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Fundamentally contradictory but inescapably joined dual attributes, wave and particle, remain a conceptually unsettling element at the heart of quantum mechanics. It was a career-long unanswered challenge for Bohr to rationalize quantum duality. The conceptual dilemma it presents has remained an open issue, a topic of continued discussion, ever since. Here we report the discovery of an experimentally manageable route to control the weirdness of duality. Ironically, entanglement, the other conceptually challenging weirdness of quantum theory, will be shown to be in control of duality. We establish a simple identity through which entanglement prescribes quantitatively the degree of duality, of combined waveness and particleness, that can be recorded in any one-quantum two-path coherence experiment.

The growing recognition that entanglement is not exclusively a quantum property, and does not even originate with Schrödinger’s famous remark about it [Proc. Cambridge Philos. Soc.31, 555 (1935)PCPSA40008-198110.1017/S0305004100013554], prompts the examination of its role in marking the quantum-classical boundary. We have done this by subjecting correlations of classical optical fields to new Bell-analysis experiments and report here values of the Bell parameter greater than B=2.54. This is many standard deviations outside the limit B=2 established by the Clauser–Horne–Shimony–Holt Bell inequality [Phys. Rev. Lett.23, 880 (1969)10.1103/PhysRevLett.23.880PRLTAO0031-9007], in agreement with our theoretical classical prediction, and not far from the Tsirelson limit B=2.828…. These results cast a new light on the standard quantum-classical boundary description, and suggest a reinterpretation of it.

We investigate theoretically the phenomenon of so-called fast light in an unconventional regime, using pulses sufficiently short that relaxation effects in a gain medium can be ignored completely. We show that previously recognized gain instabilities, including superfluorescence, can be tolerated in achieving a pulse peak advance of more than one full peak width.

The scenario described by the title can be called subradiant emission from a collection of Nindependent atoms, since only one of Natoms is supposed to be excited. We examine this situation using a quantum electrodynamic Hertz vector approach and use the result to address the directionality of the emission, considering a possible role for atomic entanglement in the multi-atom initial state.

We investigate entanglement dynamics of two isolated atoms, each in its own Jaynes-Cummings cavity. We show analytically that initial entanglement has an interesting subsequent time evolution, including the so-called sudden death effect.

Strong and/or short laser pulses provide one avenue for rapid separation of composite quantum systems. Daughter particles can exhibit subtle aspects of quantum entanglement. We show that a Gaussian approximation provides a unifying overview of rapidly separating systems in many contexts, and propose using combined single-particle and coincidence measurements of wave-packet widths of bipartite systems for experimental observation of the degree of entanglement.

We examine two-particle entanglement and ways in which it might be coherently controlled. Control is desirable for successful implementation of quantum computing. As one result, we find that reaching very high entanglement may be feasible experimentally.

The time-dependent spectrum of the light scattered by a collisionally damped two-level atom weakly excited off resonance by a partially coherent laser field is evaluated. Both the collisional and the laser noise are treated as classical Markovian, Gaussian processes while, in addition, the atom is assumed to experience damping and fluctuations that are due to its coupling to an unspecified exterior reservoir. The scattered-field spectra are determined both at steady state and at times following the abrupt turn off of the laser field (the delayed spectrum). The distinct contributions to these spectra arising from the various noise sources as well as the finite bandwidth of the detecting interferometer are investigated in each case. Where appropriate, comparisons are made with related work of Saari [ Light Scattering in Solids ( Plenum, New York, 1979)]. A general inequality is also found that must be satisfied by the longitudinal and the transverse decay rates induced by the exterior reservoir. Finally, the inverse detuning of the laser is found to provide a limit on the time in which the undressing of the atom could be observed to occur following the turn off of the laser.

The theory of generalized coherent states associated with the SU(2) and SU(1,1) Lie algebras is discussed and applied in an investigation of possible reductions of fluctuations. In the framework of a system of N two-level atoms the squeezing of angular-momentum [SU(2)] fluctuations is exhibited for optical coherent transients involving the photon echo. The SU(1,1) fluctuations are discussed and established for general two-photon processes involving dynamical variables different from the creation and annihilation operators.

