We describe the systematics of two-photon Doppler-free excitation of atoms confined in a cylindrical harmonic trap, at densities far from the regime of quantum degeneracy. The line shape is explained in terms of momentum transfer between the light beam and the trapped atoms. This formalism extends the semiclassical analysis of time-of-flight broadening. The results, which are general, were motivated by the development of two-photon Doppler-free spectroscopy of trapped atomic hydrogen.

It is shown that the reaction field induced in an atom by a strong magnetic field is of order $B{\alpha }^2$ in atomic units (for magnetic-field strength B and fine structure constant $\alpha ).\mathrm{}$ The reaction field causes a dipole-dipole interatomic potential energy to exist between a pair of atoms of order $B^{3/2}{\alpha }^{7/2},$ such that B must be of order ${\alpha }^{-7/3}$ for the interatomic energy to be of order 1 a.u. B of this order corresponds to a field strength of $1.66\times {10}^{12}$ G, which is within the regime of field strengths considered in recent studies of atoms and molecules in the presence of a strong magnetic field.

Scaling laws are derived for hydrogenlike atoms and ions interacting with laser fields. In particular, the scaling of (appearance) intensities is derived. This scaling is independent of the physical mechanism responsible for the ionization process, be it tunneling or multiphoton ionization. It provides a firm basis and explanation for the validity of earlier models for the estimation of appearance intensities and of the extrapolation into the tunneling regime of scaling laws obtained through lowest-order perturbation theory. As an example of the applicability of the scaling laws, we calculate two-, three-, and six-photon generalized cross sections and ionization rates for positronium at laser frequencies of current experimental interest.

We examine the effect of nonlinearity at a level crossing on the probability for nonadiabatic transitions P. By using the Dykhne-Davis-Pechukas formula, we derive simple analytic estimates for P for two types of nonlinear crossings. In the first type, the nonlinearity in the detuning appears as a perturbative correction to the dominant linear time dependence. Then appreciable deviations from the Landau-Zener probability $P_{\mathrm{LZ}}$ are found to appear for large couplings only, when P is small; this explains why the Landau-Zener model is often seen to provide more accurate results than expected. In the second type of nonlinearity, called essential nonlinearity, the detuning is proportional to an odd power of time. Then the nonadiabatic probability P is qualitatively and quantitatively different from $P_{\mathrm{LZ}}$ because, on the one hand, it vanishes in an oscillatory manner as the coupling increases, and, on the other, it is much larger than $P_{\mathrm{LZ}}.$ We suggest experimental situations where the predicted deviations can be observed.

We consider the first-sideband Raman excitations of a trapped ion in the strong Raman coupling regime on the basis of the splitting approximation. It is demonstrated that not only weak but strong Raman excitations can be used to displace the motional ground state to some well-localized motional states under appropriate conditions. Nonlinear and nonresonant effects are taken into account for the Raman sideband transitions. The condition and limitation for the Raman vibrational excitations to be used for preparing Schrödinger cat motional states are analyzed. Quantum interference between the displaced motional states is discussed.

We study first- and second-order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second-order or density correlations. Except for a small region around the surface of a Bose-Einstein condensate the correlations can be accurately described as those of a locally homogeneous gas with a spatially varying chemical potential. The degrees of first- and second-order coherence are therefore functions of temperature, chemical potential, and position. The second-order correlation function is governed both by the tendency of bosonic atoms to cluster and by a strong repulsion at small distances due to atomic interactions. In present experiments both effects are of comparable magnitude. Below the critical temperature the range of the bosonic correlation is affected by the presence of collective quasiparticle excitations. The results of some recent experiments on second- and third-order coherence are discussed. It is shown that the relation between the measured quantities and the correlation functions is much weaker than previously assumed.

It is known that for a weakly interacting Bose-Einstein condensate (BEC), the assumption of a two-body $\delta$ interaction described by a constant coupling strength gives rise to a divergent ground-state energy. A similar divergence occurs in the spinor condensate in which the spin-spin interaction is included in addition to the repulsive $\delta$ interaction. In this paper, we examine, in the standard Bogoliubov approximation, the ground-state energy of a homogeneous spinor BEC with hyperfine spin $f=1.\mathrm{}$ The renormalized coupling constants are calculated and expressed in terms of the bare ones using the standard second-order perturbation method. With these renormalized coupling constants, we show that the ultraviolet divergence of the ground-state energy can be exactly eliminated.

