It is shown that dipole interaction of multilevel atoms having three or more ground-state sublevels with counterpropagating circular polarized laser waves is strongly influenced by ground-state coherence produced by two-photon processes. In the simplest case of a (3+5)-level atom the ground-state coherence is shown to be responsible for constructive atomic interference that enhances upper atomic populations at small velocities. Ground-state coherence is also responsible for the coherent redistribution of the ground-state atomic populations at small velocities. It is found that a two-photon coherent redistribution of atomic populations enhances considerably the radiation force at small velocities and accordingly the friction produced by the radiation force.

We show that under certain circumstances an atom can follow an oscillatory motion in a periodic laser profile with a Gaussian envelope. These oscillations can be well explained by using a model of energetically forbidden spatial regions. The similarities and differences with Bloch oscillations are discussed. We demonstrate that the effect exists not only for repulsive but also for attractive potentials, i.e., quantum multiple reflections are also possible.

We study the ground state of a system of Bose hard spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local-density approximation, based on the energy functional derived from the low-density expansion of the energy of the uniform hard-sphere gas, and a correlated wave-function approach, which explicitly introduces the correlations induced by the potential. Both higher-order terms in the low-density expansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becomes similar to that attained in recent experiments $\left(N\sim {10}^7\right).\mathrm{}$

We present theoretical prospects for creating p-wave paired BCS states of magnetic trapped fermionic atoms. Based on our earlier proposal of using dc electric fields to control both the strength and anisotropic characteristic of an atom-atom interaction and our recently completed multichannel atomic collision calculations we discover that p-wave pairing with ${}^{40}\mathrm{K}$ and ${}^{82,84,86}\mathrm{Rb}$ in the low field seeking maximum spin-polarized state represents excellent choices for achieving superfluid BCS states and may be realizable with current technology in laser cooling, magnetic trapping, and evaporative/sympathetic cooling, provided the required strong electric field can be applied. We also comment on the prospects of similar p-wave paired BCS states in ${}^6\mathrm{Li}$, and more generally on creating other types of exotic BCS states. Our study will open a new area in the vigorous pursuit to create a quantum degenerate fermionic atom vapor.

In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate or, equivalently, by the hydrodynamic equations for the number density and current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equations for a general time-independent state of the condensate, extending previous work to include vortex states as well as the ground state. In the Thomas-Fermi limit, the semiclassical corrections can be taken into account by adding a local correction term to the Gross-Pitaevskii equation. At second order in the Thomas-Fermi expansion, the semiclassical corrections can be taken into account by adding local correction terms to the hydrodynamic equations.

We have performed quantum nondemolition measurements on the collective spin of $\sim {10}^6$ cesium atoms. In this way ensembles of atoms with sub-shot-noise fluctuations of a collective spin have been prepared. These observations open the way toward the generation of squeezed spin states of atoms.

We theoretically study atom number fluctuations between the halves of a double-well trap containing a Bose-Einstein condensate. The basic tool is the two-mode approximation, which assumes that only two one-particle states are involved. An analytical harmonic-oscillator-like model is developed and verified numerically for both stationary fluctuations in the ground state of the system, and for the fluctuations resulting from splitting of a single trap by dynamically erecting a barrier in the middle. With increasing strength of the atom-atom interactions and/or increasing height of the potential barrier, the fluctuations tend to evolve from Poissonian to sub-Poissonian. Limits of validity of the two-mode model and its relations to the phase-atom-number approach of Leggett and Sols [A. J. Leggett and F. Sols, Found. Phys. 21, 353 (1991)] are discussed in detail.

Chaotically oscillating rare-earth-doped fiber ring lasers (DFRLs) may provide an attractive way to exploit the broad bandwidth available in an optical communications system. Recent theoretical and experimental investigations have successfully shown techniques to modulate information onto the wide-band chaotic oscillations, transmit that signal along an optical fiber, and demodulate the information at the receiver. We develop a theoretical model of a DFRL and discuss an efficient numerical simulation which includes intrinsic linear and nonlinear induced birefringence, both transverse polarizations, group velocity dispersion, and a finite gain bandwidth. We analyze first a configuration with a single loop of optical fiber containing the doped fiber amplifier, and then, as suggested by Roy and VanWiggeren, we investigate a system with two rings of optical fiber—one made of passive fiber alone.  The typical round-trip time for the passive optical ring connecting the erbium-doped amplifier to itself is 200 ns, so $\approx {10}^5$ round-trips are required to see the slow effects of the population inversion dynamics in this laser system. Over this large number of round-trips, physical effects like GVD and the Kerr nonlinearity, which may appear small at our frequencies and laser powers via conventional estimates, may accumulate and dominate the dynamics. We demonstrate from our model that chaotic oscillations of the ring laser with parameters relevant to erbium-doped fibers arises from the nonlinear Kerr effect and not from interplay between the atomic population inversion and radiation dynamics.

