The effects of any quantum measurement can be described by a collection of measurement operators $\{M_m\}$ acting on the quantum state of the measured system. However, the Hilbert space formalism tends to obscure the relationship between the measurement results and the physical properties of the measured system. In this paper, a characterization of measurement operators in terms of measurement resolution and disturbance is developed. It is then possible to formulate uncertainty relations for the measurement process that are valid for arbitrary input states. The motivation of these concepts is explained from a quantum communication viewpoint. It is shown that the intuitive interpretation of uncertainty as a relation between measurement resolution and disturbance provides a valid description of measurement back action. Possible applications to quantum cryptography, quantum cloning, and teleportation are discussed.

Several recent studies on the subject of environment induced decoherence have suggested that the predictability sieve selects coherent states over squeezed states. Most of such studies have considered a system consisting of an oscillator linearly coupled to a bath of harmonic oscillators. In this paper, we consider an environment consisting of squeezed oscillators. We derive the master equation for an oscillator coupled to such an environment. We solve this master equation for the case of the oscillator being in a coherent state and for the oscillator in a squeezed state. We then compare the stability of coherent states and squeezed states in the general squeezed environment. Our aim is to find if coherent states are more stable than squeezed states in a squeezed environment as well or is this fact true only in an environment of coherent oscillator states? We argue that unless we show that coherent states are preferred in a nonclassical environment as well, we cannot assume that coherent states form most environments and therefore the study of the stability of states only in an environment of coherent oscillator states is not a general case.

We propose two probabilistic entanglement concentration schemes for a single copy of a two-mode squeezed vacuum state. The first scheme is based on the off-resonant interaction of a Rydberg atom with the cavity field while the second setup involves the cross Kerr interaction, an auxiliary mode prepared in a strong coherent state, and homodyne detection. We show that the continuous-variable entanglement concentration allows us to improve the fidelity of teleportation of coherent states.

We consider, both analytically and numerically, the evolution of two-dimensional (2D) nonlinear matter-wave pulses in a Bose-Einstein condensate with a disk-shaped trap and repulsive atom-atom interactions. Due to the strong confinement in the axial direction the sound speed of the system is ${c=(1/2\mathrm{}}^{1/4}{)c}_0,$ where $c_0$ is the corresponding value without the trap. From the 3D order-parameter equation of the condensate, we derive a soliton-bearing Kadomtsev-Petriashvili equation with positive dispersion. When the trapping potential is weak in two transverse directions, a low-depth plane dark soliton can propagate in the condensate with a changing profile but preserving its structure down to the boundary of the condensate. We show that high-depth plane dark solitons are unstable to long-wavelength transverse disturbances. The instability appears as a longitudinal modulation of the soliton amplitude decaying into vortices. We also show how a dark lumplike 2D nonlinear excitation can be excited in the system. Furthermore, a dark lump decaying algebraically in two spatial directions can propagate rather stable in the condensate, but disappears near the boundary of the condensate where two vortices are nucleated. The vortices move in opposite directions along the boundary and when meeting merge creating a new lump. Finally, we also provide results for head-on and oblique collisions of two lumps in the system.

A giant reversible increase $(>~{10}^3$ times) of the optical second-order harmonic’s (SH) absorption by optical poling of oxide glass was found. The SH’s absorption kinetics manifested anisotropy with respect to polarization of the pumping (poling) light. The observed absorption exerts the influence of optical poling on the observed processes and leads to a limitation of the maximum value of the photoinduced SH output in oxide glass. An explanation of the observed phenomenon is given. It was shown that the observed process is a typical steady-state effect with participation of trapping levels, and its polarized dependence is caused by the photoinduced anisotropy of the photocarrier diffusion and by the electron-phonon anharmonic interaction.

We study long-lived resonances (lowest-loss modes) in hexagonally shaped dielectric resonators in order to gain insight into the physics of a class of microcrystal lasers. Numerical results on resonance positions and lifetimes, near-field intensity patterns, far-field emission patterns, and effects of rounding of corners are presented. Most features are explained by a semiclassical approximation based on pseudointegrable ray dynamics and boundary waves. The semiclassical model is also relevant for other microlasers of polygonal geometry.

We study experimentally the spatial distribution of quantum noise in the twin beams produced by a type-II optical parametric oscillator operating in a confocal cavity above threshold. The measured intensity correlations are at the same time below the standard quantum limit and not uniformly distributed inside the beams. We show that this feature is an unambiguous evidence for the multimode and nonclassical character of the quantum state generated by the device.