We present an atomic model to study above-threshold ionization (ATI). We show that when the laser field is sufficiently intense the usual perturbation theory is not valid. We solve the model dynamics exactly, and several interesting quantities, including the initial-state decay rate and photoelectron spectrum, are calculated. These quantities are related to recent ATI experiments, and qualitatively they agree with these experiments. We specify the strong-field condition for continuum–continuum transitions and explore its physical meaning. Finally some comments on perturbation theory are made.

Generalized optical Bloch equations are derived and applied to free-induction decay. The resultant expression for the free decay rate is shown to give a reasonably good fit to recent experimental data of DeVoe and Brewer that cannot be explained by the usual Bloch equations with the conventional 1/T_1 and 1/T_2 relaxation parameters.

We study laser-induced autoionization in a standard strong-field near-resonance model, with an extra (third) discrete state exicted by a second laser. We show that this third state plays a significant role in creating a narrow zero in the photoelectron spectrum. Two zeros are found in the spectrum, and confluence and trapping effects are studied.

We report the production of high-order optical harmonics in computer experiments on multiphoton ionization at high laser intensity. We correlate features of the scattered light spectra with above-threshold-ionization electron spectra from the same laser pulse in a number of experiments at different wavelengths and laser intensities.

Numerical simulation of multiphoton ionization of a one-dimensional model atom reveals new features in superintense laser fields. Graphs of above-threshold ionization (ATI) electron spectra and the corresponding time-dependent ionization probability curves show drastic changes from those of lower-intensity cases. A new type of ATI peak splitting as well as ionization rate suppression occur for high-frequency excitation with intensities up to approximately 25 a.u.

Multiphoton excitation of a model negative ion is studied. The model has only a single bound level, and we choose a photon frequency appropriate to five-photon photodetachment (before ponderomotive threshold shifts). Both of these characteristics are compatible with multiphoton detachment studies of the hydrogen negative ion made with CO_2 laser radiation. We study the model in a discretized energy basis in order to study independently the influence of bound–continuum (B–C) and continuum-continuum (C–C) dipole matrix elements on the multiphoton detachment process. Because the energy-level structure of the model (and also of negative ions generally) is relatively simple compared with that of atoms, we are able to investigate a number of questions in some detail, using either perturbation theory or exact numerical solutions to Schrödinger’s equation. Interesting consequences are the explicit identification of an interference between B–C-dominated and C–C-dominated detachment channels and the emergence of energy-nonconserving contributions to above-threshold electron spectra.

We undertake an approximate low-order calculation of the ionization rate of an atom in the strong-field regime, where stabilization, i.e., suppression of ionization, has been predicted. We proceed in the Kramers–Henneberger (K–H) reference frame and take into account time-dependent corrections to the static K–H potential. Using results from a short-range model atomic potential, we conclude that three stages of ionization can be distinguished: (1) An abrupt adjustment to laser turn-on occurs and causes some ionization; (2) very rapid depletion of a major fraction of the ground-state probability ends with stabilization of the remaining fraction; and (3) a residual slower ionization ultimately eliminates stabilization.

We review the status of the double–lambda system of cavity QED and mention unexpected recent applications in which deterministic and unitary control of quantum states is exploited.

We find the N-photon state emitted by an N-step Dicke model and provide a method to construct the field coherence functions based on it. Our effort is concentrated on the second order coherence, or the one-photon density matrix. When expressed in its canonical representation, this matrix gives the photon number occupying each 'pulse eigenmode'. This number serves as an indicator of the correlation between photons. By studying the evolution of the one-photon density matrix we can trace the creation of such correlation during the emission. From the asymptotic solution we are able to find approximate scaling law relations between the photon degeneracy in the eigenmodes and the total number of photons involved.

We investigate the time-dependent spectrum of light from an observational point of view and define a time-dependent “physical spectrum” of light based on the counting rate of a photodetector. The tunable element, the filter, that allows observation of different spectral components of the light is shown to play an essential role in the time-dependent spectrum. Its bandwidth cannot be taken arbitrarily narrow. We establish the connection between our physical spectrum and other time-dependent spectra associated with Page, Lampard, Silverman, and Kolmogorov, as well as with the Wiener-Khintchine power spectrum. Also, we show the conditions under which these earlier definitions can be used as the first approximations to the complete physical spectrum, and give an expression for the correction terms.

