Table of contents

We consider the case of interaction of a three-level atom with a high intensity pulse electromagnetic field. Rabi frequencies are assumed to be of the order of the transition frequency or greater. We demonstrate that coherent population trapping exists even in such a case when the usual rotating-wave approximation is no longer valid. However, a certain condition on the phases of electromagnetic wave components has to be satisfied in order to make coherent population trapping possible. This condition is specific for the strong field case in contrast to the case where the rotating-wave approximation is valid. Also we point out some elements for which a model of an atom with a finite number of levels may still be valid while the rotating-wave approximation breaks down.

An atom passes through two standing light fields, one classical and the other quantum mechanical. By performing field measurements, we can locate the atom very accurately and uniquely, for an atomic beam initially nearly two wavelengths wide, with great improvement over previous systems.

We use two correlation functions to describe the antiphase dynamics which occurs in globally coupled systems. Explicit results are obtained for the case of intracavity second harmonic generation. Our analysis indicates the optimum timing for switching pulses and supports the concept of dynamical independence of clustered modes.

We report the results of an experiment in which the cavity losses of a single mode, titanium sapphire laser are slowly varied with time. Under the influence of this slow sweep, the net gain required for the laser intensity to reach its lasing threshold increases beyond the static gain value necessary for lasing, a phenomenon called delayed bifurcation. In contrast to recent reports, on CO₂ lasers, we find that intracavity loss modulation of a class B laser does reveal delayed bifurcations. Further, the titanium sapphire laser does not show anticipation of the static threshold that has been observed in CO₂ lasers. The results of our measurements are in qualitative agreement with a model based on class-B laser theory.

Recently obtained results in the classical limit of the maser model allowing for a simple geometrical interpretation of superradiance phenomenon are generalized here for finite temperatures. Moreover, both integrable and non-integrable finite-temperature dynamics are studied in the classical limit. The fixed points are calculated as well as their stability conditions. Bifurcation of equilibria are shown to occur in the dynamical context, and the role of the temperature is shown to be of suppressing the transition by means of weakening of the coupling between the atoms and the field.

We present an exactly solvable model for photon emission, which allows us to examine the evolution of the photon wavefunction in space and time. We apply this model to coherent phenomena in three-level systems with a special emphasis on the effects of the photon detection process.

Radiation from a mirror moving in vacuum electromagnetic fields is shown to vanish in the case of a uniformly accelerated motion. Such motions are related to conformal coordinate transformations, which preserve correlation functions characteristic of vacuum fluctuations. As a result, vacuum fluctuations remain invariant under reflection upon a uniformly accelerated mirror, which therefore does not radiate and experiences no radiation reaction force. Mechanical effects of vacuum fluctuations thus exhibit an invariance with respect to uniformly accelerated motions.

Properties of an optical field propagating inside a directional coupler containing a parametric amplifying medium are studied. Conditions for pump controlled, low noise switching between the channels are analysed.

A system of N identical two-level atoms interacting with the single mode of the boson field is considered in the rotating-wave approximation. The solution of the Schrodinger equation with the initial condition of all atoms excited and the field in the coherent state is discussed. The resulting state is interpreted as an amplified state of the field correlated with the state of the system of atoms. The system of atoms is interpreted as an example of a nonlinear quantum amplifier. The algorithm to calculate the amplitude of the field at the output and its uncertainty is described. The relation of the mean value of the output field to the input one is interpreted as the amplification coefficient. The uncertainty of the output field is interpreted in terms of the noise of the amplifier. The dependencies of the noise on the amplification coefficient are plotted for several values of N. The noise is compared with the noise of an ideal linear amplifier of the same amplification coefficient. Conditions at which the nonlinear amplifier has less noise than the linear amplifier are found. Uncertainties of quadrature components which correspond to the amplitude and phase of the field are calculated. It is shown that only one of them has an uncertainty less than the uncertainty in the case of the ideal linear amplifier. Another definition of the amplification coefficient of the nonlinear quantum amplifier is suggested. The differential amplification coefficient gives the simple lower bound of the noise of the nonlinear amplifier. It prohibits the construction of a nonlinear amplifier with a signal-to-noise ratio better than that of an ideal linear amplifier. General bounds of the minimal noise in nonlinear amplifiers are compared with results for a particular amplifier.