We investigate spatial instabilities (induced by small angular perturbations) of counterpropagating waves in nonlinear distributed feedback (DFB) structures. We determined the DFB-structure threshold length at which an absolute instability occurs and a nonhomogeneous spatial intensity distribution is generated. The evolution of the transverse intensity distribution is studied for counterpropagating waves as a function of the control parameters.

The possibility of determining the state of a quantum system after a continuous measurement of position is discussed in the framework of quantum trajectory theory. The initial lack of knowledge of the system and external noises are accounted for by considering the evolution of conditioned density matrices under a stochastic master equation. It is shown that after a finite time the state of the system is a pure state, and can be inferred from the measurement record alone. The relation to emerging possibilities for the continuous experimental observation of single quanta, as for example in cavity quantum electrodynamics, is discussed.

We consider the effect of squeezed input on quantum images in the output of the degenerate optical parametric oscillator. We find that the images can be made more intense than those produced using vacuum input. Moreover, adjusting the phase of the input light allows variation of the transverse wave vector for minimum fluctuations without affecting the output wave vector of maximum intensity. The use of spatially inhomogeneous squeezed input provides greater tuning of the spatial and nonclassical features of the output. In particular, writing quantum images becomes easy when diffractive effects and angle tuning of the input beams are utilized.

We discuss the process by which the spectrum of monochromatic modes of the laser in a double-cavity laser changes from that proper to a short cavity into that proper to a long cavity as the reflectivity of the “external” mirror is varied from $0$ to $1.$ This work is the natural continuation of our previous work [Phys. Rev. A 58, 614 (1998)], where the bifurcations occurring during this metamorphosis were studied. The transformation is mostly dictated by the boundary conditions and occurs regardless of the laser model. This transition is beyond the possibilities of simpler double-cavity laser models, such as those of Lang and Kobayashi [IEEE J. Quantum Electron. QE-16, 347 (1980)]. The stability properties of the monochromatic modes are studied as a function of the reflectivity of the external mirror R, the external cavity length L, and the applied current J. It is shown that for reflectivity values corresponding to the metamorphosis of the spectrum, by varying J and/or R, the system can give rise to a Hopf instability that involves the excitation of a roughly discrete set of frequencies. Note that these features are also beyond the possibilities of simpler models. We also discuss the role played by noise and show that it is possible for the system to show a high degree of susceptibility to noise, depending on J.

We investigate the dispersion law (relationship between ${\Omega }_k$ and $K)$ of photorefractive waves using a new experimental method based on the excitation of photorefractive waves by a spatially oscillating interference pattern and on the detection of the first non-Bragg diffraction order. The existence of a sharp resonancelike dependence of the output signal on the frequency of excitation allows us to analyze the dispersion law with high precision. ${\mathrm{Bi}}_{12}{\mathrm{TiO}}_{20}$ and ${\mathrm{Bi}}_{12}{\mathrm{GeO}}_{20}$ single crystals are used for the investigations, and the dependences of ${\Omega }_k$ on K, on external field, on index of modulation, and on light intensity are studied. The experimentally observed relation ${\Omega }_k\propto 1/K$ is in excellent agreement with theory. A contribution of nonlinear effects to the spectrum of photorefractive waves is discussed.

We investigate amplification of optical images by means of a traveling-wave optical parametric amplifier. As shown recently for a cavity-based geometry, such a scheme can amplify images without deteriorating their signal-to-noise ratio thus working as a noiseless amplifier. Here we consider a configuration without cavity, which is more realistic for a possible experimental realization. We study in detail the quantum fluctuations of the amplifier and formulate criteria for its noiseless performance. We investigate physical features of noiseless amplification, which take place for both traveling-wave and ring-cavity configurations. We demonstrate how the optimum phase matching of a phase-sensitive wave front of an image (by means of a thin lens or a small displacement of the crystal) can improve the noise performance of the amplifier and bring it to the ultimate value achievable under given physical conditions. We discuss the possibility of using detectors with the area much smaller than the area of the input image elements. We compare our results with those obtained for the ring-cavity configuration.

