Table of contents

The decoherence in a trapped ion induced by coupling the ion to the engineered reservoir is studied in this paper. The engineered reservoir is simulated by random variations in the trap frequency, and the trapped ion is treated as a two-level system driven by a far-off-resonant plane wave laser field. The dependence of the decoherence rate on the amplitude of the superposition state is given.

A relation of the Wigner quasiprobability to the Bargmann representation of pure and mixed states by convolution is derived and generalized to the main class of quasiprobabilities and its inversion is given. The derivation uses a realization of the abstract group SU(1,1) by second-order differentiation and multiplication operators for a pair of complex conjugated variables and disentanglement of exponential functions of these operators by group-theoretical methods. Examples for the calculation of the Wigner quasiprobability via the Bargmann representation of states demonstrate the action of this relation. A short collection of different basic representations of the Wigner quasiprobability is given. An appendix presents results for the disentanglement of SU(1,1)-group operators by products of special operators in different ordering.

The stochastic simulations of quantum evolution are introduced, alternatively, to the Ito-stochastic simulations, for the normal, symmetrical and antinormal ordering in the double-dimensional phase space. The nonclassical effects in the linearized parametric amplifier can be very well simulated in contrast to the collapses-revivals effect in a nonlinear version, which is stimulated by the discreteness of light. The reason is that the stochastic simulations use the continuous variables, whereas the quantum noise in nonlinear systems cannot generally be treated continuously.

We are in the midst of a renaissance in the study and interpretation of fundamental quantum mechanics, from quantum coherence and quantum entanglement to the quantum measurement process. This stems partly from the impressive advances in experimental techniques that are making yesterday's gedanken experiment today's reality. Another reason quantum coherence and entanglement have come to the forefront is the emerging and tantalizing field of quantum information science. The ability to store information in quantum systems may someday yield devices that process quantum superpositions of inputs in parallel or improve communication through the `wiring' implicit in quantum entanglement. Indeed, quantum computing has the remote prospect of revolutionizing the way we store and process information. This has become particularly important in the face of impending limits on the miniaturization of conventional computers due to quantum effects.

Of course, all real systems face limits imposed by decoherence, or the environmentally-induced destruction of quantum coherence. Here, superpositions of quantum states suddenly become probabilistic mixtures of states when they interact with the environment or when the system parameters are fluctuating. Decoherence theory is commonly interpreted as a way to quantify the elusive boundary between quantum and classical worlds and almost always precludes the existence of complex quantum superpositions, except at extremely short time scales. In practice, it is very important to study how decoherence appears in particular quantum systems and try to fight against it.

In this special issue of Journal of Optics B: Quantum and Semiclassical Optics, we highlight recent results in the exciting area of quantum coherence and entanglement, including generating interesting and complex quantum states, characterizing coherence and entanglement in these systems, and triumphing over relevant decoherence processes. We hope this issue will not only act as a bookmark in the ongoing study of fundamental quantum mechanics, but will also help guide the rapid developments in quantum information science.

Amplification of the Schrödinger-cat state (even coherent-state superposition) can be accompanied by its non-exponential decoherence and strong squeezing effect in the degenerate optical parametric amplifier. In the classical pump approximation and small thermal noise limit, the Wigner function behaviour illustrates that this non-exponential effect is induced by the phase-selective character of amplification. The non-exponential decoherence is much slower, in contrast with phase-unselective amplification exhibiting faster exponential decay. Thus, if one is able to produce the Schrödinger-cat state with at least a small amplitude, then it can be partially amplified with only a weak decoherence effect.

We analyse the Hanle effect on a closed F_g→F_e = F_g + 1 transition. Two configurations are examined, for linearly and circularly polarized laser radiation, with the applied magnetic field collinear to the laser light wavevector. We describe the peculiarities of the Hanle signal for linearly polarized laser excitation, characterized by narrow bright resonances at low laser intensities. The mechanism behind this effect is identified, and numerical solutions for the optical Bloch equations are presented for different transitions.

We discuss the dynamics of a two-level model in a strong coupling regime through the analysis of the probability amplitudes. It is seen that the theory recovers Rabi flopping also for strong coupling. Population trapping can occur and a decay constant for the excited state is also computed. Then, spontaneous emission can be made to disappear or, otherwise, the emitted photon turns out to have a frequency being an odd harmonic of the frequency of the perturbation.

A scheme is proposed for preparing delocalized mesoscopic states of the motion of two or more atoms trapped at distantly separated locations. Generation of entanglement is achieved using interactions in cavity quantum electrodynamics which facilitate motional quantum state transmission, via light, between separate nodes of a quantum network. Possible applications of the scheme are discussed.