We present a quantum theory of an optical four-wave mixing oscillator under pumping by two laser fields of different frequencies. Our analysis includes all the physical processes that are relevant in the parametric limit of interaction in a medium with cubic non-linearity: four-wave mixing, self- and cross-phase modulation. Dynamical aspects of stable above-threshold generation of an intracavity signal mode, the bistability and squeezing phenomena are studied.

We derive the quantum statistical properties of light beams involved in an asymmetric nonlinear coupler composed of a linear waveguide and a nonlinear waveguide operating using second harmonic generation. Examining quadrature and integrated intensity fluctuations, photon number distribution, reduced factorial moments and the uncertainty product, we demonstrate non-classical behaviour of single and compound modes. We show that squeezing of vacuum fluctuations, sub-Poissonian photon statistics and oscillations in photon number distribution created by nonlinear dynamics can be transferred to the linear signal mode. Also effects of non-classical incident beams and smoothing effects of external noise are demonstrated.

Lasers with two-photon saturable absorbers exhibit a phase instability similar to that of two-photon optical bistability. Beyond the phase instability threshold the output intensity breaks into spontaneous oscillations. Analytical perturbative solutions have been found and we have linearized the Fokker-Planck equation around these solutions. The drift and diffusion matrices have been perturbatively developed and we obtained a time-dependent Ornstein-Uhlenbeck stochastic process. We have calculated the amplitude correlations and squeezing spectrum near but above the threshold for a Hopf bifurcation in bad cavity conditions.

It is well known that two quasi-probability distributions for an optical mode, the Wigner (W) and Husimi (Q) functions, can be measured by homodyne and heterodyne detection, respectively. These harmonic oscillator distribution functions can be generalized to apply to other algebras, in particular, the su(2) algebra of a two-level atom. In this paper I investigate the relationship between these quasi-probability functions on the Bloch sphere, and the probability distributions for the integrated homodyne and heterodyne photocurrents from the fluorescence of the atom. While there is no particularly close relation between the su(2) Wigner function and homodyne detection, the su(2) Husimi function is simply equal to the heterodyne distribution function multiplied by a weighting factor. I also show that the two-level atom heterodyne distribution function can be expressed in a form identical to the corresponding optical mode distribution function. This correspondence defines the natural analogue of optical coherent states for a two-level atom. In deriving these results the theory of effects (positive-operator-valued measures) is essential.

If a laser is made sufficiently small, its (unavoidable) technical noise can be overwhelmed by the quantum noise, i.e. the spontaneous emission. We discuss the conditions which are required for this situation to occur, specializing to the case of a small gas laser. Experimental examples taken from recent work are used to illustrate the quantum regime of phase noise and polarization noise. Using scaling arguments we compare these quantum-noise effects in small gas lasers with those in semiconductor lasers.

We have investigated the intensity and phase noise of single-mode laser diodes, either free-running or using different types of line narrowing techniques at room temperature, namely feedback from an external grating and injection locking. We have measured an intensity squeezing of 1.2 dB in the first case, and 1.4 dB in the second case (respectively, 1.6 dB and 2.3 dB inferred at the laser output). We have observed that the intensity noise of a free-running 'single-mode' laser diode actually results from a cancellation effect between large anticorrelated fluctuations of the main mode and of weak longitudinal side modes. It is also shown that free-running diodes exhibit very large excess phase noise. Typically more than 80 dB above shot noise at 10 MHz, which can be significantly reduced by the above-mentioned techniques.

The probability distribution for rotated, squeezed and shifted quadratures is shown to be expressed in terms of the Wigner function (as well as in terms of the Q-function and density operator in the coordinate representation). The inverse transformation generalizing the homodyne detection formula is obtained.

In this paper the output quadrature phase correlations of a frequency nondegenerate parametric amplifier characterized by asymmetric losses, analysed in a preceding paper are applied to the discussion of the Einstein-Podolsky-Rosen (EPR) paradox. We use the formalism developed by Caves et al to describe the combined field modes and adopt the dual local oscillator homodyning scheme to construct an inferred Heisenberg uncertainty principle. The noise level required to demonstrate the existence of the EPR paradox is calculated and the sensitivity of the EPR inference on the asymmetry of the cavity mirror partial transmittivities and on the detuning in frequency between the two detected output fields is analysed. Such an analysis therefore provides a generalization of previous results reported by Reid and Drummond.

