Annual Report 2006 - Univerzita Palackého v Olomoucioptics.upol.cz/userfiles/file/MIO_report_2006.pdfQuantum information experiments based on ber optics Lucie Barust kova , 1 Anton

Annual Report 2006Measurement and Information in Optics

MSM 6198959213

and

Center of Modern Optics

LC06007

This is the Annual Report 2006 of the projects supported by the Czech

Ministry of Education MSM 6198959213 Measurement and Information in

Optics and LC06007 Center of Modern Optics. The Report covers all the

activities carried on the Department of Optics, Palacky University within one

year period. The Report is written on ”one-page basis” where each activity and

results achieved should be described on a single page of standard format. We

believe that this is the most effective way how to inform the scientific community

about our current problems, international collaboration and progress of our

research in the fields of modern optics and quantum information.

Olomouc, January 2006

Zdenek Hradil

coordinator of the project MSM6198959213

Jaromır Fiurasek

coordinator of the project LC06007

Quantum information experiments based on fiber optics

Lucie Bartuskova,1 Antonın Cernoch,2 Radim Filip,1 Jaromır Fiurasek,1 Jan Soubusta,2 Miloslav Dusek1

1Department of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc, Czech Republic and2Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Sciences of the Czech Republic,

17. listopadu 50A, 772 00 Olomouc, Czech Republic

FIG. 1: Part of the experimental setup with the shieldedMach-Zehnder interferometer.

Our laboratory is focused on various aspects of quan-tum information processing. In most experiments, time-energy entangled photon pairs obtained from type-I para-metric fluorescence in nonlinear crystals are used. Theirpolarization states, space-time properties and other fea-tures are manipulated and then the photons undergo var-ious combinations of second- and fourth-order interfer-ence schemes. The results obtained from detection sys-tems, ranging from simple two-detector coincidence toincomplete Bell-state analysis, are interpreted in quan-tum information terms.

In this subproject the experimental implementationsare based on fiber optics. Qubits (qutrits) are encodedto spatial modes, e.i. single photons propagate throughtwo (three) distinct fibers. We have experimentally real-ized an optical scheme for encoding of two quantum bitsinto one qutrit. From this qutrit, either of the originalqubits can be error-free restored, but not both of themsimultaneously [1, 2, 4, 5].

Figure 1 shows the essential part of the setup, a fiberbased Mach-Zehnder interferometer. Due to the fact,that the interferometer is highly sensitive to thermal fluc-tuations, it is situated in a shielding box. Moreover, theinterferometer has to be actively stabilized during themeasurement.

During the last half year we rebuilded the setup to en-sure experimental implementation of the optimal 1 → 2phase-covariant cloning of photonic qubits, see Fig. 2.The cloning operation is realized by the interference ofthe input photon with an ancilla photon on a variable-ratio couplers. The main advantage of this implemen-tation is based on the fact, that the splitting ratio ofthe couplers can be easily changed. This condition en-ables us to set the asymmetry of the fidelities of the twoclones. In the experiment, we demonstrated the optimalsymmetric cloning with fidelities: FA = (85.4 ± 0.4)%,

FB = (83.4 ± 0.4)%. Then we enhanced the asymme-try. With this scheme we were able to exceed the limitof universal cloning machine [3].

FIG. 2: Scheme of the asymmetric-cloning setup.

This research was supported by the projects of theMinistry of Education of the Czech Republic (MSM6198959213, LC06007 and 1M06002) and by the SEC-OQC project of the EC (IST-2002-506813).

[1] L. Bartuskova, A. Cernoch, R. Filip, J. Fiurasek, J. Sou-busta, M. Dusek, Optical implementation of the encodingof two qubits to a single qutrit, Phys. Rev. A 74, 022325(2006).

[2] L. Bartuskova, A. Cernoch, R. Filip, J. Fiurasek, J. Sou-busta, M. Dusek, Encoding two qubits into a single qutrit:Experiment, Acta Physica Hungarica (in print).

[3] L. Bartuskova, M. Dusek, A. Cernoch, J. Soubusta,J. Fiurasek, Fiber-optics implementation of asym-metric phase-covariant quantum cloner, submitted to

Phys. Rev. Lett.

[4] L. Bartuskova, Experimental realization of the encoding oftwo qubits to one qutrit, 13th CEWQO, Vienna (Austria),May 23-27, 2006.

