Showing papers in "Journal of Modern Optics in 1997"
TL;DR: In this paper, the authors give an explicit way to experimentally determine the evolution operators which completely describe the dynamics of a quantum-mechanical black box: an arbitrary open quantum system.
Abstract: We give an explicit way to experimentally determine the evolution operators which completely describe the dynamics of a quantum-mechanical black box: an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible and illustrate the general theory by considering specifically one-and two-quantum-bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication and computation systems.
834 citations
TL;DR: In this paper, a multiply-entangled state is defined, and a non-maximally entangled state is realizable, in which the amplitudes of the contributing terms are not equal.
Abstract: Entangled states are key ingredients to the new field of quantum information, including quantum dense coding, teleportation, and computation. However, only a relatively small class of entangled states has been investigated experimentally, or even discussed extensively. In particular, efforts to date have focused on two particles entangled in a single degree of freedom, for example polarization, or energy, or momentum direction. Novel phase-matching arrangements in spontaneous parametric down-conversion allow the preparation of pairs of photons that are simultaneously entangled in all of these. We shall call such a multiply-entangled state ‚hyper-entangled‘. In addition, an even more general state–-a non-maximally entangled state–-should be realizable, in which the amplitudes of the contributing terms are not equal.
304 citations
TL;DR: In this article, a high efficiency scheme for generating a single-photon state transmitted out of an optical cavity was proposed, with a probability exceeding 99% in a user-specified time interval.
Abstract: We report a high efficiency scheme for generating a single-photon state transmitted out of an optical cavity. For realistic cavity QED parameters, we show that the scheme can produce a single-photon pulse with a probability exceeding 99% in a user-specified time interval. By recycling the system, the scheme can be used to create a bit-stream of single-photon pulses.
171 citations
TL;DR: In this article, the authors estimate the regions in which each mode of evaluation is preferable according to computing efficiency and accuracy considerations, and a fast numerical algorithm is introduced for each region.
Abstract: One of the most basic optical ‘components’ is free-space propagation. A common approximation used when calculating the resultant field distribution after propagation is the Fresnel integral. This integral can be evaluated in two ways: directly or by using the angular spectrum. In this paper, we estimate the regions in which each mode of evaluation is preferable according to computing efficiency and accuracy considerations. A fast numerical algorithm is introduced for each region. The result is relevant also for the evaluation of the Rayleigh-Sommerfeld diffraction formula.
121 citations
TL;DR: In this article, analytical theory and numerical modelling for the prism coupling of light to long range surface modes supported by a thin absorbing film is presented. But the results are limited to the case of indium tin oxide (ITO).
Abstract: Analytic theory and numerical modelling are presented for the prism coupling of light to long range surface modes supported by a thin absorbing film. If both transverse magnetic and transverse electric modes can be excited, then by comparing theory to angle dependent reflectivity data the optical permittivity and thickness of the film may be unambiguously established. An experimental confirmation is presented for thin films of indium tin oxide (ITO) on glass substrates. The environment of the ITO is made optically symmetric, to support the long range mode, by use of a fluid which is index matched to the glass substrate. Attenuated total reflection, with prism coupling through the matching fluid, gives, with suitable fluid thickness, sharp resonant modes in the angle dependent reflectivity. Comparison of such data with modelling theory yields the ITO parameters.
119 citations
TL;DR: In this paper, a white-light phase-shifting method for interferometry is proposed, in which the absolute phase of each point is measured individually and the fringe order is deduced from the evolution of the fringe envelope between two consecutive PZT positions and from the computed relative phase.
Abstract: This paper proposes a white-light phase-shifting method for interferometry, in which the absolute phase of each point is measured individually. During the axial scanning of the sample, eight phase-shifted intensities are recorded, while the fringe visibility is maximum. A seven-point algorithm, which compensates for the variation in the fringe visibility due to the coherence envelope, allows the computation of the relative phase. Then, the absolute phase is computed from this relative phase, the piezoelectric transducer (PZT) position at the beginning of the data recording and from the fringe order. The fringe order is deduced from the evolution of the fringe envelope between two consecutive PZT positions and from the computed relative phase. This method allows unambiguous profilometry with a nanometric resolution by using a phase-shifting method. Furthermore, both the necessary storage memory and the computation time can be significantly reduced by comparing with already-demonstrated white-light...
115 citations
TL;DR: The Hermitian optical phase operator cannot be represented exactly in the usual-infinite Hilbert space but can be constructed in a subspace of it and provides a valid representation of phase if used together with a suitable limiting procedure.