We discuss the frequency dependence of the spontaneous-emission rate (power) in a Fabry-Perot microcavity containing a Lorentz dielectric, with emphasis on modifications of the spectrum under the circumstances of the strong medium-cavity coupling. With the standard-cavity tuning, the total spontaneous-emission power spectrum consists of a multiwave version of the familiar low-frequency vacuum Rabi split peak and a broad structure on the high-frequency side coming from the enhanced spontaneous emission into the continuum of the obliquely propagating waves. This form of the spectrum derives from the properties of the (single-wave) radiation-intensity spectrum of the molecule. Depending on the observation direction, the radiation-intensity spectrum exhibits either a double-peak structure characteristic of the vacuum Rabi splitting, as observed in light transmisssion and reflection experiments, or a single-peak structure describing the enhanced spontaneous emission at the corresponding cavity resonant frequency.

A numerical model is used to investigate the conversion efficiency of second-harmonic generation with “nondiffracting” Bessel beams. We experimentally validate the model and show, in contrast to a previous prediction, that the conversion efficiency is always less than for Boyd-Kleinman focused Gaussian beams.

We examine the effects of loss and gain on a quantum soliton using a configuration-space approach. A simple microscopic model of local photon-matter interaction is applied to solitons with arbitrary quantum superpositions of momentum. Such a theory is needed in the analysis and design of systems that manipulate the wave function of soliton center-of-mass coordinates. The formalism is tested by calculating the momentum noise induced by loss and gain, and by comparison with the well-known Gordon-Haus calculation [J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986)]. The comparison provides physical insight and reproduces the old result as a special case.

The standard technique for measuring the phase of a single-mode field is heterodyne detection. Such a measurement may have an uncertainty far above the intrinsic quantum phase uncertainty of the state. Recently it has been shown [H. M. Wiseman and R. B. Killip, Phys. Rev. A 57, 2169 (1998)] that an adaptive technique introduces far less excess noise. Here we quantify this difference by an exact numerical calculation of the minimum measured phase variance for the various schemes, optimized over states with a fixed mean photon number. We also analytically derive the asymptotics for these variances. For the case of heterodyne detection our results disagree with the power law claimed by D’Ariano and Paris [Phys. Rev. A 49, 3022 (1994)].

We developed a semiclassical theory for emission spectra of optical microcavities. The spontaneous emission is taken into consideration by adding a spontaneous-emission current term into the Maxwell’s equations. The spontaneous-emission current is found to be equal to the element of the quantum current operator between the initial and final states of the spontaneous-emission transition. We showed that the optical-field distribution of the light emitted from optical cavities can be expressed as a superposition of eigenmodes, and the eigenvalue equation for eigenmodes is established. A detailed expression for emission spectra is also obtained. Numerical results for the emission spectra carried out for a microdisk laser match well with experimental data. By applying this theory in the calculation of the spectral linewidth of conventional lasers, we found the modified Schawlow-Townes spectral linewidth formula for gas lasers, and obtained an excellent agreement between the theoretical and experimental results in the case of semiconductor laser diodes.

A strongly driven $\left(\Omega \gg \gamma \right)$ two-level atom relaxes towards an equilibrium state $\rho$ which is almost completely mixed. One interpretation of this state is that it represents an ensemble average, and that an individual atom is at any time in one of the eigenstates of $\rho$. The theory of Teich and Mahler [Phys. Rev. A 45, 3300 (1992)] makes this interpretation concrete, with an individual atom jumping stochastically between the two eigenstates when a photon is emitted. The dressed-atom theory is also supposed to describe the quantum jumps of an individual atom due to photoemissions. But the two pictures are contradictory because the dressed states of the atom are almost orthogonal to the eigenstates of $\rho$. In this paper we investigate three ways of measuring the field radiated by the atom, which attempt to reproduce the simple quantum jump dynamics of the dressed state or Teich and Mahler models. These are spectral detection (using optical filters), two-state jumps (using adaptive homodyne detection), and orthogonal jumps (another adaptive homodyne scheme). We find that the three schemes closely mimic the jumps of the dressed-state model, with errors of order $\frac{3}{4}(\gamma /\Omega {)}^{2/3},$ $\frac{1}{4}(\gamma /\Omega {)}^2$, and $\frac{3}{4}(\gamma /\Omega {)}^2$, respectively. The significance of this result to the program of environmentally induced superselection is discussed.