We investigate the time-dependent spectrum of light from an observational point of view and define a time-dependent “physical spectrum” of light based on the counting rate of a photodetector. The tunable element, the filter, that allows observation of different spectral components of the light is shown to play an essential role in the time-dependent spectrum. Its bandwidth cannot be taken arbitrarily narrow. We establish the connection between our physical spectrum and other time-dependent spectra associated with Page, Lampard, Silverman, and Kolmogorov, as well as with the Wiener-Khintchine power spectrum. Also, we show the conditions under which these earlier definitions can be used as the first approximations to the complete physical spectrum, and give an expression for the correction terms.

We report on an experimental characterization of Bessel beams with finite apertures. We show that real Bessel beams can be generated with intensity profiles that closely resemble the ideal Jo^2 transverse-intensity distribution of Bessel beams. We also show interferometrically that these beams have planar phase fronts with π-phase shifts from one Bessel ring to the next. We report tolerance conditions for Bessel beam generation and give an example of this generation that uses an unstable resonator as the light source.

The local effective emissivity for a point on the interior surface of a diffusely reflecting blackbody cone obeys an integral equation. A new analytic approximate solution of the integral equation is presented. This approximation is very good for interior portions of narrow cones where the effective emissivity is very close to unity. Another approximation of Kelley is better near the mouth of a narrow cone. Either approximation works for wide angle cones. The new approximation is modified to give a quantitative estimate of the effects of a temperature gradient along the side of the cone.

The theory of generalized coherent states associated with the SU(2) and SU(1,1) Lie algebras is discussed and applied in an investigation of possible reductions of fluctuations. In the framework of a system of N two-level atoms the squeezing of angular-momentum [SU(2)] fluctuations is exhibited for optical coherent transients involving the photon echo. The SU(1,1) fluctuations are discussed and established for general two-photon processes involving dynamical variables different from the creation and annihilation operators.

We present a study of the ability of three basic spectrometers—the diffraction grating, the Fabry–Perot, and the prism—to measure the Fourier energy spectra of pulses, that is, signals that are time limited. It is shown that under certain conditions prior knowledge of a finite upper bound on the maximum length of the input pulse can make it possible to violate the classical uncertainty principle and achieve enhanced spectral resolution. The resolution enhancement is obtained simply by recording the spectrometer output intensity only during a specific time interval after the entire pulse has been received.

We propose a deterministic method to generate an arbitrary (pure or mixed) density matrix of a harmonic oscillator. The general density matrices are achieved by manipulating quantum entanglement between the oscillator and an auxiliary oscillator. We discuss how our preparation scheme can be realized by cavity quantum electrodynamics interactions so that a general density matrix of a single-mode electromagnetic field can be created.

We use an exactly solvable two-colour model of multiphoton ionization to exhibit the similarities and differences between the light scattering spectra predicted by the model's dipole expectation value and its dipole correlation function.

We examine the correlation between a pair of photons in the information entropy context. Either in two-photon cascade decay of a three-level system or in parametric down-conversion a pure state of two distinguishable photons is produced, with the states of the individual photons entangled. We obtain state amplitudes in the Weisskopf-Wigner approximation and use them to derive the two-photon density matrix in the 'arrival time' basis. It is found that only a finite number of eigenvectors of the appropriate density matrices is required to describe the system. That is, despite the continua of wave-vectors involved in the double spontaneous decay the two-photon entanglement is effectively discrete; furthermore, the eigenvectors in the arrival time basis can be interpreted as the fundamental orthogonal spontaneous emission pulses of the two systems.

We present theoretical work on high-order harmonic generation accompanying multiphoton ionization of atoms in intense laser fields. We first review some elements of the theory of harmonic generation, particularly the limitations imposed by perturbation theory and some aspects of phase-matching at high pump intensities. A new non-perturbative approach to the theory based on the direct numerical solution of the time-dependent Schrödinger wave equation is described.Selected results of this theory are presented, including: (a) evidence for a plateau of high-order harmonic peak intensities and a relatively abrupt cut-off of this plateau, closely similar to what has been reported experimentally in noble gas atoms, (b) specific predictions for harmonic production by H, He and Xe atoms, and (c) analytical and numerical evidence for the correlation of harmonic production spectra with above-threshold photoelectron spectra under certain circumstances.

