Table of contents

Guest editors: Joszef Janszky, Young S Kim and Margarita A Man'ko

This topical issue is in connection with the Wigner Centennial Conference, Pécs, Hungary, 8-12 July 2002. Participants of the conference, as well as other researchers working in this field, are invited to submit research papers to this topical issue. More information about the conference and its coverage can be found at http://quantum.ttk.pte.hu/~wigner.

Topics to be covered include:

• phase-space formalism

• fundamentals of quantum mechanics and quantum optics

• quantum interference and quantum entanglement

• quantum paradoxes such as the EPR paradox methods of measuring quantum states, quantum tomography, quantum teleportation, uncertainty relations and paradigmatic quantum inequalities such as Bell inequalities

• nonclassical states including Schrödinger cat states such as even and odd coherent states

• nonlinear coherent states

• photon statistics of nonclassical states

• the generation of quantum states in cavities

• trapped ion motion.

The topical issue is scheduled for publication in June 2003. All papers will be refereed according to the high standards of the journal. The new Editorial Division of the Institute of Physics Publishing at the P. N. Lebedev Physical Institute in Moscow will oversee editorial procedures in association with the main Publishing office in Bristol. Authors will receive 25 free offprints of their published paper and a complimentary copy of the topical issue. There are no page charges for publication. Manuscripts should be prepared following the general guidelines for authors published in the journal. Full instructions can be found in our Notes for authors.

Manuscripts should be submitted by e-mail to the Guest Editors at IOPP@sci.lebedev.ru, quoting `Special Issue/Wigner~100', by 1 October 2002, although authors are strongly encouraged to submit their work as soon as possible.

Elaborating on a previous work by Simon et al (2000 Phys. Rev. Lett.85 1783) we propose a realizable quantum optical single-photon experiment using standard present day technology, capable of discriminating maximally between the predictions of quantum mechanics (QM) and noncontextual hidden variable theories (NCHV). Quantum mechanics predicts a gross violation (up to a factor of 2) of the noncontextual Bell-like inequality associated with the proposed experiment. An actual maximal violation of this inequality would demonstrate (modulo fair sampling) an all-or-nothing type contradiction between QM and NCHV.

The behaviour of a V-type three-level atomic system in a ring cavity driven by a coherent field is studied. We consider a V configuration under conditions such that interference between decay channels is important. We find that when quantum interference is taken into account, optical bistability can be realized with a considerable decrease in the threshold intensity and the cooperative parameter. On the other hand, we also include the finite bandwidth of the driving field and study its role in the optical bistable response. It is found that at certain linewidths of the driving field optical bistability is obtained even if the system satisfies the trapping condition and the threshold intensity can be controlled. Furthermore, a change from the optical bistability due to quantum interference to the usual bistable behaviour based on saturation occurs as the driving field linewidth increases.

A pair of coherent femtosecond pulse excitations applied to a molecule with strong electron-phonon coupling creates a coherent superposition of a low-momentum and a high-momentum wavepacket in the vibrational states of both the excited state and the ground state of the coherent transition. As the excited state is accelerated further, interference between the high-momentum ground state contribution and the low-momentum excited state contribution causes a photon echo. This photon echo is a direct consequence of quantum interference between separate vibrational trajectories and can therefore provide experimental evidence of the non-classical properties of molecular vibrations.

We studied the dissipative dynamics of a degenerate-level atom interacting with a single linearly polarized mode field in the dispersive approximation. It is found that the degeneracy of the atomic levels affects the dissipation of the system, of the atom and the field. The period of entanglement becomes much longer than that in the usual Jaynes-Cummings model dissipation. The degeneracy of the atomic level increases the maximum value of the degree of the statistical mixture.

Real sources of entangled photon pairs (such as parametric down conversion) are not perfect. They produce quantum states that contain more than only one photon pair with some probability. Several aspects of the use of such states for the purpose of quantum key distribution are discussed. It is shown that the presence of `multi-pair' signals (together with low detection efficiencies) causes errors in transmission even in the absence of an eavesdropper. Moreover, it is shown that even the eavesdropping, that draws information only from these `multi-pair' signals, increases the error rate. This fact represents the important advantage of entanglement-based quantum key distribution. Information, that can be obtained by an eavesdropper from the `multi-pair' signals, is also calculated.

Noisy teleportation of nonclassical quantum states via a two-mode squeezed-vacuum state is studied with the completely positive map and the Glauber-Sudarshan P-function. Using the nonclassical depth as a measure of transmission performance, we compare the teleportation scheme with the direct transmission through a noisy channel. The noise model is based on the coupling to the vacuum field. It is shown that the teleportation channel has better transmission performance than the direct transmission channel in a certain region. The bounds for such a region and for obtaining the nonvanished nonclassicality of the teleported quantum states are also discussed. Our model shows a reasonable agreement with the teleportation fidelity observed in the experiment performed by Furusawa et al (1998 Science282 706). We finally mention the required conditions for transmitting nonclassical features in real experiments.