[5] L. Bartuskova, Experimental realization of the encodingof two qubits to one qutrit, XVth Czech-Polish-Slovak Op-

tical Conference, Liberec (Czech Republic), September 11-16, 2006.

2

Quantum information experiments based on bulk optics

Antonın Cernoch,1 Lucie Bartuskova,2 Jan Soubusta,1 Miroslav Jezek,2 Jaromır Fiurasek,2 Miloslav Dusek2

1Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Sciences of the Czech Republic,

17. listopadu 50A, 772 00 Olomouc, Czech Republic and2Department of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc, Czech Republic

FIG. 1: Essential part of the experimental setup with thecustom-made beamsplitter in the center.

Our laboratory is focused on various aspects of quan-tum information processing. In most experiments, time-energy entangled photon pairs obtained from type-I para-metric fluorescence in nonlinear crystals are used. Theirpolarization states, space-time properties and other fea-tures are manipulated and then the photons undergo var-ious combinations of second- and fourth-order interfer-ence schemes. The results obtained from detection sys-tems, ranging from simple two-detector coincidence toincomplete Bell-state analysis, are interpreted in quan-tum information terms.

In this subproject the experimental implementationsare based on bulk optics. Qubits are encoded into po-larization states of individual photons. During the lastyear we built and tested several setups, that can be usedfor cloning of polarization qubits. Linearity of quantummechanics forbids exact copying of unknown quantumstates. However, approximate cloning is possible.

Figure 1 shows one scheme, where the key element isa special beamsplitter with splitting ratio different forhorizontal polarization (21:79) and vertical polarization(79:21) [1–3]. Because the splitting ratio of the custom-

made beamsplitter manufactured by Ekspla is not per-fect, we balanced it by a glass plate (GP), shown infig. 2. This quantum-state filtering is based on polar-ization dependent losses. The fidelities of both clonesmeasured with the GP coincide within the measurementerror, F1 = F2 = 82.2 ± 0.2%. From the measured datawe estimated the implemented cloning transformation us-ing the maximum-likelihood method. The result showsthat this realized transformation is very close to the idealone and the map fidelity reaches 94%.

In the next period our aim is to thoroughly comparedifferent cloning techniques. These experiments are actu-ally in the run. This research is interesting not only fromthe theoretical point of view, but it demonstrates differ-ent cloning technologies and strategies of compensationof unperfect optical components.

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FIG. 2: Scheme of the cloning setup.

This research was supported by the projects of theMinistry of Education of the Czech Republic (MSM6198959213, LC06007 and 1M06002) and by the SEC-OQC project of the EC (IST-2002-506813).

[1] A. Cernoch, L. Bartuskova, J. Soubusta, M. Jezek, J.Fiurasek, M. Dusek, Experimental phase-covariant cloningof polarization states of single photons, Phys. Rev. A 74,042327 (2006).

[2] A. Cernoch, Several experimental implementations ofphase covariant quantum cloner, 3rd International Work-

shop Advances in Foundations of Quantum Mechan-

ics and Quantum Information with atoms and photons,

Torino (Italy), May 2-5, 2006, poster.[3] A. Cernoch, Several experimental implementations of

phase covariant quantum cloner, XVth Czech-Polish-

Slovak Optical Conference - Wave and Quantum As-

pects of Contemporary Optics, Liberec (Czech Republic),September 11-16, 2006.

3

Photon-counting detectors, spatial correlations in down-conversion and new sources ofentangled photon-pairs

Ondřej Haderka, Jan Peřina, Jr., Martin Hamar, Václav MichálekJoint Laboratory of Optics, Palacký University and Institute of Physics of Academy of Science of the Czech Republic,

17. listopadu 50A, 772 00 Olomouc, Czech Republic

We have continued our research towards constructionand application of two types of photon-counting detectors— fiber-loop detectors and iCCD cameras. An experi-ment devoted to the measurement of a pairwise characterof photon-number distribution generated in the processof second-subharmonic generation and using a fiber-loopdetector is in preparation. Motivated by one of our pre-vious experiments, a source of photons with selectablesuper-poissonian statistics is being developed. It is basedon a well characterized laser diode, the pumping currentof which undergoes random fluctuations with prescribedstatistics. Its experimental characterization will be doneusing a fiber-loop detector. On the other hand, an iCCDcamera [1] has been extensively used in the measurementof the dependencies of the size of area of correlation onthe geometry of the pumping beam [2, 3]. Correlationareas both in the near field (position correlation) and farfield (momentum correlation) have been determined bothfor femtosecond and cw pumping. Agreement of the expe-rimental data with approximate theories is not perfect atpresent but a great improvement has been done compa-red to the initial results [2]. This improvement has beenreached also due to new and improved algorithms for thereadout of the data from the iCCD camera [4]. A newgeneration of the data processing software is currently inthe development.

