We report experiments on evaporative cooling of spin-polarized atomic hydrogen gas confined in a cryogenic magnetic trap, and present a model of the trapped gas based on a generalized truncated Boltzmann approximation for the phase-space distribution function. The model takes into account the dimension of the evaporation [three-dimensional (3D) or 1D] and the time dependence of both the depth and the shape of the confining potential. Our observations are consistent with 1D evaporative cooling. To attain maximal phase-space density, we used the model assuming 1D evaporative cooling to optimize the evaporation procedure. With this work, the low dimension of evaporation was identified as the bottleneck thus far preventing us from achieving Bose-Einstein condensation in trapped atomic hydrogen.

We study the creation of vortex states in a trapped Bose-Einstein condensate by a rotating force. For a harmonic trapping potential the rotating force induces only a circular motion of the whole condensate around the trap center which does not depend on the interatomic interaction. For the creation of a pure vortex state it is necessary to confine the atoms in an anharmonic trapping potential. The efficiency of the creation can be greatly enhanced by a sinusoidal variation of the force’s angular velocity. We present analytical and numerical calculations for the case of a quartic trapping potential. The physical mechanism behind the requirement of an anharmonic trapping potential for the creation of pure vortex states is explained.

We report on recent theoretical and experimental developments on the problem of quantum noise reduction in a laser beam interacting with a cloud of cold atoms. We have used a three-level model for the trapped atoms which allows a more realistic treatment of the problem including the effects of the trapping and repumping beams. Moreover, we have observed squeezing under stable conditions and our experimental results are in good agreement with the theoretical model developed.

Saturation of a low pump energy x-ray laser utilizing a transient inversion mechanism on the $3p-3s$ transition at 32.63 nm in Ne-like Ti has been demonstrated. A close to saturation amplification was simultaneously achieved for the $3d-3p,$ $J=\overrightarrow{1}1$ transition at 30.15 nm. Small signal effective transient gain coefficients of $g\sim 46$ and $\sim 35{\mathrm{cm}}^{\mathrm{-}1}$ and gain-length products of 16.7 and 16.9 for these lines were obtained. Experiments demonstrate that it is possible to achieve saturated laser action in a transient regime with Ne-like Ti for a pump energy as low as $\sim 5\mathrm{J}.$

In this paper the dynamics of wave fields in a cavity with one sinusoidally moving mirror are investigated. The wave equation is solved approximately using the method of multiple time scales. Frequency shifts as well as amplitude and phase modulations of cavity modes are given. In all cases when it is possible, an approximate effective field Hamiltonian operator is derived. In the adiabatic case it is then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic motion of a mirror can lead to suppression of the Rabi oscillations of atomic inversion.

We characterize the propagation of short optical pulses through dispersive media with a cubic self-focusing nonlinear polarization, which incorporates self-steepening and self-frequency shifting. These effects can significantly affect pulse propagation dynamics, both in the normal but especially in the anomalous dispersion regimes. The nature of the dynamics is significantly different in the two regimes.

We investigate the quantum-mechanical state of motion of an atom strongly coupled to an optical cavity. The atomic motion is coupled to the environment through cavity decay and this leads to nonclassical effects due to the dissipative evolution. The scheme is examined as an atomic position measurement and the symmetry of the cavity field mode is found to lead to Schrödinger cat states of the motion in the selective evolution.

Starting from Maxwell’s equations for a linear, nonconducting, absorptive, and dispersive medium, characterized by the constitutive equations $\mathit{D}(\mathbf{x},t)={\varepsilon }_1\left(\mathbf{x}\right)\mathit{E}(\mathbf{x},t)+{\int }_{-\infty }^t\mathrm{ds}\chi (\mathbf{x},t-s)\mathit{E}(\mathbf{x},s)$ and $\mathit{H}(\mathbf{x},t)=\mathit{B}(\mathbf{x},t)$, a unitary time evolution and canonical formalism is obtained. Given the complex, coordinate, and frequency-dependent, electric permeability $\varepsilon (\mathbf{x},\omega )$, no further assumptions are made. The procedure leads to a proper definition of band gaps in the periodic case and a new continuity equation for energy flow. An $S$-matrix formalism for scattering from lossy objects is presented in full detail. A quantized version of the formalism is derived and applied to the generation of Čerenkov and transition radiation as well as atomic decay. The last case suggests a useful generalization of the density of states to the absorptive situation.

The stochastic theory presented by Drummond, Gardiner, and Walls [Phys. Rev. A 24, 914 (1981)] is an interesting approach to problems in quantum optics. In this theory, an exact, quantum evolution is written in terms of classical functions (not operators) driven by explicit, quantum noise. We examine the origin of uncertainty in the formalism through the simple example of a single, nonlinear oscillator. We then test the stochastic theory applied to the problem of soliton propagation. We extend the linearized stochastic model by computing analytically quantum uncertainties in the four basic soliton parameters: photon number, momentum, phase, and position. Agreement with second-quantized and configuration-space soliton theories verifies the stochastic formalism.

