We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-$P$ and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-$P$ approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial state for the condensate and compare results to those for single-mode models.

We perform a mean-field study of the binary Bose-Einstein condensate mixtures as a function of the mutual repulsive interaction strength. In the phase segregated regime, we find that there are two distinct phases: the weakly segregated phase characterized by a “penetration depth” and the strongly segregated phase characterized by a healing length. In the weakly segregated phase the symmetry of the shape of each condensate will not take that of the trap because of the finite surface tension, but its total density profile still does. In the strongly segregated phase even the total density profile takes a different symmetry from that of the trap because of the mutual exclusion of the condensates. The lower critical condensate-atom number to observe the complete phase segregation is discussed. A comparison to recent experimental data suggests that the weakly segregated phase has been observed.

We present a generic model of an atom laser by including a pump and loss term in the Gross-Pitaevskii equation. We show that there exists a threshold for the pump above which the mean matter field assumes a nonvanishing value in the steady state. We study the transient regime of this atom laser, and find oscillations around the stationary solution even in the presence of a loss term. These oscillations are damped away when we introduce a position-dependent loss term. For this case we present a modified Thomas-Fermi solution that takes into account the pump and loss. Our generic model of an atom laser is analogous to the semiclassical theory of the laser.

We study the time evolution of a system of interacting bosons in a harmonic trap. In the low-energy regime, the quantum system is not ergodic and displays rather large fluctuations of the ground-state occupation number. In the high-energy regime of classical physics we find nonergodic behavior for modest numbers of trapped particles. We give two conditions that assure the ergodic behavior of the quantum system even below the condensation temperature.

We investigate numerically the distribution functions of photon number and phase in third-harmonic generation in the region of instability. It is shown that in this system the quantum superposition states for the third harmonic and fundamental mode can appear.

We discuss the spontaneous emission from a coherently prepared and microwave-driven doublet of potentially closely spaced excited states to a common ground level. Multiple interference mechanisms are identified that may lead to fluorescence inhibition in well-separated regions of the spectrum or act jointly in canceling the spontaneous emission. In addition to phase-independent quantum interferences due to combined absorptions and emissions of driving field photons, we distinguish two competing phase-dependent interference mechanisms as means of controlling the fluorescence. The indistinguishable quantum paths may involve the spontaneous emission from the same state of the doublet, originating from the two different components of the initial coherent superposition. Alternatively the paths involve a different spontaneous photon from each of two decaying states, necessarily with the same polarization. This makes these photons indistinguishable in principle within the uncertainty of the two decay rates. The phase dependence arises for both mechanisms because the interfering paths differ by an unequal number of stimulated absorptions and emissions of the microwave field photons.

A fully quantum-mechanical theory of bistable inversionless lasers is developed by generalizing the Scully-Lamb laser theory to this kind of laser systems. By converting the quantum master equation of the system into a Fokker-Planck equation, we obtain the steady-state properties and the fluctuation properties of the laser field for both coherently and incoherently injected atomic systems. It is shown that both the intensity and phase fluctuations of the laser system with coherent atomic injection are reduced corresponding to their counterpart of the incoherent atomic injection. The phase noise of bistable inversionless lasers can be quenched down to the vacuum-noise level for both atomic injections.

It has been shown recently [see, for example, S.-Y. Zhu and M. O. Scully, Phys. Rev. Lett. 76, 388 (1996)] that a dynamical suppression of spontaneous emission can occur in a three-level system when an external field drives transitions between a metastable state and two decaying states. What is unusual in the decay scheme is that the decaying states are coupled directly by the vacuum radiation field. It is shown that the decay dynamics required for total suppression of spontaneous emission necessarily implies that the level scheme is isomorphic to a three-level Λ system, in which the lower two levels are both metastable and each is coupled to the decaying state. As such, the total suppression of spontaneous emission can be explained in terms of conventional dark states and coherent population trapping.

The nonlinear dynamics of dissipative quantum systems in incoherent laser fields is studied in the framework of a master equation with the random telegraph model describing the laser noise and the Markovian approximation dealing with the system-bath couplings. Floquet theory and time-dependent perturbation methods are used to facilitate both analytical and numerical solutions. We develop a theoretical formalism that provides a powerful tool for the detailed analysis of the dissipative quantum dynamics of multilevel systems driven by intense stochastic laser fields. It is found that the system relaxes to a steady state from the effect of the laser phase and frequency noise and the kinetics of this relaxation increases with the addition of dissipative terms, introduced by the coupling to the reservoir. Amplitude fluctuations show a different behavior. Other results concerning the destruction of quantum coherence and the dynamical localization will be established and further relaxation mechanisms such as spontaneous emission and the ionization process will also be considered.

Input-output relations are derived for a lossless beam splitter with two input arms and two output arms. The inputs are two-particle states, either fermions or bosons, with both particles in the same arm or one in each of the input arms. The output states are derived for the four distinct two-particle input states. The statistics of the outputs for fermion and boson inputs are compared with each other and with the statistics for classical particles. For input particles in the same arm, the output statistics are the same for all three varieties of particle. For input particles in different arms, the output particle-number variances are reduced for fermions but increased for bosons, while the interarm correlation is increased for fermions but reduced for bosons in comparison to classical particles.