Abstract: Simple physical ideas lead us to identify the phase of a single mode of the electromagnetic field as the quantity conjugate to the photon number. This in turn leads to the form of the phase probability distribution. The phase operator cannot be represented in the conventional infinite dimensional Hilbert space but can be expressed by means of a finite-dimensional state space together with a suitable limiting procedure. We introduce the Hermitian optical phase operator and describe its most important properties.
96 citations
TL;DR: In this paper, the detection of a spontaneously emitted photon from a three-level atom, in which the two upper levels are driven by a classical standing light field, yields information about the centre-of-mass position of the atom relative to the nodes of the driving field.
Abstract: The detection of a spontaneously emitted photon from a threelevel atom, in which the two upper levels are driven by a classical standing light field, yields information about the centre-of-mass position of the atom relative to the nodes of the driving field. We present a pure state treatment of the system and show that the measurement leads to a reduction of the system's wavefunction, which manifests itself in a localization of the atom.
89 citations
TL;DR: In this paper, the field distribution in the focal region of a high-aperture optical system is calculated using an expansion into multipole components, which is expressed as analytic expressions in terms of associated Legendre functions and spherical Bessel functions, thus avoiding computational problems in evaluation of diffraction integrals.
Abstract: The field distribution in the focal region of a high-aperture optical system is calculated using an expansion into multipole components. For any angular illumination distribution and numerical aperture, the incident field is expanded into spherical harmonics and the field in the focal region is then determined by a sum of multipole fields. These are expressed as analytic expressions in terms of associated Legendre functions and spherical Bessel functions, thus avoiding computational problems in evaluation of diffraction integrals. As a result, focal distributions can be calculated much more efficiently than by using direct quadrature.
86 citations
TL;DR: In this article, occupation number fluctuations of an ideal Bose gas in a trap which is isolated from the environment with respect to particle exchange (canonical ensemble) were analyzed. And they showed that the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature.
Abstract: We analyse occupation number fluctuations of an ideal Bose gas in a trap which is isolated from the environment with respect to particle exchange (canonical ensemble). We show that in contrast to the predictions of the grandcanonical ensemble, the counting statistics of particles in the trap ground state changes from monotonously decreasing above the condensation temperature to single-peaked below that temperature. For the exactly solvable case of a harmonic oscillator trapping potential in one spatial dimension we extract a Landau–Ginzburg functional which–despite the non-interacting nature of the system–displays the characteristic behaviour of a weakly interacting Bose gas. We also compare our findings with the usual treatment which is based on the grand-canonical ensemble. We show that for an ideal Bose gas neither the grand-canonical and canonical ensemble thermodynamically equivalent, nor the grand-canonical ensemble can be viewed as a small system in diffusive contact with a particle reservoir.
83 citations
TL;DR: In this paper, a special issue on quantum state preparation and measurement is presented, with a focus on quantum quantum state measurement. But this paper is not a comprehensive review of the literature.
Abstract: (1997). Special issue on quantum state preparation and measurement. Journal of Modern Optics: Vol. 44, No. 11-12, pp. 2021-2022.
TL;DR: In this paper, an absolute surface topography measurement with a tuneable diode laser with an external cavity that has a tuning range of as much as 25 nm without mode hops and a very high tuning speed of less than 1 s for the whole range.
Abstract: In this paper we present an absolute surface topography measurement with a tuneable diode laser with an external cavity that has a tuning range of as much as 25 nm without mode hops and a very high tuning speed of less than 1 s for the whole range. With this laser, an absolute wavelength-shift speckle pattern interferometer was realized, capable of measuring optically smooth and rough surfaces. We briefly explain the principles of operation, and the importance of wavelength tuning without mode hops. We discuss the capabilities, possible measuring ranges and some results as well as calibration methods of wavelength-shift speckle profilometry.
TL;DR: In this article, the three-dimensional localization of a single ion to the Lamb-Dicke limit in a radio-frequency trap has been combined with the technique of heterodyne detection to provide high-resolution spectroscopy of the fluorescent light of the ion.