Quantum fluctuations impose fundamental limits on measurement and spacetime probing. Although using optimized probe fields can allow sensitivity in a position measurement to be pushed beyond the 'standard quantum limit', quantum fluctuations of the probe field still result in limitations which are determined by irreducible dissipation mechanisms. Fluctuation-dissipation relations in vacuum characterize the mechanical effects of radiation pressure vacuum fluctuations, which lead to an ultimate quantum noise for positions. For macroscopic reflectors, the quantum noise on positions is dominated by gravitational vacuum fluctuations, and takes a universal form deduced from quantum fluctuations of spacetime curvatures in vacuum. These can be considered as ultimate spacetime fluctuations, fixing ultimate quantum limits in spacetime measurements.

We analyse schemes for linear measurements of the photon number of a light beam and address how much information it is possible to extract from a quantum detector in single or repeated measurements, how much information is destroyed in non-ideal situations, and how much backaction is imposed for the extracted information.

We consider the construction of a Hamiltonian system performing a preassigned unitary transformation on optical modes. We indicate how to derive microscopically the effective interactions leading to linear networks. Simple examples are presented as illustrations of the theory.

An extended theoretical and experimental analysis is reported of the classic problem, first discussed by E Fermi, of the interaction between two quantum systems A and B. In our case, the two systems are confined within an optical microcavity and the interaction takes place in the transverse direction, i.e. orthogonal to the only k-wavevector allowed by the cavity with the minimum spacing d= 1/2 lambda ₀. In these conditions, our theory analyses in detail the process of two-atom super-radiance. The experiment consists of an investigation, by the use of a femtosecond laser, of the process of coupling of two microlasers active over the same transverse mode of an optical microcavity.

Recently a novel homodine tomographic technique has been proposed which allows us to detect the density matrix experimentally in terms of averages on data. The method has been further extended to a general matrix element ( psi mod Q mod phi ) of the density operator Q, along with the possibility of using low-efficiency detectors. In this paper this technique is reconsidered as a new genuine quantum measurement. Numerical results for measured probabilities are given, and the mechanism underlying the generation of statistical errors in the measured matrix is illustrated. It is shown that the data processing of the novel technique can also be used as a new imaging algorithm for conventional tomography.

A Gaussian wave theory is developed to analyse the sub-Poissonian light generated by means of a travelling-wave optical parametric deamplification. The Gaussian spatial profile of the pump beam limits the observable Fano factor to -3 dB (0.5). Gain-induced diffraction of the signal beam and classical fluctuations of the pump-signal relative phase cause further degradation. The theory is compared with our recent experimental results, and excellent agreement is found after the effect of non-ideal photoelectron efficiency is taken into account.

Real lasers show intrinsic noise well above the standard quantum noise limit. We review the properties of lasers and of techniques to suppress this noise. Experimental results of electro-optic feedback techniques and of squeezing in a second harmonic generator are presented. Finally we show that the optimum light source could well be a cascade of different cavities, each one performing a specific task in the noise suppression.

We calculate the triple quadrature correlations in non-degenerate quantum parametric amplifiers and oscillators. Firstly, at low signal intensities, a highly non-classical triple correlation can emerge in a parametric amplifier. This cannot be represented using the positive Wigner function approximation, sometimes called the semiclassical method. For this reason, measurements of triple quadrature correlations are a very strong test of stochastic electrodynamics and other hidden variable theories. As the corresponding local oscillator measurements involve a macroscopic particle flux at the detector, a high detector efficiency is possible. We show that triple correlations also feature in the critical fluctuations of the non-degenerate quantum parametric oscillator at threshold. This result allows us to asymptotically calculate the critical squeezing produced for large system size.

We discuss the potential of nonlinear atomic optics to achieve phase conjugation of atomic de Broglie waves. We discuss specifically two examples which help illustrate the analogies and differences between the cases of conventional optics and of atomic optics. In the first case, the upper electronic level of the atoms is adiabatically eliminated, leading to a scalar theory formally identical to conventional four-wave mixing. In the second case, both electronic levels are kept, leading to a vector field for which the 'coupled-mode equations' of phase conjugation involve the coupling between the wavefunctions of the two electronic levels.