A theoretical analysis of the oscillator with a photorefractive gain is presented. The steady multimode oscillation is considered. In such a system, the cavity light beam undergoes a frequency ‘‘pulling’’ due to the nonlinear interaction between light and matter. This frequency shift is evaluated with respect to the empty-cavity frequency. We show that it can be as large as necessary depending on the experimental parameters. This can be a physical interpretation for the periodic (and chaotic) oscillation of several transverse family modes already observed in these setups.

We show that a linear Fabry-Pérot cavity with an oscillating end mirror can be used for quantum noise reduction. For a high-quality factor of the mechanical oscillator the output quantum fluctuations of the monochromatic light beam can be significantly squeezed at a frequency very close to that of the impinging light. The analysis is performed by taking into account the coupling of the system with the external world.

Many materials of potential interest for nonlinear optical applications exhibit optical activity and this is generally not taken into account in the standard theoretical treatments of nonlinear optical effects. In this paper we examine the conditions under which optical activity significantly alters the nonlinear optical properties of a material and show how this mechanism might be used in designing a nonlinear optical device. First, an algorithm is developed to calculate the exact optimum phase-matching angles and conversion efficiency for three-wave interactions in optically active biaxial crystals. Corrections to the standard theoretical expressions for birefringent phase-matching angles and conversion efficiency are obtained for application to biaxial crystals with large natural birefringence. Second, a generalized quasi-phase-matching scheme based on the presence of optical activity is formulated for three-wave interactions in second-order nonlinear crystals. It is shown that quasi-phase-matching via optical activity can be achieved by way of an effective harmonic modulation of ${\mathit{d}}_{\mathrm{eff}}$, the effective second-order nonlinear coefficient. For both these effects, it is found that optical activity makes a negligible change in the nonlinear optical properties of a material such as ${\mathrm{KTiOPO}}_4$, but they may become important for liquid crystals or polymers with high optical rotation and small birefringence.

The theory of continuous measurement is generalized so as to be applicable to a two-mode radiation field whose properties are monitored by using a Λ system with initial coherence between two ground states. The two-mode system is shown to offer the possibility of generating a number of new quantum states. Quantum statistics of the field following continuous measurements is calculated. Results for the phase distribution, quasiprobability distribution, and the photon-number distribution of the resulting field are also presented.

The spatiotemporal self-focusing of chirped optical pulses propagating in a nonlinear dispersive medium has been studied analytically and numerically. The analytic theory shows that the critical power for self-focusing occurring in a dispersive media changes quadratically with the chirp parameter in both two and three dimensions. It is found that the critical wave action depends on the sign of the total chirp parameter. Analytic results show that the effect of chirp is similar to that of beam ellipticity except that ellipticity always increases the critical wave action. Numerical simulations are used to study the effect of chirp and group-velocity dispersion on self-focusing. It is shown numerically and analytically that the self-focusing process can be controlled by changing the chirp parameter.

We present a quantum-mechanical analysis of an above-threshold laser amplifier made phase sensitive by an injected field. The gain and noise are calculated in a high-Q cavity with four-level atoms as the lasing medium. We find that for coherent-state inputs this amplifier can preserve the signal-to-noise ratio thus achieving the theoretical best noise performance.

The general theory of quantum angular momentum is used to derive the unique Wigner distribution function for arbitrary angular-momentum states. We give the explicit distribution for atomic angular-momentum Dicke states, coherent states, and squeezed states that correspond to a collection of N two-level atoms. These Wigner functions W(θ,cphi) are represented as a pseudoprobability distribution in spherical phase space with spherical coordinates θ and cphi on the surface of a sphere of radius ħ √j(j+1) where j is the total angular-momentum eigenvalue.

All-optical feedback can be effected by putting the output of a source cavity through a Faraday isolator and into a second cavity which is coupled to the source cavity by a nonlinear crystal. If the driven cavity is heavily damped, then it can be adiabatically eliminated and a master equation or quantum Langevin equation derived for the first cavity alone. This is done for an input bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the intercavity coupling involves only the intensity (or one quadrature) of the driven cavity, then the effect on the source cavity is identical to that which can be obtained from electro-optical feedback using direct (or homodyne) detection. If the coupling involves both quadratures, this equivalence no longer holds and a coupling linear in the source amplitude can produce a nonclassical state in the source cavity. The analogous electro-optic scheme using heterodyne detection introduces extra noise which prevents the production of nonclassical light. Unlike the electro-optical case, the all-optical feedback loop has an output beam (reflected from the second cavity). We show that this may be squeezed, even if the source cavity remains in a classical state.