Coherent Raman scattering using broadband, incoherent (noisy) light (termed ${\mathrm{I}}^{\mathrm{}\left(2\right)\mathrm{}}\mathrm{CRS}$—the I for interferometric and the superscript 2 for twice acting noisy fields) is treated for a multiply resonant, multicomponent mixture of molecules. Both the resonant-resonant and resonant-nonresonant hyperpolarizability contributions to the signal intensity are included in this formalism. The emphasis is on the physical understanding of this spectroscopy. To this end, factorized time correlator (FTC) diagram analysis is used to characterize the ${\mathrm{I}}^{\mathrm{}\left(2\right)\mathrm{}}\mathrm{CRS}$ signal. The FTC diagram technique also serves to organize the terms that arise through the stochastic averaging of the noise at the intensity level. In addition to the FTC diagram analysis, a spectral filter analogy is employed to provide further insight into the physics behind ${\mathrm{I}}^{\mathrm{}\left(2\right)\mathrm{}}\mathrm{CRS}.$

We present a theoretical and experimental study of the molecular orientation induced in a light-absorbing liquid of rodlike molecules by a laser pulse that explains the large enhancement of anisotropic optical Kerr nonlinearity observed in liquids in which a small amount of dye has been dissolved. Our model is based on the assumption that a molecule changes significantly its rotational kinetic and equilibrium behavior when it is electronically excited by the absorption of a photon. The anisotropy of the absorption probability then results in a corresponding orientational anisotropy of the molecules involved in electronic transitions, which in turn orient the whole liquid via intermolecular interactions. To test our model, we performed nanosecond pump-and-probe measurements of nonlinear birefringence at varying pump pulse energy and temperature. In our experiments the host was a liquid-crystal mixture in its isotropic phase and the dye was an anthraquinone derivative. Both the decrease in the nonlinearity enhancement observed for increasing pulse energies and the pretransitional behavior occurring for temperatures approaching the isotropic-nematic transition point are in good agreement with the predictions of our model. The contribution of secondary effects related to light absorption and light-induced heating has been also taken into account in order to properly compare the nonlinearity of an absorbing liquid with that of a transparent one.

Using a semiclassical approach we derive a general expression for the quantum-limited linewidth of a single-mode laser. We include both nonuniform properties of the laser medium and localized losses at mirrors and apertures. For such systems the transverse modes are known to be nonorthogonal, giving rise to an enhancement of the laser noise. The transverse factor varies, in general, along the propagation direction. The combination of transverse and longitudinal noise enhancement is far from trivial. In particular, we show that for an aperture in the cavity, the transverse excess noise factor is the geometric mean of the factors pertaining to the two regions in which the aperture divides the cavity.

We study analytically equations that extend the Tang-Statz-deMars rate equations for a multimode Fabry-Perot laser by including the low-spatial-frequency population grating and the inhomogeneous pumping rate along the cavity axis [Quant. Semiclassic Opt. 5, L17 (1997)]. First, we prove the theorem that is the foundation of the antiphase dynamics: The total intensity transients are characterized by only one frequency, the single-mode relaxation oscillation. Second, we study the three-mode laser operation. In this context, we derive analytic expressions for the steady-state intensities, their linear stability, and the bifurcation points. We prove that strictly multimode solutions display a Hopf bifurcation leading to passive Q-switched solutions. Numerically, we have found that these time-periodic regimes may bifurcate to quasiperiodic and chaotic states and that there are many domains of bistability.

A Fibonacci optical superlattice (FOS) made from a single crystal with a quasiperiodic laminar ferroelectric domain structure was proposed to realize a third-harmonic generation (THG) process. Due to its quasiperiodic structure, a FOS can provide more plentiful reciprocal-lattice vectors to compensate for the mismatch phase in optical parametric processes, which causes most of third-harmonic peaks labeled by the corresponding reciprocal-lattice vector indices. Numerical calculation shows that the THG spectrum exhibits a self-similarity property in real space. Effects of the phase mismatch of second-harmonic generation and THG, the bandwidth, and the relative intensity of the second harmonic peak on THG are discussed. We also found THG peaks for which the quasi-phase-matching condition in THG process is not completely satisfied. The physical origins of the phenomenon are presented and discussed.

Coherent Raman scattering can generate Stokes and anti-Stokes fields of comparable intensities. When the Raman shift is due to a magnetic resonance transition (usually in the MHz to GHz range), the Raman fields are generally detected by optical heterodyne detection, using the excitation laser as the local oscillator. In this case, the two sidebands generate beat signals at the same frequency and are therefore indistinguishable. Separation of the two contributions becomes possible, however, by superheterodyne detection with a frequency-shifted optical local oscillator. We compare the two scattering processes, and show how the symmetry between them can be broken in ${\mathrm{Pr}}^{3+}{:\mathrm{Y}\mathrm{A}\mathrm{l}\mathrm{O}}_3.$

In this paper the correlation function of an arbitrary order is derived for an electron field in which the components corresponding to different particle numbers and momenta are mutually uncorrelated. The result is expressed in terms of the complex degree of coherence. The correlation functions clearly demonstrate the antibunching effect. All the computational steps are shown in detail.

In contrast to the well-known CO and ${\mathrm{N}}_2$ molecules, isoelectronic SiO and PN form thermodynamically stable conventional (valence) and dipole-bound anion states upon attachment of an extra electron. According to the results of our high-quality ab initio calculations, binding energies of the electron in these states are 38 and 1.6 meV $\left({\mathrm{SiO}}^{\mathrm{-}}\right)$ and 76 and 1.0 meV $\left({\mathrm{PN}}^{\mathrm{-}}\right),$ respectively. Dissociation trends of the ${\mathrm{SiO}}^{\mathrm{-}}$ and ${\mathrm{PN}}^{\mathrm{-}}$ anions are discussed.

General formulas are found for potentials that lead to the same motions in both classical and quantum mechanics. A class of time-dependent potentials with the above property is also discussed.

A measurement of the infrared collision-induced absorption spectrum of collisional pairs of Ar and Xe atoms is reported. An improved empirical collision-induced dipole model is obtained, which, if combined with quantum line-shape computations, permits an accurate reproduction of the measured spectrum.