We have made an extensive test of a new type ofsingle-photon cameras - electron-multiplying cameras(EMCCD) - in our typical laboratory setups and conclu-ded that EMCCDs show spurious charge noise [5] that istoo high for our needs.

As one of the perspective sources of entangled photonpairs nonlinear layered structure made of GaN/AlN havebeen considered both theoretically and experimentally.A quantum vectorial model of spontaneous parametricdown-conversion [6–8] has been developed to study pro-perties of the generated photon pairs and suggest suitablestructures [9]. We have reached progress in the develop-ment of the detection methods for detecting low signals,however no provable detection of the down-convertedfield has been achieved yet, mainly due to large luminousnoise coming from the substrate of the samples. Also anonlinear waveguide with perpendicular pumping madeof LiNbO3 has been studied [10]. This configuration ishighly tunable in the parameters characterizing the emit-ted photon pairs.

Two members of the group, O. Haderka and J. PeřinaJr., were awarded by Otto Wichterle prize of Academyof Sciences of the Czech Republic.

This work was supported by researchs projects of theCzech Ministry of Education MSM6198959213, 1M06002,AVOZ10100522, and COST P11.003.

[1] O. Haderka, Multichannel detectors of single photons,Workshop ”Classical and Quantum Interference”, Olo-mouc, September 28-29, 2006.

[2] M. Hamar, O. Haderka, J. Peřina Jr.: The spatial dis-tribution of the mode generated by the parametric flo-rescence, XVth Czech-Polish-Slovak Optical Conference- Wave and Quantum Aspects of Contemporary Optics,Liberec (Czech Republic), September 11-16, 2006.

[3] J. Peřina Jr., Ondřej Haderka, Martin Hamar, Jan Pe-řina: Direct measurement of photon-number statisticsand spatial correlations of photon pairs, 3rd InternationalWorkshop Advances in Foundations of Quantum Mecha-nics and Quantum Information with atoms and photons,Torino (Italy), May 2-5, 2006, invited lecture.

[4] O. Haderka, The use of an intesified CCD camera PI-MAX 512-HQ for the detection of single photons, tech-nical report of the Joint Laboratory of Optics No.285/SLO/2006 (2006).

[5] O. Haderka, V. Michálek, Testing an EM-CCD camerafor photon counting, technical report of the Joint Labo-ratory of Optics No. 286/SLO/2006 (2006).

[6] J. Peřina Jr., M. Centini, C. Sibilia, M. Bertolotti,M. Scalora: Properties of entangled photon pairs ge-nerated in one-dimensional nonlinear photonic-band-gap structures, Phys. Rev. A 73, (2006), 033823;http::/xxx.lanl.gov/abs/quant-ph/0604017.

[7] J. Peřina Jr., M. Centini, C. Sibilia, M. Bertolotti, M.Scalora: Nonlinear photonic-band-gap structures as asource of entanged two-photon states, CLEO/QELS 2006Technical Digest CD-Rom (ISBN: 15-57-52813-6).

[8] J. Peřina Jr., M. Centini, C. Sibilia, M. Bertolotti,M. Scalora: Entanged two-photon states generated fromGaN/AlN photonic-band-gap structures, COST P11 Me-eting, Brussels (Belgium) 2006.

[9] J. Peřina Jr., M. Centini, C. Sibilia, M. Bertolotti,M. Scalora: Anti-symmetric entangled two-photon sta-tes generated in nonlinear GaN/AlN photonic-band-gapstructures, Phys. Rev. A, Jan 2007.

[10] J. Peřina Jr.: Quantum properties of counter-propagatingtwo-photon states generated in a planar waveguide, sub-mitted to Phys. Rev. A.

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6

Minimal disturbance measurements

Ladislav Mista, Jr., Jaromır Fiurasek, and Radim FilipDepartment of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc, Czech Republic

FIG. 1: Optical set-up implementing the MDM. The outputqubit is characterized adopting the analysis setup illustratedin the dashed box.