We investigate the effect of collisional broadening, of population trapping and repumping, and of detuning of the atomic levels on the quantum-statistical properties of Raman laser radiation. We find that under suitably chosen operating conditions the effect of such additional incoherent relaxation mechanisms for the atomic polarization and populations can be made very small. One obtains highly nonclassical values for the Mandel Q parameter and the output-intensity fluctuation spectrum S(ω) for experimentally reasonable parameters. Including detuning of the laser and the pump light from the atomic levels in certain cases can lead to further narrowing of the intracavity photon number distribution, as compared to the resonant case, down to a Mandel Q parameter close to the optimum possible value of Q=-1. A subsequent preliminary analysis prevails that inhomogeneous Doppler broadening of the atomic lines, both for collinear and for counterpropagating pump and laser light, is not detrimental to the nonclassical intracavity state.

We show that significant squeezing in a strong signal light field can be generated with three-level atoms in a ghost-transition setup by tuning a weak probe beam inside the Autler-Townes doublet created by the strong signal light. Close to the Rabi level, i.e., within the absorption line, processes involving both amplitude quadratures become important. Significant atomic two-photon coherence provides a vehicle for signal-amplitude fluctuations to trigger fluctuations in the probe amplitude. Subsequently, atomic coherence will feed these probe fluctuations back into the signal and enable substantial noise suppression.

A theory of electron-counting processes is formulated in terms of the Liouville space method. The developed model is based on the quantum Markov processes developed by Davies and Srinivas. The time evolution of an electron system interacting with an electron counter and the counting probability distribution are investigated. The average value, fluctuation, and correlation function of the electron number registered by the counter are calculated, and the sub-Poissonian distribution and antibunching correlation of the electrons are obtained for an arbitrary noncorrelated initial state of electrons. For a correlated initial state, depending on the initial correlation among the electrons and on the electron counters used in the measurement, the statistics for the electron number registered by the counter is characterized as a sub-Poissonian, Poissonian, or super-Poissonian distribution, and the intensity correlation function exhibits antibunching or bunching correlation. As an example, the state with correlation between the up-spin and down-spin electrons is considered. The electron counting processes under the influence of a chaotic electron source are also considered, and the effect of the chaotic electron source on the counting statistics is investigated.

The dynamical behavior of a sodium-filled Fabry-Pérot resonator in a static magnetic field is studied systematically over a braod parameter range. The experiments reveal that all apparent types of nonlinear oscillations form a distinct scenario, including a parameter range of generalized bistability. The theoretical descripton includes the influence of radiation trapping on the dynamics of the ground-state orientation. Numerical simulations yield an almost quantitative reproduction of the experimentally observed scenario, with the inclusion of chaotic oscillations, and show the dominant role of radiation trapping as a nonlinear mechanism leading to chaotic behavior.

We analyze the so-called Monte Carlo wave-function (MCWF) method from a conceptual point of view. This method has been recently introduced as a technique to simulate dissipative processes in quantum optics. For the case where dissipation consists of spontaneous emission, we find that the coherent decay part of the MCWF method is identical to neoclassical radiation theory. This unexpected reappearance of the neoclassical theory suggests the identification of the MCWF coherent decay with classical radiation reaction. It leads to an alternative interpretation of the MCWF method instead of the usual one which is based upon quantum measurmeent theory. We give a derivation of the MCWF method, illustrated by simple Feynman diagrams, in which the appearance of radiation reaction is shown to be a natural feature of the coherent decay part.

Is it possible to detect the interference from an extended incoherent source with Young’s slits when the source-slits distance is such that all dimensions of the coherence area of the incident light beam are smaller than the distance between the slits? We have experimentally demonstrated that, under the above conditions, interference fringes can be obtained with a controlled degree of visibility by means of coincidence measurements between conujugated beams of the down-conversion luminescence.

