appears if such a trajectory is a closed loop in the projective Hilbert space. A specific example involving neutron spin is considered and a similar situation with photon polarization is investigated.  [page 677]

 
On the bistability of parametric generation process

Author(s):  R. Filip

Abstract: Non-equilibrium steady state transitions in nonlinear parametric generation process are analyzed. When driven by external coherent light in signal and idler beams, the parametric generator exhibits a strongly bistable behaviour. Under certain circumstances, the bistabilities in signal and idler beams mutually compete. From presented analysis, it follows, the competition can in principle be controlled with the input light signals in a way to implement some model of measurement device. In particular, we suggest operation of the nonlinear parametric generator as an ``all optical comparator'', analogous to routinely used electronic devices.  [page 683]

 
Quantum phase properties of Kerr couplers

Author(s):  J. Fiurásek, J. Krepelka, J. Perina

Abstract: We use the concept of the phase space and the Husimi quasidistribution to study quantum phase properties of the optical fields propagating in Kerr couplers. Fourier coefficients of the phase distributions are introduced and utilized to examine their spatial development. The collapses and revivals of the mean photon number oscillations between the two waveguides are due to the bifurcation of the phase-difference probability distribution, which has a two-fold symmetry in the interval of collapse.  [page 689]

 
Decoherence due to statistically distributed jump-like events

Author(s):  U. Herzog

Abstract: We investigate an interacting quantum system which is additionally subjected to jump-like events occurring at time instants that are distributed according to a given statistics. Assuming that the latter can be descibed by a stationary renewal process, we consider a Poissonian and a regular distribution as well as a super-Poissonian one. To apply our method we study a two-level system being resonantly driven by a classical field and undergoing jump-like phase decoherence (e.g. caused by quantum-nondemolition measurements of the level population). We obtain analytical results for the steady state and for the quantum Zeno dynamics that illustrate the influence of the statistics. It turns out that a Poissonian distribution of the dephasing events is still half as effective as a regular one in increasing the lifetime of the initial state.  [page 695]

 
Electron antibunching

Author(s):  H. Kiesel, F. Hasselbach, T. Tyc, M. Lenc

Abstract: Two-electron correlation function is introduced and the basic property of multiparticle electron correlations -- antibunching -- is derived from its form. Two-particle correlations of photons and electrons are compared as well as the influence of a Wien filter on one- and two-electron coherence.  [page 701]

 
Three-photon states for quantum teleportation

Author(s):  M. Koniorczyk, J. Janszky, Z. Kis

Abstract: A three-particle generalization of the quantum teleportation of polarization states is discussed. A possible nonlinear optical process is discussed, which can lead the required EPR-states. The Bell-state analysis of our three-photon Bell-states applying a beam-splitter and polarization analyzers is discussed.  [page 707]

 
Finite energy states for periodically kicked nonlinear oscillator

Author(s):  W. Leonski, R. Tanas

Abstract: We study a nonlinear oscillator interacting with a one-mode cavity field. We assume, that the cavity is periodically kicked by a series of ultra-short coherent pulses. We show that for a special choice of parameters the system evolution is restricted to a finite set of n-photon states. In consequence, the mean energy of the cavity remains finite despite the fact that the cavity is continuously pumped. We study the properties of the cavity field showing that the field exhibits nonclassical features.  [page 713]

 
From the continuous measurement theory back to operator-valued processes

Author(s):  A. Luks, V. Perinová

Abstract: We show that a continuous-time Hermitian operator-valued process is measured in the continuous measurement. We illustrate the utility of the eigenkets of this quantum process for the explicit solution of the quantum stochastic equation describing the interaction between a field and a reservoir.  [page 719]

 
Stochastic control of quantum dynamics for trapped systems

Author(s):  S. Mancini

Abstract: A stochastic control of the vibrational motion for a single trapped ion/atom is proposed. It is based on the possibility to continously monitor the motion through a light field meter. The output from the measurement process should be then used to modify the system's dynamics.  [page 725]

 
Quantum statistics of two coupled down-convertors. Part I

Author(s):  J. Herec

Abstract: The quantum-statistical properties of light beams in a directional symmetric nonlinear coupler composed of two nonlinear waveguides operating by the down-conversion processes are examined. By means of short-length approximation non-classical behaviour of single and compound modes in such a device is analyzed. Linear and nonlinear mismatches are taken into account.  [page 731]

 
Quantum statistics of two coupled down-convertors. Part II

Author(s):  L. Mista Jr.