0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

F

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FIG. 2: Optimal Gaussian (dashed line) and non-Gaussian(solid line) fidelity trade-off.

There is not a quantum operation that would allowto extract some information on an unknown quantumstate without disturbing it. Within the framework of theproject we went on investigating the operations that in-

troduce for a given information gain the least possibledisturbance that are traditionally called minimal distur-bance measurements (MDMs). For this purpose we useda convenient approach based on quantification of the in-formation gain by the mean estimation fidelity G and thestate disturbance by the mean output fidelity F [1]. For aMDM the two fidelities satisfy a specific trade-off relationthat cannot be overcome by any quantum operation. Incollaboration with the group of professor F. De Martiniwe proposed and experimentally demonstrated [2, 3] theMDM for a completely unknown and equatorial state ofa 2-level particle (qubit) realized by a polarization stateof a single photon (see Fig. 1).

Our studies did not restrict to finite-dimensional quan-tum systems and also optimal Gaussian MDM for a com-pletely unknown coherent state of an optical field wasfound and experimentally demonstrated [4] in collabora-tion with the group of professor G. Leuchs. Both the ex-perimental MDMs were reported in [5]. We further exam-ined optimal fidelity trade-off for a completely unknowncoherent state beyond the framework of Gaussian opera-tions. We found that the aforementioned optimal Gaus-sian trade-off can be improved by up to 2.77% if we usea suitable non-Gaussian operation [6] (see Fig. 2). Thisoperation can be implemented by the standard coherentstate teleportation where the shared state is a suitablenon-Gaussian entangled state. We also derived analyti-cally optimal fidelity trade-off for N identical qubits andthe corresponding MDM assuming quantum operationswith a single output qubit [7].

The research has been supported by the researchprojects “Measurement and Information in Optics,”(MSM 6198959213) and Center of Modern Optics(LC06007) of the Czech Ministry of Education and bythe COVAQIAL (FP6-511004) and SECOQC (IST-2002-506813) projects of the sixth framework program of EU.

[1] K. Banaszek, Fidelity balance in quantum operations,Phys. Rev. Lett. 86, 1366 (2001).

[2] F. Sciarrino, M. Ricci, F. De Martini, R. Filip, and L.Mista, Jr., Realization of a minimal disturbance quantummeasurement, Phys. Rev. Lett. 96, 020408 (2006).

[3] R. Filip, L. Mista, Jr., F. De Martini, M. Ricci, andF. Sciarrino, Probabilistic minimal disturbance measure-ment of symmetrical qubit states, Phys. Rev. A 74, 052312(2006).

[4] U. L. Andersen, M. Sabuncu, R. Filip, and G. Leuchs,Experimental demonstration of coherent state estimation

with minimal disturbance, Phys. Rev. Lett. 96, 020409(2006).

[5] A. Cho, Measurement schemes let physicists tiptoe throughthe quanta, Science 311, 451 (2006).

[6] L. Mista, Jr., Minimal disturbance measurement for co-herent states is non-Gaussian, Phys. Rev. A 73, 032335(2006).

[7] L. Mista, Jr. and J. Fiurasek, Optimal partial estimationof quantum states from several copies, Phys. Rev. A 74,022316 (2006).

7

Composed vortex fields and their orbital angular momentum

R. Celechovsky, V. Kollarova and Z. BouchalDepartment of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc, Czech Republic

In recent time, optical vortex structures have attractedincreasing attention because they possess unique physicalproperties useful for applications. In the last year, wedeveloped theoretical models and experimental methodsproviding results promissing for applications of opticalvortices in wireless communications and MEMS (MicroElectro Mechanical Systems).

In [1], recent findings concerning nondiffracting beams,vortex beams and combinations of the two were reviewed.Particular attention was devoted to physical properties,experimental methods, and potential applications of sin-gle and composite vortex fields carried by a pseudo-nondiffracting background beam. Such beams may bedynamically controlled with a Spatial Light Modulator(SLM) for applications where beam reshaping, informa-tion encoding, or optical manipulation are required.