In this paper we investigate the quantum optics of a double-ended optical cavity. We show that an impedance matched, far-detuned cavity can be used to separate the positive and negative sidebands of a field. The `missing' sideband will be replaced by the equivalent sideband incident on the cavity from the other direction. This technique can be used to convert the quantum correlations between the sidebands of the incident fields into quantum correlations between the two spatially distinct output fields. We show that, under certain experimental conditions, the fields emerging from the cavity will display entanglement.

We present intensity noise investigations of a free-running InGaAs quantum-well laser diode operating at 980 nm at room temperature. The laser had a threshold current of 17 mA. Photon-number squeezing was achieved for drive currents of 48 mA when the laser was operating on two dominant longitudinal modes. The degree of squeezing obtained was 9%, which was in reasonable agreement with the current-to-current efficiency of 11%. No squeezing was observed at 35 K.

From a quantum information point of view we study the entropy squeezing of a two-level atom interacting with two modes with intensity-dependent coupling. The Hamiltonian we consider consists of all acceptable forms of nonlinearities. A definition of squeezing is presented for this system, based on information theory. The utility of the definition is illustrated by examining squeezing in the information entropy of a two-level atom in the presence of a nonlinear medium. We examine the influence of the nonlinear interaction, the atomic coherence and the detuning parameter on the properties of the entropy and squeezing of the atomic variables. It is shown that features of the quantum entropy are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields.

Minimization of error probability is considered in entanglement-assisted quantum communication systems. It is shown that although quantum state signals being sent are not symmetric at a sender side, the square root measurement becomes optimum when they are made symmetric at the receiver side. For communication systems of coherent signals, where a two-mode squeezed-vacuum state is used as an entanglement resource, the quantum entanglement greatly reduces the average probability of error. The relation to the quantum dense coding of continuous variables is also discussed.

We report on the experimental investigation of the dynamics of semiconductor lasers subjected to external optical injection. We have mapped the nonlinear regions in the parameter space consisting of the detuning between the master and slave lasers and the injection intensity. The map is based on optical and radio-frequency spectra sampled and collected continuously as one parameter is changed while the other is fixed. The chaotic oscillations of the slave laser can clearly be seen to form distinct regions in the map. Within the chaotic regions islands of periodic oscillation are found.

A generalized Mach–Zehnder-type interferometer equipped with cross-Kerr elements is proposed to convert N-photon truncated single-mode quantum states into (N + 1)-mode single-photon states, which are suitable for further state manipulation by means of beamsplitter arrays and ON/OFF-detections, and vice versa. Applications to the realization of unitary and non-unitary transformations, quantum state reconstruction and quantum telemanipulation are studied.

A very brief comment concerning the literature relating to the angular momentum of light is followed by a précis of a review article on the orbital angular momentum of light published in 1999. An outline is then given of the key developments since 1999 in the study of the angular momentum of light and of the related topic of optical vortices.

We introduce the angular-momentum flux as the natural description of the angular momentum carried by light. We present four main results: (i) angular-momentum flux is the flow of angular momentum across a surface and, in conjunction with the more familiar angular-momentum density, expresses the conservation of angular momentum. (ii) The angular-momentum flux for a light beam about its axis (or propagation direction) can be separated into spin and orbital parts. This separation is gauge invariant and does not rely on the paraxial approximation. (iii) Angular-momentum flux can describe the propagation of angular momentum in other geometries, but the identification of spin and orbital parts is then more problematic. We calculate the flux for a component of angular momentum that is perpendicular to the axis of a light beam and for the field associated with an electric dipole. (iv) The theory can be extended to quantum electrodynamics.

Cylindrical-lens mode converters (Beijersbergen M W, Allen L, van der Veen H E L O and Woerdman J P 1993 Opt. Commun.96 123-32) are used to transform between Hermite-Gaussian and Laguerre-Gaussian modes with a resulting transfer of angular momentum to the light beam and a corresponding torque on the lenses. By numerically analysing both the total and local angular momentum of the light beam, we explain the origin of this torque and confirm that is not evenly distributed between the lenses. We also confirm that any vortex contained within the beam may change sign even when the orbital angular momentum of the beam remains constant.

We present a theoretical and experimental study on the transfer of angular momentum from a light beam to a nematic liquid crystal film. In the angular momentum transfer process photons are not destroyed, but scattered in a different angular momentum state: a process known as self-induced stimulated light scattering (Santamato E, Daino B, Romagnoli M, Settembre M and Shen Y R 1988 Phys. Rev. Lett.61 113-16). Each photon in the incident beam transfers to the material only the change of its angular momentum, producing a torque on the body. Under the action of this torque, the body starts to rotate, changing, in turn, the amount of angular momentum extracted from the light beam. The process is intrinsically nonlinear and, as proved by the experiments reported in this paper, it can be initiated by a light beam carrying no angular momentum at all.