Abstract: The three-dimensional localization of a single ion to the Lamb–Dicke limit in a radio-frequency trap has been combined with the technique of heterodyne detection to provide high-resolution spectroscopy of the fluorescent light of the ion. A coherent component with a linewidth of 0·7 Hz, corresponding to elastic scattering of the incident laser light, was observed in the heterodyne signal. The method may be extended to observe the narrow sidebands related to the secular motion in the trap, yielding information on the dynamics of the ion. Quantum properties of the fluorescent radiation can be detected by probing higher order field correlations. As an example we investigated the phenomenon of antibunching which appears as intensity anticorrelations of the emitted radiation. A measurement of intensity cross-correlations of the fluorescent light superimposed with a weak local oscillator is expected to permit the observation of squeezing in the resonance fluorescence of a single ion.
TL;DR: In this paper, the authors report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap, which is coherently prepared from an ion which has been initially laser cooled to the zero-point of motion.
Abstract: We report the creation and full determination of several quantum states of motion of a 9Be+ ion bound in a RF (Paul) trap. The states are coherently prepared from an ion which has been initially laser cooled to the zero-point of motion. We create states having both classical and non-classical character including thermal, number, coherent, squeezed, and ‚Schrodinger cat‘ states. The motional quantum state is fully reconstructed using two novel schemes that determine the density matrix in the number state basis or the Wigner function. Our techniques allow well controlled experiments decoherence and related phenomena on the quantum-classical borderline.
TL;DR: In this paper, a general principle for the tomographic approach to quantum state reconstruction is established, which is based on a simple rotation transformation in the phase space; this allows us to consider other types of transformation.
Abstract: We establish a general principle for the tomographic approach to quantum state reconstruction, which until now has been based on a simple rotation transformation in the phase space; this allows us to consider other types of transformation. Then, we shall present different realizations of the principle in specific examples.
TL;DR: In this paper, an iterative algorithm for design diffractive optical elements capable of forming light fields with longitudinal periodicity and modal composition was proposed, and conditions were specified under which the beam transverse intensity distribution, which is dependent on the azimuth angle and lacking radial symmetry, undergoes rotation as the beam propagates along the axis, making an integer number of revolutions per period.
Abstract: The paper deals with an iterative algorithm for design diffractive optical elements capable of forming light fields with longitudinal periodicity and modal composition. In addition, the conditions are specified under which the beam transverse intensity distribution, which is dependent on the azimuth angle and lacking radial symmetry, undergoes rotation as the beam propagates along the axis, making an integer number of revolutions per period.
TL;DR: In this article, an experimental realization of discrimination between non-orthogonal polarization states at the Helstrom bound for minimum probability of error was performed with highly attenuated laser light with a mean number of about 0·1 photons per pulse.
Abstract: We present an experimental realization of discrimination between non-orthogonal polarization states at the Helstrom bound for minimum probability of error. The experiment was performed with highly attenuated laser light with a mean number of about 0·1 photons per pulse.
TL;DR: In this paper, the authors consider the conversion of a Gaussian beam into a flat-top profile by using a phase-plate which consists of a single-zone binary optic and deduce the conditions required to produce super-Gaussian profiles of order 6 at the focal plane of a converging lens.
Abstract: We consider the conversion of a Gaussian beam into a flat-top profile by using a phase-plate which consists of a single-zone binary optic. The near- and far-field distributions are studied. We deduce the conditions required to produce super-Gaussian profiles of order 6 at the focal plane of a converging lens.
TL;DR: In this paper, the authors studied the three-dimensional field distribution of a focused axially symmetric flattened Gaussian beam and provided exact closed-form expressions for the intensity along the optical axis and at the focal plane.
Abstract: We study the three-dimensional field distribution of a focused axially symmetric flattened Gaussian beam. In particular, exact closed-form expressions for the intensity along the optical axis and at the focal plane are provided, together with a comparison between our results and those pertinent to the case of a converging spherical wave diffracted by a hard-edge circular aperture. Some hints for future investigations are also given.
TL;DR: The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed in this paper.
Abstract: The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the latter is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite pol...
TL;DR: A method for improving the accuracy of spatial fringe analysis, based on fringe scanning and interpolation techniques, is put forward and two-dimensional fringe analysis based on this new method is proposed.
Abstract: Fringe analysis is used in engineering fields as a precise measurement technology. In this paper, a method for improving the accuracy of spatial fringe analysis is discussed. A new method, based on fringe scanning and interpolation techniques, is put forward. Two-dimensional fringe analysis based on this new method is also proposed. Measured results obtained using the new two-dimensional method and those obtained using the FFT method are compared. Results showed that while the accuracy of the two methods is equivalent, the calculation time for the new method is five times as speedy as that for the FFT method.
TL;DR: In this article, states with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analyzed by tomographical methods.