Considerable effort was also devoted to a developmentof the previously proposed method enabling encoding andtransfer of information by means of mixed vortex fields.In this case, information is encoded into a spatial struc-ture of optical field composed of several vortex beamswith different topological charges. In a practical opera-tion, information codes must be created sequentially. Inexperiments, it can be achieved adopting holographicalmethods realized by means of the SLM. Unfortunately, arelatively low repetition rate of available SLMs preventsutilization of this method in real communication systems.In [2], the holographical method was modified to enablean exploitable dynamical information encoding. In thiscase, various information codes can be created by thesame single hologram. A required sequentiality of theinformation codes was ensured by a conventional switch-ing of an array of point sources illuminating the singlehologram. To transform incoming light into a coaxialsuperposition of vortices with well defined weight coeffi-cients, the special phase only masks were designed andrealized holographically. The phase masks were success-fully tested in our laboratory. It was verified that theyare applicable to both information encoding and decod-ing in a good agreement with theoretical predictions [3].

In the last year, the mechanical consequences of sin-gle and composed optical vortex fields were also exam-ined. As is well known, the Orbital Angular Momentum(OAM) of a single vortex beam depends on its power andwavefront helicity. In [4], this relation was generalized formixed vortex beams composed of several coaxial vorticeswith different topological charges. The obtained inter-ference law indicated interference effects of the OAM re-sulting in local spatial gradients of the OAM density. De-scription of the OAM of mixed vortex beams was used fordemonstration of a possibility to tune the OAM density

FIG. 1: Optical set up for transfer of information by meansof composed vortex beams.

of a composite vortex field without changing topologicalcharges or intensity distribution. Experimental demon-stration of the OAM tuning was discussed for interfer-ence of two focused vortex beams generated by meansof a spiral phase mask. The specific distributions of theOAM density promising for trapping experiments wereexplored and demonstrated.

This work was supported by the Research Project ofthe Czech Ministry of Education ”Measurement andInformation in Optics” MSM 6198959213 and Grant202/06/0307 of Czech Grant Agency.

[1] Z. Bouchal, R. Celechovsky, G. Swartzlander Jr.: Spa-tially localized vortex structures, Chapter of the Mono-graph Localized waves, Eds. M. Zamboni-Rached and H.Figueroa, J. Wiley & Sons, New York (accepted).

[2] R. Celechovsky, Z. Bouchal: Generation of variable mixedvortex fields by a single static hologram, J. Mod. Opt. 53,473-480 (2006).

[3] R. Celechovsky, Z. Bouchal: Design and testing of thephase mask for transfer of information by vortex beams,Proc. SPIE (in print).

[4] Z. Bouchal, V. Kollarova, P. Zemanek, T. Cizmar: Orbitalangular momentum of mixed vortex fields, Proc. SPIE (inprint).

8

Tomographic methods for quantum information processing

J. Rehacek, Z. Hradil, Z. Bouchal, R. Celechovsky,Department of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc, Czech Republic1

D. MogilevtsevInstitute of Physics, Belarus National Academy of Sciences, F.Skarina Ave. 68, Minsk 220072 Belarus

L. L. Sanchez-SotoDepartamento de Optica, Facultad de Fısica, Universidad Complutense, 28040 Madrid, Spain

The investigation on tomographic methods and quan-tum estimation started recently was successful and re-sulted in several publications [1] last year. The currentresearch has merged the fields of quantum informationprocessing with vortex beams and advanced reconstruc-tion techniques. The state of the art of this field is sum-marized in several items.

The publication [2] published at the end of the yearhas established the proper framework for quantum de-scription of classical optics in terms of singular waves.This leads to novel formulation of uncertainty relationsfor orbital momentum and angle variable. Current prob-lems discussed in the team are focussing on the improveddetection of orbital momentum, on the issue of alterna-tive resolution measures and full description of possiblenon-classical behavior. Special attention is payed to thenovel concept of generalized measurements achieved bymeans of complex (amplitude and phase masks). The ex-perimental capabilities has been enhanced by acquiringthe Hartmann-Schak sensor, which is capable to analyzethe wavefront of propagating wave.