We present a theoretical model for two-colour strong-field photodetachment of a negative ion. Our model can be solved analytically in a certain approximation. We discuss the phenomenology predicted by the model and test its numerical reliability under various conditions that might be realized experimentally.

We present a continuation of a general theoretical approach to noisy laser-atom interactions based on a special Markov-cham description of external fluctuations. This chain, composed of n independent two-state jump processes, forms a non-Gaussian stochastic process from which a detailed discussion of the atomic response can be given. We show that the n-component Markov chain also has the property of pre-Gaussian noise, because in the limit of n ? ∞ it converges to a Gaussian stochastic process. We exhibit solutions for the field spectrum and the atomic-fluorescence spectrum for phase, frequency, and amplitude pre-Gaussian fluctuations of the driving-laser light.

We discuss the effect of a laser field on the ionization potential of atoms and compare the ponderomotive-potential interpretation of the apparent threshold shift with experimental results of the above-threshold ionization of noble-gas atoms.

We consider a category of transient processes that is usually hidden from view in coherent-transient experiments. These are the very fast noise processes that give rise to relaxation effects. We present different Markov-type models of a class of these noise processes, namely, laser phase and frequency fluctuations. These models lead to different forms for the laser-field autocorrelation function, depending on which quantity, the phase or the frequency, is the primary source of noise. We show that it is possible to establish a regime such that all these kinds of noise will lead to a Lorentzian laser power spectrum. Despite this common feature, N-photon absorption exhibits observable differences depending on the source of fluctuations. For example, for diffusive noises the absorption linewidth increases as N^2, but for jumplike or shotlike phase fluctuations it can be N independent.

We identify classical light fields as physical examples of nonquantum entanglement. A natural measure of degree of polarization emerges from this identification, and we discuss its systematic application to any optical field, whether beamlike or not.

The coherent propagation of four optical pulses through a multilevel resonant medium is investigated theoretically. We present a self-consistent analytic solution without steady-state or adiabatic approximations and use numerical simulations to indicate that the analytic formulas can be used as a guide in an experimental setting.

We analyze the propagation of fast-light pulses through a finite-length resonant gain medium both analytically and numerically. We find that intrinsic instabilities can be avoided in attaining a substantial peak advance with an ultrashort rather than a long or adiabatic probe.

We present new pendulum-type equations for the propagation of two nonoverlapping pulses in a model swept-gain three-level amplifier. The predictions of these equations are compared numerically with corresponding predictions of the two-level Burnham–Chiao equations and with the full coupled three-level Maxwell–Bloch equations.

WE report evidence that suggests that narrow-line spectra can be obtained for many organic compounds without the difficulties commonly found with traditional mixed-crystal line-narrowing techniques. Furthermore, our findings suggest a new method by which low temperature line-broadening mechanisms may be studied.

Interactions between a three-level atom and two amplitude-fluctuating lasers are studied theoretically. One interesting feature of the interactions is the influence of the finite laser bandwidth and the two-laser cross-bandwidth on the absorption rate into the third level. As an example, it is shown how the partially saturated absorption process depends on both the autocorrelated and cross-correlated laser bandwidths.

Visibility V and distinguishability D quantify wave-ray duality: V^2+D^2≤1. We join them to polarization P via the Polarization Coherence Theorem, a tight equality: P^2=V^2+D^2.

We reply to the comment [Optica6, 829 (2019)OPTIC82334-253610.1364/OPTICA.6.000829] on our recent polarization coherence theorem (PCT): P^2=V^2+D^2 [Optica4, 1113 (2017)OPTIC82334-253610.1364/OPTICA.4.001113]. The main contribution of the PCT is its elucidation of the mostly overlooked two-party nature of degree of polarization. Its two-party foundation is an intrinsic property of the degree of ordinary light polarization and is equally true for other more general “polarizations” available in light beams. As one consequence, the PCT leads to the establishment of a new quantitative formation of the concept of wave-particle duality of light.