Abstract: States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.
TL;DR: The problem of optical homodyne tomography is considered in the context of a Bayesian model-fitting or inverse problem approach, and an algorithm is formulated, based on matrix computation rather than the numerical approximation of an analytic inverse transform.
Abstract: The problem of optical homodyne tomography is considered in the context of a Bayesian model-fitting or inverse problem approach. An algorithm is formulated, based on matrix computation rather than the numerical approximation of an analytic inverse transform. This automatically takes into account the effects of noise, detector inefficiencies and incomplete sampling of the data. The relationships with conventional reconstruction schemes, methods for including various forms of prior information and for calculating error estimates are discussed. The process of reconstructing the photon number distribution and the density matrix are illustrated using both simulated and experimental data.
TL;DR: In this paper, the authors investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides, where the linear coupling between the guides is a variable function of the propagation distance.
Abstract: We investigate a codirectional nonlinear coupler composed of two Kerr nonlinear waveguides. Unlike the conventional device, the linear coupling between the guides is supposed to be a variable function of the propagation distance. We calculate quantum statistical and dynamical properties of the Kerr nonlinear coupler with a coherent input and analyse the influence of coupling variation on oscillations in mean photon number. The possibility to control the switching characteristics and principal squeezing effect by adjusting the form of coupling function is shown.
TL;DR: In this article, the development of optical techniques for non-invasive imaging in biology and medicine is reviewed and some fundamental considerations of light propagation in random media are discussed, including coherent unscattered light and diffuse light.
Abstract: Recent progress in the development of optical techniques for non-invasive imaging in biology and medicine is reviewed. We start with some fundamental considerations of light propagation in random media. We then discuss imaging using coherent unscattered light and diffuse light. Microscopic techniques based on one- and two-photon fluorescence are described and several types of nonlinear and time-resolved microscopy are explained. We conclude with some application examples and an outlook.
TL;DR: In this paper, the correlation-induced spectral changes, discovered several years ago and extensively studied since then, is shown to offer the possibility of contructing novel types of spectral filter which have several properties that are not achievable with conventional filters.
Abstract: The phenomenon of correlation-induced spectral changes, discovered several years ago and extensively studied since then, is shown to offer the possibility of contructing novel types of spectral filter which have several properties that are not achievable with conventional filters. For example such filters can have different prescribed filtering properties in different directions of observation. In this paper the underlying theory is discussed and is illustrated by a few examples.
TL;DR: A model is developed to understand better the mechanisms involved in the measurement of ζ, the directionality factor of photoreceptors from the human retina, which is determined much more by photoreceptor characteristics than by the retinal pigment epithelium properties.
Abstract: The directionality of photoreceptors from the human retina may be measured by psychophysical or reflectometric methods. Oddly the directionality factor ζ provided by the phororeceptor alignment reflectometer (PAR) is four times the shape factor ρ of the Stiles-Crawford function, instead of twice as we could guess from the PAR design. We have thus developed a model to understand better the mechanisms involved in the measurement of ζ. The model predicts that: first the factor ζ is determined much more by photoreceptor characteristics than by the retinal pigment epithelium properties, second the high value of ζ is due to the poor excitation of the modes TE01, TM01 and HE21 backwards, and third the instrumental anisotropy of the PAR is small. Consequently the PAR affords a tool for characterizing photoreceptors and allows us to determine the principal directions along which photoreceptors are stretched.
TL;DR: In this article, the non-classical properties of Schrodinger cat states given as superpositions of two-mode SU(1, 1) and SU(2) coherent states were studied.
Abstract: We study the non-classical properties of Schrodinger cat states given as superpositions of two-mode SU(1, 1) and SU(2) coherent states. The SU(1, 1) and SU(2) coherent states themselves have strong non-classical properties and we find that these properties are enhanced at least for some superpositions. We propose a method of generating such states in the context of cavity quantum electrodynamics.
TL;DR: In this article, a magnetooptical trap was used as a source of a pulsed beam of slow atoms and experiments were performed on the cloud of atoms in free fall over a distance of 45 cm.
Abstract: We report on atom optical experiments employing a magnetooptical trap as a source of a pulsed beam of slow atoms. After turning off the trap, experiments are performed on the cloud of atoms in free fall over a distance of 45 cm. We give a detailed description of the apparatus and discuss experimental results on the diffraction of atoms from a standing light wave in the regimes of short, intermediate and long interaction times. PACS: 03.75Be, 32.80Pj, 42.50Vk.