The research on formal issues of Maximum-Likelihoodalgorithm has continued and resulted in submitted pub-lication [3]. Here the generic form of numerical algo-rithm guaranteeing the convergence has been presentedand detailed on several valuable examples. The conceptof objective and biased tomography scheme was furtherdetailed in accepted publication [4]. The intrinsic rela-

tionship between the maximum-likelihood quantum-stateestimation and the representation of the signal was elabo-rated. A quantum analogy of the transfer function deter-mines the space where a successful reconstruction can beachieved. This provides a tool for reducing the numberof dimensions of the observed system based on physicalcharacteristics of the reconstruction scheme rather thansome ad hoc truncations. The method is illustrated withtwo examples of practical importance: an optical quan-tum homodyne tomography and a novel, simple, and ro-bust tomography of an optical signal recorded by realisticbinary detectors. The seminal scheme of homodyne de-tection from the viewpoint of objective tomography isdetailed in [5]. The unpublished papers announced asComment previous year will be further elaborated withItalian colleagues. The topic of standard tomography en-countered certain progress recently [6]. Maximum like-lihood assisted by maximum entropy is developed as arobust tool for analysis of noisy signals. Further researchwill focus on better numerical implementation of this al-gorithm.

This work was supported by the Research Project ofthe Czech Ministry of Education ”Measurement andInformation in Optics” MSM 6198959213 and LC06007,EU project COVAQIAL FP6- 511004 and projectsGACR 202/06/307.

[1] Hradil Z, Mogilevtsev D, Rehacek J., Biased tomographyschemes: An objective approach, PHYSICAL REVIEWLETTERS 96 (23): Art. No. 230401 (2006); Badurek G,Facchi P, Hasegawa Y, Hradil Z, Pascazio S, Rauch H,Rehacek J, Yoneda T, Neutron wave-packet tomography,PHYSICAL REVIEW A 73 (3): Art. No. 032110 (2006);Rehacek J, Hradil Z, Perina J, Pascazio S, Facchi P, Za-wisky M, Advanced neutron imaging and sensing, in ”Ad-vances in Imaging and Electron Physics”, volume 142,edited by P.W. Hawkes (Elsevier Academic Press, Ams-terdam, 2006) ISBN-10:0-12-014784-X, ISBN-13:978-0-12-014784-7, page 53;Banas P, Rehacek J, Hradil Z, Pertur-bative quantum-state estimation, PHYSICAL REVIEWA 74 (1): Art. No. 014101 (2006).

[2] Z. Hradil, J. ehek, Z. Bouchal, R. elechovsk, L.Snchez-Soto,Minimum uncertainty measurements of angle and an-gular momentum, Phys. Rev. Lett. 97, 243601(2006).

[3] Rehacek J, Hradil Z, Knill E., Lvovsky A.I., Dilutedmaximum-likelihood algorithm for quantum tomography,zaslano do PRA

[4] Mogilevtsev D, Hradil Z, Rehacek J, Objective approachto biased tomography schemes, accepted for publicationin PRA 2007

[5] Mogilevtsev D, Rehacek J, Hradil Z, Biased reconstruc-tion:homodyne tomography, submitted to Proceedings ofNATO workshop, September 2006.

[6] Rehacek, Hradil, Zawisky, 8th World Conference on Neu-tron Radiography, NIST Gaithersburg MD, USA, poster:

9

Quantum optics and statistics of nonlinear optical processes

J. Perina, V. Perinova, A. Luks,1 J. Krepelka,2 M. Sebawe Abdalla,3 and Faisal A.A. El-Orany4

1Department of Optics, Palacky University, 17. listopadu 50, 772 00 Olomouc, Czech Republic2Joint Laboratory of Optics, Palacky University,

17. listopadu 50, 772 07 Olomouc, Czech Republic3Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

4Department of Mathematics and Computer Science,Faculty of Science, Suez Canal University, 41522 Ismailia, Egypt

Multimode joint integrated intensity and photon-number probability distributions were derived for thestimulated process of optical parametric down-conversionin relation to measured experimental data and a bor-der between classical and quantum behavior was deter-mined [1, 2]. Quantum statistical properties for multi-photon three-boson coupled oscillators in the frame-work of the Tavis-Cummings model were obtained andthe corresponding nonclassical properties of the systemwere deduced [3]. Such nonclassical behavior, includingsqueezing of vacuum fluctuations, sub-Poissonian behav-ior of photon statistics and collapse-revival phenomenawere also investigated in a two-level atom influenced byKerr-like medium [4] and for combined Kerr and down-conversion processes [5], which can be also interpreted interms of nonlinear optical couplers.