Teleportation of some pure entangled states of discrete and continuous variables is considered using a multi-particle quantum channel; particularly a Greenberger-Horne-Zeilinger channel. Both the protocols we have found for the discrete and continuous versions have identical features due to the properties of the quantum channel. In this way some entangled states can be teleported perfectly; a non-Bell-state measurement is needed in contrast to the one-by-one protocol where an unknown state can be recovered by all receivers only. For teleportation of continuous variables an optical implementation using squeezed light states is discussed.

We present a method to protect the entangled states of distant particles against decoherence due to local (but collective) phase errors, and local exchange-type interactions, by pairing up the entangled particles. The method is based on a four-qubit code which forms a decoherence-free subspace for collective phase errors and exchange errors affecting the qubits in pairs. We also show how the scheme can be generalized to protect certain entangled states of more than two particles.

We have cooled a two-ion crystal to the ground-state of its collective modes of motion. Laser cooling, more specifically resolved sideband cooling, is performed sympathetically by illuminating only one of the two ⁴⁰Ca⁺ ions in the crystal. The heating rates of the motional modes of the crystal in our linear trap have been measured, and we found them considerably smaller than those previously reported by Turchette et al (2000 Phys.Rev.A 61 063418) in the case of trapped ⁹Be⁺ ions. After the ground state is prepared, coherent quantum state manipulation of the atomic population can be performed. Up to 12 Rabi oscillations are observed, showing that many coherent manipulations can be achieved. Coherent excitation of each ion individually and ground state cooling are important tools for the realization of quantum information processing in ion traps.

We show that the exponential phase moments associated with the s-ordered generalized Wigner function can be sampled from homodyne data for s⩽0. The tomographic sampling functions are evaluated for non-unit homodyne quantum efficiency, and the statistical reliability of the reconstruction is tested by Monte Carlo simulated experiments. The reconstruction of the s-ordered phase distribution from sampled moments is discussed, and the reduction of statistical fluctuations by adaptive techniques is also analysed.

In this paper we investigate the fourth-order coherence of biphoton beams from spontaneous parametric downconversion resulting from a nonlinear crystal as exemplified in a double-slit interference configuration where the signal and idler beams both pass through the same double slits. We find that the angle of the crystal optical axis and the crystal length are important factors, along with the double-slit separation and system bandwidth, in determining the nature of the fourth-order interference pattern obtained behind the slits. Only careful planning of system parameters and understanding of the tuning curves of the downconversion will illuminate the obtained coincidence patterns.

We show that the value at the origin of phase space of the Wigner function of entangled GHZ states, involving three modes of the electromagnetic field either in the same cavity or in different ones, is a signature of the quantum character of those states. This multimode Wigner function can be directly measured by a simple extension of a method previously proposed by two of the present authors. A single measurement on an atom which crosses the three modes is enough to distinguish between quantum mechanics and local hidden variable theories.

This paper proposes a realistically feasible experiment, within the realm of existing technology and proved techniques, to measure the mean photon number of a coherent source by means of a quantum non-demolition scheme, exploiting the parametric amplification of correlated photons in χ⁽²⁾ media. We deduce the number of photons of an input source interacting with a high-intensity pump field in a nonlinear crystal, using as the probe the shift in the quadrature amplitude of the pump beam induced by the source under measurement. We perform a theoretical evaluation of the noise level associated with this measurement and compare it with the quantum limit. We explore the possible implications of this method for radiometry.

We study the phenomena that arise in the transverse structure of an electromagnetic field impinging on a linear Fabry-Pérot cavity with an oscillating end mirror. We find quantum correlations among transverse modes, which can be considered as a signature of their entanglement.

We study the possible limitations and sources of decoherence in the scheme for the deterministic generation of polarization-entangled photons, recently proposed by Gheri et al (Gheri K M et al 1998 Phys. Rev. A 58 R2627) based on an appropriately driven single atom trapped within an optical cavity. We consider in particular the effects of laser intensity fluctuations, photon losses and atomic motion.

We show that in parametrically driven systems and, more generally, in systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the nonlinear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomenon as an optical analogue of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions.

We derive a theory for mapping a quantum state of nonclassical light onto a collective, excited atomic state via complete absorption of the light. We allow for an arbitrary polarization-squeezed state of light and an arbitrary spin of the atomic ground state. The present derivation thereby generalizes the results of Kuzmich et al. We compare the theory to the recently published experimental results on atomic spin squeezing.