Abstract: In a framework of strong-pumping approximation, the quantum dynamics and statistics of the coupler composed of two waveguides based on the down-conversion processes are investigated. The qualitative discussion of possibilities of generation of non-classical light based on the numerical calculations is performed.  [page 737]

 
Reconstruction of quantum states with binary detectors

Author(s):  D. Mogilevtsev

Abstract: The scheme is proposed to perform the reconstruction of a multi-mode quantum state of light with help of non-ideal detectors able to test only presence or absence of photons.  [page 743]

 
Testing of operational phase concepts

Author(s):  J. Rehácek, Z. Hradil, J. Perina, M. Zawisky, H. Rauch, S. Pascazio

Abstract: Various phase concepts may be treated as special cases of the maximum likelihood estimation. For example, the discrete the operational phase of Noh, Fougères and Mandel is obtained for continuous Gaussian signals with phase modulated mean. Although the Gaussian estimation gives a satisfactory approximation for fitting the phase distribution of almost any state the optimal phase estimation offers in certain cases a measurably better performance. This has been demonstrated in a neutron-optical experiment.  [page 749]

 
Quantum cloning and signaling

Author(s):  C. Simon, G. Weihs, A. Zeilinger

Abstract: We discuss the close connections between cloning of quantum states and superluminal signaling. We present an optimal universal cloning machine based on stimulated emission recently proposed by us. As an instructive example, we show how a scheme for superluminal communication based on this cloning machine fails.  [page 755]

 
On decoherence in neutron interferometry

Author(s):  M. Suda

Abstract: Consistency concerning decoherence in neutron interferometry is achieved by using stochastic differential equations. In interferometry inhomogeneities of the density and/or of the surface roughness of a phase shifter are of great influence to coherent beam superposition. The interferometric process is described by Wigner's quasi-probability which is a solution of the diffusion equation.  [page 761]

 
Phase distribution of the micromaser field with injected atomic coherence

Author(s):  J. Skvarcek, M. Hillery

Abstract: We present the solution for the phase distribution of the steady state micromaser field for the case with injected atomic coherence in the semiclassical approximation.  [page 765]

 
Realizations of SU(1,1) by boson operators with application to phase states

Author(s):  A. Wünsche

Abstract: A class of realizations of the abstract Lie algebra su(1,1) in the basis (K_-,K₀,K₊) by one-mode boson operators $(a,a^\dagger)$ is derived. It corresponds to the unitary irreps (irreducible representations) of SU(1,1) with a state of lowest weight which are characterized by a number k>0. The SU(1,1) coherent states to these irreps are discussed and it is shown that they are eigenstates of a non-Hermitean operator. For each k>0, there exists a countable number of subdivisions of the Fock space spanned by the basis vectors $\vert sn+j\rangle,\: (n=0,1,\ldots)$ with fixed values $s=1,2,\ldots$ and $j=0,\ldots,s-1$. The same is true for the realizations of the Heisenberg-Weyl algebra in the Fock space by basis operators $(A,A^\dagger,I=[A,A^\dagger])$. The coherent phase states are discussed as an example of SU(1,1) coherent states. Some of their properties are related to the unorthodox integer function $f(z)=\sum_{n=0}^\infty z^n/\sqrt{n!}$ for which the first 4 pairs of its complex conjugated zeros are determined. The phase-optimized states are discussed and it is found that they hardly can be accepted as really ``phase-optimized''. The roots of the failure to find a Hermitean phase operator are found already in classical mechanics in a grave topological defect of the transition from canonical coordinates to action-angle coordinates as a canonical transformation in the coordinate origin.  [page 771]

 
Quantum superpositions of two coherent states generation based on a single-atom conditional measurement

Author(s):  A. Napoli, A. Messina

Abstract: A new and simple way of engineering quantum superpositions of two coherent states of a single-mode quantized electromagnetic field is presented. Our proposal, developed in the context of micromaser theory, exploits the passage of one atom only through a high-Q bimodal cavity supporting two electromagnetic modes of different frequencies.  [page 783]

 
List of participants & conference photo (Warning: too large ps file)

Related links:         [Acta PhysicaSlovaca]         [Institute of Physics, Bratislava]         [Quantum Optics Group, Bratislava]