The concepts listed in the title are introduced and clarified. The relations among them are pointed out. It is shown that the corresponding optical phenomena are definitely of a quantum nature. The basic quantities which are measured in correlation optical experiments are discussed. Manifestations of photon antibunching and of sub-Poisson photon statistics in the recording of delayed coincidences, in the distribution of photon counts, and in intensity fluctuation spectra are analyzed. (More precisely, what is involved is the spectrum of fluctuations in the photocurrent; all the results of the theoretical analysis in this review are expressed in terms of directly measurable quantities.) A diagram technique for calculating the correlation characteristics of the radiation from a polyatomic system is outlined. Photon correlations in nonlinear resonance fluorescence are analyzed. There is a discussion of approaches to the development of macroscopic sources of radiation with sub-Poisson photon statistics: the production of a squeezed state of a field in phase-sensitive parametric effects in nonlinear optics and the introduction of repulsive statistics in luminescence excitation events and in the pumping of a laser. Experiments in these directions which had been reported through April 1986 are discussed. The practical importance of reducing the quantum noise in radiation for extremely precise measurements and for optical data transmission is pointed out.

https://iopscience.iop.org/article/10.1070/PU1987v030n10ABEH002966/pdf

New phenomena in quantum optics: photon antibunching, sub-Poisson photon statistics, and squeezed states

Quantum fluctuations in unstable dissipative systems

The occurrence of photon antibunching and squeezing is strongly connected with nonlinear optical phenomena in general. Recent results are presented for two-atom resonance fluorescence, the anharmonic oscillator, nonlinear propagation of light and higher-harmonic generation.

Photon Antibunching and Squeezing: Two Non-trivial Effects of the Nonlinear Interaction of Laser Light with Matter

The complete normal quantum characteristic function is calculated from which fluctuations in photon and phonon modes as well as the correlations among them are obtained. They are particularly discussed from the point of view of antibunching assuming that the phonon and the photon modes are initially coherent.

Statistical properties of brillouin scattering

lyapunov analysis of chaos in a system governing second-harmonic generation of light

Self-pulsing and chaotic dynamics in an optical three-mode system

The statistics of a system of four boson modes in Stokes-Antistokes interaction is considered with respect to the influence of damping in one mode. The time evolution of the system is calculated. The mean particle numbers and the factorial moments of photon number distribution are calculated. Numerical results show strong dependence on bath temperature but only weak influence of the bath coupling strength. In the combined Stokes-Antistokes system Antibunching appears if the bath temperature is low.



Statistisches Verhalten eines in Stokes-Antistokes-Art wechselwirkenden Bosonensystems mit Dampfung



Ein System von vier Bosonenmoden mit Stokes-Antistokes-Wechselwirkung wird im Hinblick auf den Einflus der in einer Mode wirkenden Dampfung untersucht. Als Reprasentanten der Veranderung seiner Statistik mit der Zeit werden mittlere Photonenzahlen und faktorielle Momente der Photonenzahlverteilung berechnet. Die numerischen Resultate zeigen starke Abhangigkeit der Zeitentwicklung von der Temperatur des Dampfungsbades, jedoch nur geringen Einflus der Bad-Moden-Kopplung. Bei hinreichend niedriger Badtemperatur kann im kombinierten System von Stokes- und Antistokes-Mode Antibunching auftreten.

Statistics of a Stokes‐Antistokes Interacting Boson System with Damping

An externally driven light mode in a ring cavity may show multistable behaviour if linear losses and dispersive nonlinear coupling compete with each other. The paper considers the trilinear (sum frequency) system with two externally driven modes which shows bistability simultaneously in these two modes. It is described in a fully quantum manner. The master equation and the Fokker-Planck equation for the Glanmber-Sudarshan quasi-probalbility are deduced with appropriate consideration of fluctuations. A closed steady solution of the Fokker-Planck equation is given for one mode only under strong restrictive assumptions.



Quantenstatistik optischer Bistabilitat in einem Mehrmodensystem mit trilinearer Wechselwirkung



Eine in einem Ringresonator von ausen angeregte Lichtmode kann sich multistabil verhalten, wenn lineare Verluste und dispersive nichtlineare Kopplung zusammenwirken. In der Arbeit wird ein trilinear wechselwirkendes (Summenfrequenz-) System betrachtet, bei dem zwei Moden von ausen angeregt werden, die unter gewissen Bedingungen gleichzeitig Bistabilitat zeigen. In voll quantentheoretischer Behandlung werden Mastergleichung und Fokker-Planck-Gleichung fur die Glauber-Sudarshan-Quasiwahrscheinlichkeit unter angemessener Berucksichtigung der Fluktuationsquellen hergeleitet. Eine geschlossene Losung der Fokker-Planck-Gleichung fur stationare Falle gelingt unter stark einschrankenden Annahmen fur eine der Moden.

Quantum Statistics of Multimode Optical Bistability with Trilinear interaction

Mutual optical bistability is found for several modes in open cavities containing second- or third-order nonlinear materials. The quantum-statistical treatment yields the Fokker-Planck equation for any system of damped boson modes. Under certain conditions it is possible to state the extrema of the steady solution of the Fokker-Planck equation. They are compared with the steady states resulting from the classical deterministic treatment. In some cases both statements coincide.

Optical Bistability in Multimode Systems with Second-and Third-order Dispersive Nonlinearity

The influence of fluctuations in the driving fields on an optical bistable multimode system inside a ring resonator with a second order nonlinear material is considered. Steady state solutions of the resulting Fokker-Planck equations are found for different approximations in which one or two of the modes can be eliminated adiabatically. The results of the stochastics are compared with the deterministic behaviour.



Einflus des Rauschens auf ein dispersives optisch bistabiles System mit trilinearer Wechselwirkung



Es wird der Einflus von Fluktuationen in den treibenden Feldern auf ein optisch bistabiles Mehrmodensystem innerhalb eines Ringresonators mit einem nichtlinearen Medium zweiter Ordnung betrachtet. Stationare Losungen der resultierenden Fokker-Planck-Gleichungen werden fur verschiedene Naherungen gefunden, in denen eine oder zwei Moden adiabatisch eliminiert werden konnen. Die Ergebnisse der Stochastik werden mit dem deterministischen Verhalten verglichen.

F.‐J. Schütte

Papers

Self-pulsing and chaotic dynamics in an optical three-mode system

Statistics of a Stokes‐Antistokes Interacting Boson System with Damping

Quantum Statistics of Multimode Optical Bistability with Trilinear interaction

Optical Bistability in Multimode Systems with Second-and Third-order Dispersive Nonlinearity

Noise Influence on a Dispersive Optical Bistable System with Trilinear Interaction