A theory determining the electric and magnetic properties of vortex states in Bose-Einstein condensates (BECs) is presented. The principal ingredient is the Lagrangian of the system, which we derive correct to the first order in the atomic centre-of-mass velocity. For the first time using centre-of-mass coordinates, a gauge transformation is performed and relevant relativistic corrections are included. The Lagrangian is symmetric in the electric and magnetic aspects of the problem and includes two key interaction terms, namely the Aharanov-Casher and the Röntgen interaction terms. The constitutive relations, which link the electromagnetic fields to the matter fields via their electric polarization and magnetization, follow from the Lagrangian as well as the corresponding Hamiltonian. These relations, together with a generalized Gross-Pitaevskii equation, determine the magnetic (electric) monopole charge distributions accompanying an order n vortex state when the constituent atoms are characterized by an electric dipole (magnetic dipole). Field distributions associated with electric dipole active (magnetic dipole active) BECs in a vortex state are evaluated for an infinite- and a finite-length cylindrical BEC. The predicted monopole charge distributions, both electric and magnetic, automatically satisfy the requirement of global charge neutrality and the derivations highlight the exact symmetry between the electric and magnetic properties. Order of magnitude estimates of the effects are given for an atomic gas BEC, superfluid helium and a spin-polarized hydrogen BEC.

The structure and stability of vortices in hybrid atomic-molecular Bose-Einstein condensates is analysed in the framework of a two-component Gross-Pitaevskii-type model that describes the stimulated Raman-induced photoassociation process. New types of topological vortex states are predicted to exist in the coherently coupled two-component condensates even without a trap, and their nontrivial dynamics in the presence of losses is demonstrated.

Recent experiments on the classic Einstein-Podolsky-Rosen (EPR) setting claim to test the compatibility between nonlocal quantum entanglement and the (special) theory of relativity. Confirmation of quantum theory has led to the interpretation that Einstein's image of physical reality for each photon in the EPR pair cannot be maintained. A detailed critique on two representative experiments is presented following the original EPR notion of local realism. It is argued that relativity does not enter into the picture, however for the Bell-Bohm version of local realism in terms of hidden variables such experiments are significant. Of the two alternatives, namely incompleteness of quantum theory for describing an individual quantum system, and the ensemble view, it is only the former that has been ruled out by the experiments. An alternative approach gives a statistical ensemble interpretation of the observed data, and the significant conclusion that these experiments do not deny physical reality of the photon is obtained. After discussing the need for a photon model, a vortex structure is proposed based on the space-time invariant property-spin, and pure gauge fields. To test the prime role of spin for photons and the angular-momentum interpretation of electromagnetic fields, experimental schemes feasible in modern laboratories are suggested.

Two different experimental techniques for preparing and analysing superpositions of Gaussian and Laguerre–Gaussian modes are presented. These involve exploiting an interferometric method in one case and using computer-generated holograms in the other. It is shown that by shifting a hologram with respect to an incoming Gaussian beam, different superpositions of the Gaussian and the Laguerre–Gaussian beam can be produced. An analytical expression connecting the relative phase, the amplitudes of the modes and the displacement of the hologram is given. The application of such orbital angular momenta superpositions in quantum experiments such as quantum cryptography is discussed.

We report the first experimental generation of high-order Mathieu beams and confirm their propagation invariance over a limited range. In our experiment we use a computer-generated phase hologram. The peculiar behaviour of the vortices in Mathieu beams gives rise to questions about their orbital-angular-momentum content, which we calculate by performing a decomposition in terms of Bessel beams.

We describe different types of ring-profile optical solitary wave and clusters of fundamental solitons propagating in isotropic nonlinear optical media. Such ringlike solitons carry a finite angular momentum and, depending on the value of the total momentum and structure, they either fragment quickly into several fundamental solitons that fly off the ring, or propagate stably for many diffraction lengths with rotating intensity and phase. Stabilization of the ring-profile optical beams and rotating soliton clusters due to vectorial interaction is also demonstrated.

A theory is presented for the detailed formulation of the nonlinear optics of laser beams endowed with orbital angular momentum. Following an introductory excursion into the general principles of such twisted beams, a quantum electrodynamical formulation is developed for representing the photonics of their interaction with matter. Detailed results are given for Laguerre–Gaussian beams in the large-Rayleigh-range limit. Utilization of the theory in nonlinear optics is illustrated by application to second-harmonic generation.

We consider the exchange of spin and orbital angular momenta between a circularly polarized Laguerre–Gaussian beam of light and a single atom trapped in a two-dimensional harmonic potential. The radiation field is treated classically but the atomic centre-of-mass motion is quantized. The internal levels in the atom are taken to be Rydberg circular states. The spin and orbital angular momenta of the field are individually conserved upon absorption, with the result that the electronic and motional degrees of freedom of the atom are entangled. We suggest applications in quantum information processing.

Particles of helical shape trapped in laser tweezers are rotated by light, independently of its polarization state. Light scattering by such propeller-like particles generates the momentum to drive the rotation. The efficiency of the rotation depends on the geometry of the particles. We used photopolymerization of light curing resins to create micrometre-size rotors with different shapes. The rotation of such particles was studied: the effect of shape and size on the rotation, as well as on the stability of the position in the laser tweezers.

The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates.

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