In this paper we investigate the scattering of a two-level atom in a traveling or standing wave in the limit of large detuning. We show that these two systems are examples of nontrivial motion which is straightforward to treat using the unified scattering formalism of Tanguy and co-workers [J. Phys. B 17, 4623 (1984)]. This enables us to compare the diffractive and diffusive approximations with the exact solution of the effective master equation. Our analysis is fully quantum mechanical and in our numerical treatment of the effective master equation we are able to include spontaneous emission to all orders. We find that whereas the diffractive approximation correctly describes scattering from a traveling and a standing wave for short interaction times, the diffusive approximation cannot account for the persistence of diffractive structure for the case of the standing wave. To get good agreement we use an approximation which incorporates both diffractive and diffusive effects.

Transverse pattern evolution is investigated in single-longitudinal-mode two-level and Raman lasers with flat end reflectors, subjected to uniform transverse pumping. The natural nonlinear modes of the laser are identified as spatially homogeneous when the detuning from the gain peak is negative and as ‘‘local’’ plane traveling waves when the detuning is positive. The latter correspond to an off-axis emission of the laser. Stability characteristics of the underlying patterns are predicted to be quite different for one-dimensional and two-dimensional (2D) lasers. As an illustration, we provide direct numerical evidence for weakly turbulent behavior of a 2D Raman laser where Eckhaus and zigzag phase instabilities act in concert to spontaneously nucleate topological defects and ridgelike illuminated regions. Our numerics also confirm that the complicated patterns persist for finite transverse pumping as long as the characteristic width of the pump source contains a sufficient number of selected pattern wavelengths.

Complex order-parameter equation descriptions of pattern evolution in large-aspect-ratio two-level and Raman lasers are derived systematically as solvability conditions in a multiple-scales asymptotic expansion of the original Maxwell-Bloch laser equations in powers of a small parameter. These amplitude equations, although strictly valid near threshold for lasing, are shown to capture the essential features of pattern instability and evolution well beyond lasing threshold. A technical difficulty that can arise in the Raman laser, namely, subcriticality of the bifurcation near the critical wave number, is not addressed in the present paper and the order-parameter equations as derived are valid only when this situation does not arise. Analytical expressions for long-wavelength phase instabilities of the underlying traveling-wave pattern, which appears as the natural nonlinear lasing mode when the detuning of the laser from the gain peak is positive, are obtained from the coefficients of a Cross-Newell phase equation. Phase and amplitude instability boundaries, when computed via the original laser equations, the complex order-parameter equations and the phase equation, are shown to be consistent for all cases studied with the exception of the case when a subcritical bifurcation approaches the critical wave number ${\mathit{k}}_{\mathit{c}}$.

Many-world, decoherence, and modal interpretations of quantum mechanics suffer from a ‘‘basis degeneracy problem’’ arising from the nonuniqueness of some biorthogonal decompositions. We prove that when a quantum state can be written in the triorthogonal form Ψ=${\mathit{tsum}}_{\mathit{i}}$${\mathit{c}}_{\mathit{i}}$‖${\mathit{A}}_{\mathit{i}}$〉⊗‖${\mathit{B}}_{\mathit{i}}$〉⊗‖${\mathit{C}}_{\mathit{i}}$〉, then, even if some of the ${\mathit{c}}_{\mathit{i}}$’s are equal, no alternative bases exist such that Ψ can be rewritten ${\mathit{tsum}}_{\mathit{i}}$${\mathit{d}}_{\mathit{i}}$‖${\mathit{A}}_{\mathit{i}}$’〉⊗‖ ${\mathit{B}}_{\mathit{i}}$’〉⊗‖${\mathit{C}}_{\mathit{i}}$’〉. Therefore the triorthogonal decomposition picks out a ‘‘special’’ basis. We can use this preferred basis to address the basis degeneracy problem.

In our theoretical studies with replacement operators, we found the use of a graphical method very useful for operating with them. Now, for working with spin-orbital fermion operators, we have devised another easy graphical method which has proven to be very helpful to us. This method is presented here and as an example the square of the Hamiltonian operator is evaluated.

The transfer of negative pions captured by hydrogen to deuterium has been studied in ${\mathrm{H}}_2$O+${\mathrm{D}}_2$O mixtures. The ${\mathrm{D}}_2$O-concentration dependence of the transfer rate was analyzed on the basis of a phenomenological model in order to determine the transfer parameters. The fit gives an asymptotic transfer of about 42%, which is smaller than the previous results, but slightly larger than the value for ${\mathrm{H}}_2$+${\mathrm{D}}_2$ gas mixtures. A mesomolecular effect of HOD molecules was discussed on the basis of the concentration dependence of the transfer rate.