A unified approach for estimating the cosine of phaseand cosine of double phase in the Mach Zehnder inter-ferometer has been proposed [6]. The phase sensitivityrelated to the Cramer-Rao lower bound of the estimatorvariance has been addressed. Fisher’s measure of infor-mation has been compared with the usual measure of sen-sitivity of the SU(2), SU(1,1), and M(2) interferometers.The states of optimum Fisher information measure havebeen defined and their properties have been studied forthe SU(2) interferometer [7]. Quantum-mechanical mea-

surement of the z component of the angular momentumand the minimum uncertainty states with respect to theincompatible y and z components have been investigated[10].

The solutions of the time-independent Maxwell equa-tions have been dealt with in the framework of Floquettheory for a particular choice of the dielectric function.A connection of the solutions (modal functions) with theresults of the coupled mode theory has been investigated[8]. These results will be used to a “synthesis” of thequantum electromagnetic field in a dielectric medium.Quantum statistical properties of the light in periodicdielectric media, disordered media, and in the novel op-tical left-handed materials will be investigated as well.

The unitary evolution operator of a pure state of twomodes of a quantized field has been factorized providedthat the coupled modes of radiation are described witha quadratic Hamiltonian. A connection with the Baker–Campbell–Hausdorff formula has been explained [9].

One of us (M.S.A.) is grateful for the financial sup-port from the project Math 2005/32 of the Research Cen-ter, College of Science, King Saud University. J.K., J.P.V.P. and A.L. acknowledge the Research Project ”Mea-surement and Information in Optics” MSM 6198959213,the Project Center of Modern Optics LC06007 and EUProject COST OCP11.003.

[1] J. Perina, J. Krepelka, Opt. Commun. 265 (2006) 632-641.

[2] J. Perina, J. Krepelka, J. Eur. Opt. Soc. RP 1 (2006)06002-1—5.

[3] M.S. Abdalla, J. Perina, J. Krepelka, J. Opt. Soc. Am.B 23 (2006) 1146-1160.

[4] M.S. Abdalla, J. Krepelka, J. Perina, J. Phys. B: At. Mol.Opt. Phys. 39 (2006) 1563-1577.

[5] F.A.A. El-Orany, M.S. Abdalla, J. Perina, Eur. Phys. J.D (2006), DOI: 10.1140/epjd/e2006-00222-0.

[6] A. Luks, V. Perinova, Cosine-of-phase sensitivity of aMach–Zehnder interferometer for the Fock state inputs.Journal of Physics: Conference Series 36 (2006) 103–112.

[7] V. Perinova, A. Luks, J. Krepelka, States of optimumFisher measure of information for quantum interferome-try. Physical Review A 73 (2006) 063807-1–9.

[8] V. Perinova, A. Luks: Quantization of light field in pe-riodic dielectrics with and without the coupled mode the-ory. In: Proceedings of the Conference on Differentialand Difference Equations and Applications, Eds. Ravi P.Agarwal and Kanishka Perera, 2006, Hindawi PublishingCorporation, New York, pp. 925–934 (ISBN 977-5945-380).

[9] V. Perinova, A. Luks: Baker–Campbell–Hausdorff for-mulae and time evolutions of pure and mixed states. (in-vited lecture.) International conference: Operator The-ory in Quantum Physics. 9. 9.– 14. 9. 2006, Praha.

[10] V. Perinova, A. Luks: Minimum-uncertainty states andoptimal states satisfying a constraint, (contributed lec-ture) Second Czech-Catalan Conference in Mathematics,20. 9.–24. 9. 2006, Barcelona, Spain.

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The group of statistical and wave optics in 2006

Petr Smıd, Pavel Horvath, Miroslav Hrabovsky, Petra Neumannova, Pavel PavlıcekJoint Laboratory of Optics of Palacky University and Institute of Physics of the Academy of Sciences of the Czech Republic,

Tr. 17. listopadu 50a, 772 07 Olomouc, Czech Republic

Detection of components of small deformation tensoris an object of interest to industry and many researchfields. The research of the group shows applicability ofthe speckle correlation method in measurement of elasticdeformation, object’s surface slope and object’s velocity.The outputs of measurement of the elastic deformationcomponent ǫxx proved equality of the results obtainedby the optical method and direct contact method withinthe interval (0 – 2100)×10−6 [1]. Research into detectionof tilt of object’s surface showed that the geometricalparameters of the designed experimental set-up limit themeasuring range of the tilt [2, 3]. The proposed opticalset-up enables one to detect tilt of object’s surface withinthe interval (10 – 30)◦.