The Bloch equations are solved for a two-level system interacting with a strong pulsed laser pump and a weak pulsed laser probe. It is shown that the four-wave-mixing excitation spectrum, which is symmetrical with respect to the pump-probe detuning $\delta$ in the steady-state regime, becomes asymmetrical under pulsed conditions. The asymmetry is ascribed mainly to the linewidths of the pump and probe laser pulses.

We propose an optical scheme to control the degree of excitation of spatially localized regions inside an absorbing three-level medium using two suitably delayed laser pulses. Only selected localized regions inside the medium are changed by the pulses, the remaining medium remains unchanged in its ground state. We present an approximate but analytical theory of the coupled Liouville and Maxwell equations and propose an experimental verification of this control excitation scheme for potassium vapor.

We report a lasing without inversion (LWI) experiment on the basis of coherent population trapping, realized in low-pressure cadmium vapor. A single-pass inversionless amplification by more than a factor of 10 has been measured, a significant improvement over previous experiments. In addition, we report synchronously pumped laser oscillation without inversion. Using a simple model to fit the gain/absorption curves as a function of magnetic field, we have obtained values for the populations in the system, showing that there is no inversion in the atomic basis. Combined with a simple optical method to measure absolute densities of a gas, this model results in a completely optical method to determine the absolute populations and density in the system.

We investigate the possibilities of preserving and manipulating the coherence of atomic two-level systems by ideal projective homodyne detection and feedback. For this purpose, the photon emission process is described on time scales much shorter than the lifetime of the excited state using a model based on Wigner-Weisskopf theory. The backaction of this emission process is analytically described as a quantum diffusion of the Bloch vector. It is shown that the evolution of the atomic wave function can be controlled completely using the results of homodyne detection. This allows the stabilization of a known quantum state or the creation of coherent states by a feedback mechanism. However, the feedback mechanism can never compensate the dissipative effects of quantum fluctuations even though the coherent state of the system is known at all times.

The excess noise factor due to the nonorthogonality of the transverse modes of a geometrically stable cavity subject to large diffraction losses is measured. This transverse excess noise factor is isolated from other sources of modification of the laser linewidth due to a differential measurement method, leading to the experimental evidence of values as large as 13 in cylindrical symmetry. Moreover, it is shown experimentally that the introduction of a well-chosen second diffracting aperture inside the cavity permits one to drastically reduce the overall laser excess noise factor, without altering the laser losses and intracavity power.

An interaction scheme involving nonlinear ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ media is suggested for the generation of phase-coherent states (PCSs). The setup is based on parametric amplification of the vacuum followed by up-conversion of the resulting twin beam. The involved nonlinear interactions are studied by the exact numerical diagonalization. An experimentally achievable working regime to approximate PCSs with a high conversion rate is given and the validity of the parametric approximation is discussed.

Self-organization, resulting from the locking of two different family eigenmodes in a ${\mathrm{CO}}_2$ laser, is investigated in a coupled longitudinal and transverse approach. We show that within the near-field region the spatial evolution of the transverse pattern along the propagation axis involves bistability and symmetry breaking. The dynamics of prelocking, already suggesting the locked pattern to come, is also described.

We theoretically investigate the response of optical phase conjugators to incident probe pulses. In the stable (subthreshold) operating regime of an optical phase conjugator it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability.

We argue that in nonlinear optical systems with randomly distributed atoms one should go beyond the Clausius-Mossoti limit in order to take into account the effect of local-field fluctuations induced by configurational disorder in atom positions. This effect is analyzed by means of a random local-mean-field approach with the neglect of the correlations between dipole moments of different atoms. The formalism is applied to three-level Λ-type systems with quantum coherence possessing an absorptionless index of refraction and lasing without inversion. We show that the effect of configurational fluctuations results in the significant suppression of the atom susceptibility compared to the predictions based on the Clausious-Mossoti equation.

We investigate the propagation of an electromagnetic (EM) wave in a heterostructure formed by spatially modulated density of $\Lambda$ three-level atoms. A new regime of propagation and amplification of EM waves with frequencies lying in the forbidden frequency range is found. An application of this phenomenon is discussed.

The damping factors that occur in nonlinear-optical response tensors are commonly assigned signs that depend upon the temporal ordering of the associated photon interactions. However, time-reversal symmetry is satisfied only if all these signs are identical. For example, only then is there a formal equivalence between the amplitudes for second-harmonic generation and parametric down-conversion and only then is electro-optic rotation forbidden in fluids. This correction reflects deficiencies in certain commonly employed semiclassical approaches to nonlinear optics.