Entwined space-time paths are bound pairs of trajectories which are traversed in opposite directions with respect to macroscopic time. In this paper, we show that ensembles of entwined paths on a discrete space-time lattice are simply described by coupled difference equations which are discrete versions of the Dirac equation. There is no analytic continuation, explicit or forced, involved in this description. The entwined paths are “self-quantizing.” We also show that simple classical stochastic processes that generate the difference equations as ensemble averages are stable numerically and converge at a rate governed by the details of the stochastic process. This result establishes the Dirac equation in one dimension as a phenomenological equation describing an underlying classical stochastic process, in the same sense that the diffusion and telegraph equations are phenomenological descriptions of stochastic processes.

It is shown that a two-qubit phase gate and SWAP operation between ground states of cold trapped ions can be realized in one step by simultaneously applying two laser fields. Cooling during gate operations is possible without perturbing the computation. On the contrary, the cooling lasers even stabilize the desired time evolution of the system. This affords gate operation times of nearly the same order of magnitude as the inverse coupling constant of the ions to a common vibrational mode.

The ${}^2{S}_{1/2}{\mathrm{}(F=0\mathrm{})\mathrm{}}^2{F}_{7/2}{(F=3,m}_F=0)$ transition at 467 nm in a single trapped, laser-cooled ion of ${}^{171}{\mathrm{Yb}}^{+}$ has been measured to be $f_{{\mathrm{Yb}}^{+}}=642\mathrm{}121496771.26\left(23\right)\mathrm{}\mathrm{kHz}$ using a femtosecond laser frequency comb generator. The measurement is limited by measurement statistics and by the ac Stark shift, both related to the 4.5 kHz linewidth of the probe laser at the time. The systematic shifts of the transition, including ac Stark, second-order Zeeman, quadrupole, and blackbody shifts, have been evaluated.

A three-dimensional (3D) analysis of the spontaneous decay of a single dipole embedded in a planar multilayer structure is given, with special emphasis on Kerr-tunable photonic band-gap materials for single-photon emission on demand. It is shown that the change in the density of states near a defect resonance is much more pronounced than that near the band edges. In particular, operation near the band edge as suggested from a 1D analysis is little suited for controlling the photon emission.

We compare a recently proposed perturbation method for quantum-mechanical observables with the well-known standard perturbation approach and the Magnus expansion.

Given a quantum state of the electromagnetic field, one is, in principle, free to redefine the field modes. We show here how the amount of entanglement in a given state depends on redefinitions of the modes, and calculate the minimum and maximum entanglement over all such redefinitions for several examples. Redefinitions can also be interpreted as transformations that one can apply actively, for example, in order to create nonlocal entanglement.

Quantum interference is shown to deliver a means of regulating the diffraction pattern of a thermal atomic beam interacting with two standing-wave electric fields. Parameters have been identified to enhance the diffraction probability of one momentum component over the others, with specific application to Rb atoms.

We propose an experiment for entangling two spatially separated Bose-Einstein condensates by Bragg scattering of light. When Bragg scattering in two condensates is stimulated by a common probe, the resulting quasiparticles or particles in the two condensates get entangled due to quantum communication between the condensates via the probe beam. The entanglement is shown to be significant and occurs in both number and quadrature phase variables and depends strongly on the relative detuning of the two pumps and the relative atom-field coupling strengths of the two condensates. We present two methods of detecting the generated entanglement.

We present a simple spectroscopic method based on Autler-Townes spectroscopy to determine the center-of-mass atomic wave function. The detection of spontaneously emitted photons from a three-level atom, in which two upper levels are driven by a classical standing light, yields information about the position and momentum distribution of the atom [A. M. Herkommer, W. P. Schleich, and M. S. Zubairy, J. Mod. Opt. $44,$ 2507 (1997)]. In this paper, we show that both the amplitude and phase information of the center-of-mass atomic wave function can be obtained from these distributions after a series of conditional measurements on the atom and the emitted photon.

We discuss a long code problem in the Bennett-Brassard 1984 (BB84) quantum-key-distribution protocol and describe how it can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol.

The hypothesis of treating three-electron systems as a two-electron core plus a bound electron in the hyperspherical adiabatic approach introduces a second adiabatic separation into hyperangular equations. Differently from the main radial-angular hyperspherical adiabatic separation, the resulting couplings are necessary to guarantee permutational and rotational invariance of the Hamiltonian. Thus, any kind of approximation, disregarding such couplings, represents a loss of symmetry. This paper explores the consequences of such approximations in the potential curve calculations for the lithium atom, showing that this symmetry breaking is quite smooth and can be recovered within a good precision adding few couplings to the system of angular differential equations.

Aharonov and Reznik have argued [in Phys. Rev A 65, 052116 (2002)] that the form of the probabilistic predictions of quantum theory can be seen to follow from properties of macroscopic systems. An error in their argument is identified.