Gaining from knowledge of measurement of a transla-tion component of the small deformation tensor a tech-nique for measurement of in-plane velocity in one direc-tion of diffusely reflective object is developed [4, 5]. Nu-merical correlations of speckle patterns recorded periodi-cally by a linear CMOS detector during motion of the ob-ject under investigation give information used to evaluateobject translations between each two consecutive recordsof the speckle patterns. The simulation analysis showsthe way of controlling the measuring range and enablesone to select a proper exposure time and acquisition rate.Proposed optical set-up similar to the one designed formeasurement of object’s surface slope uses a detectionplane in the image field and enables one to detect theobject’s velocity within the interval (10 – 150)µm · s−1.

Next research into statistical properties of speckled

speckle is under way. Comparison of statistical proper-ties [6] (first-order statistics) of order and fractal speckleis presented. The subject of research is a diffractal gen-erated by amplitude filters described by random Weier-strass functions.

White-ligth interferometry is an established methodfor measurement of the geometrical form of objects withoptically smooth or rough surface. When the form of anobject with optically rough surface is measured, specklepattern arises in the image plane. The statistical natureof the speckle pattern gives rise to the measurement er-ror of surface location. Numerical calculations show thatmeasurement error caused by the surface roughness obeysGaussian distribution [7]. The standard deviation of thisdistribution is the measurement uncertainty. The numer-ically calculated measurement uncertainty is comparedwith the measurement uncertainty that was derived ana-lytically (but with strongly simplified conditions) in theprevious work.

A spatial coherence analogy to white-light interferom-etry is spatial coherence profilometry [8]. It is interestingto compare the properties of both methods. A glass plateintroduced into one arm of the white-light interferome-ter elongates the optical path. The influence of the glassplate on spatial coherence profilometry is opposite. Inthis case the arm with the glass plate seems to be short-ened [9].

This work was supported by the Research Project ofthe Czech Ministry of Education “Measurement and In-formation in Optics” MSM 6198959213.

[1] P. Horvath, P. Smıd, M. Hrabovsky and P. Neumannova,“Measurement of deformation by means of correlation ofspeckle fields,” Exp. Mech. 46, (2006). (in print, to bepublished in December 2006)

[2] P. Smıd, P. Horvath and M. Hrabovsky, “Speckle corre-lation method used to detect an object’s surface slope,”Appl. Opt. 45, pp. 6932–6939 (2006).

[3] P. Horvath, P. Smıd, P. Wagnerova and M. Hrabovsky,“Usage of the speckle correlation for object surface topog-raphy,” in Optical Design and Fabrication, J. Breckinridgeand Y. Wang, eds., Proc. SPIE 6034, 511-516 (2006).

[4] P. Smıd, P. Horvath, P. Neumannova and M. Hrabovsky,“The use of speckle correlation for measurement of objectvelocity,” in Speckle06: Speckles, From Grains to Flow-ers, P. Slangen and Ch. Cerruti, eds., Proc. SPIE 6341,634131-1–634131-6 (2006).

[5] P. Smıd, P. Horvath and M. Hrabovsky, “Speckle correla-

tion method used to measure object’s in-plane velocity,”submitted to Appl. Opt. (2006).

[6] P. Horvath, P. Smıd and M. Hrabovsky, “Comparison ofstatistical properties of fractal and order speckle pattern,”submitted to Optik (2006).

[7] P. Pavlıcek and O. Hybl, “Meßunsicherheit bei Weißlicht-interferometrie auf rauen Oberflachen,” in Proc. of 107thconference of German Society for Applied Optics (DGaO)(6. – 10. 6, Weingarten, Germany, 2006) B 14.

[8] P. Pavlıcek, “Profilometry with spatial coherence,” inProc. of 15. Conference of Slovak and Czech physicists(5. – 8. 9, Kosice, Slovak Republic, 2006) 41–42.

[9] P. Pavlıcek and O. Hybl, “Spatial coherence profilome-try,” in Book of Abstracts XV Czech-Polish-Slovak opticalconference - Wave and Quantum Aspect of ContemporaryOptics (11. – 15. 9, Liberec, Czech Republic, 2006) 49.

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Documents

Annual Report 2006 - Univerzita Palackého v Olomoucioptics.upol.cz/userfiles/file/MIO_report_2006.pdfQuantum information experiments based on ber optics Lucie Barust kova , 1 Anton