A neutron polarimetric textbook experiment is performed to demonstrate the noncommutation properties of the Pauli spin operator. The polarization of the transmitted neutron beam depends upon the sequential order of two successive spin-flip devices with mutually inclined precession axes. Furthermore, an interpretation of the observed results is presented in terms of an intrinsic phase shift between two interfering mutually orthogonal spin states, which in a sequence of two successive spinor transformations stores particular information about the intermediate state. This phase shift is discussed with respect to its geometrical and dynamical components, and its formal connection with the noncommuting properties of Pauli spin operators is explicitly shown.

We use a simple two-mode model to investigate the quantum state dynamics of a two-species Bose-Einsten condensate, such as that produced in recent experiments, undergoing weak Josephson coupling. We find that in certain parameter regimes the quantum state of the system evolves into a macroscopic superposition of two states which differ in the atom number difference between the two species. The “size” of the macroscopic superposition created by such a method can be varied by adjusting the Josephson coupling coefficient, and is found to be near maximal for a certain critical value of this coefficient.

A Bose-Einstein condensate may be used to make precise measurements of weak forces, utilizing the macroscopic occupation of a single quantum state. We present a scheme which uses a condensate in a double-well potential to do this. The required initial state of the condensate is discussed, and the limitations on the sensitivity due to atom collisions and external coupling are analyzed.

We report on a detailed study of the focusing properties of inhomogeneous magnetic fields. The experiment is performed using cold cesium atom clouds released from a magneto-optical trap. The sample longitudinal distributions are being compressed under the influence of a pulsed parabolic magnetic potential. Achromatic imaging potentialities are demonstrated. Analogies with usual optics are pointed out. A velocity compression is obtained, leading to a cloud longitudinal effective temperature down to 220 nK for a proper choice of the experimental parameters. The observation of strong compressions is corroborated by numerical simulations in excellent agreement with the experimental data. The principle of the method is presented in view of an elementary one-dimensional model and its limits are discussed.

We provide a fully quantal treatment of a beam of two-state particles interacting with temporally oscillating potentials, and propose a number of longitudinal atom optics devices. A single oscillatory potential, in coupling the two internal states, generally entangles each with a different longitudinal momentum. An oscillatory potential can also act as an amplitude modulator, creating momentum coherences within a single internal state. Two successive oscillatory fields (DSOF’s), if differentially detuned, can couple an initially monochromatic state to a coherent momentum superposition, or alternatively may be used to detect a pre-existing momentum superposition. DSOF’s can create amplitude modulation which, despite the presence of a broad velocity distribution, rephases at a selected distance downstream of the device. Phase modulation generates coherent momentum sidebands which can evolve into amplitude modulation at a particular location downstream.

Motivated by the recent success of optical trapping of alkali-metal bosons, we have studied the zero sound modes of dilute Fermi gases with arbitrary spin-$f$, which are spin-$S$ excitations $(0\mathrm{}<~S<~2f)$. The dispersion of the mode (S) depends on a single Landau parameter $F^{\mathrm{}\left(S\right)\mathrm{}}$, which is related to the scattering lengths of the system through a simple formula. Measurement of (even a subset of) these modes in finite magnetic fields will enable one to determine all the interaction parameters of the system.

The critical temperature for Bose-Einstein condensation, ground-state fraction, and heat capacity of an ideal gas of Bose particles that are confined by an n-dimensional generic power-law potential trap are derived. The conditions for Bose-Einstein condensation and the discontinuous conditions of the heat capacity at critical temperature are obtained. All these quantities and conditions are found to vary markedly with the dimensionality of space, characteristics of particles, and shape of the external potential. The results obtained here are universal.

A basic four-level model for polarization switching of a quantum-well vertical-cavity surface-emitting laser [called the SFM model, San Miguel, et al., Phys. Rev. A 52, 1728 (1995)] is reduced to two equations by using asymptotic methods. The reduced model leads to expressions for all steady and Hopf bifurcation points and allows a systematic bifurcation study of the time-periodic solutions. The bifurcation diagram exhibits several stable states and suggests different types of switching transitions. We show that these transitions strongly depend on unstable limit cycles and that stable elliptically polarized states as well as stable time-periodic states may appear as alternate attractors to the x- or y-polarized states.

We perform an optical study of sulforhodamine B and sulforhodamine 101 molecules solved in water droplets (reversed micelles) that are stabilized by a surfactant and suspended in various mixtures of heptane and toluene. While the dielectric permittivity of the surrounding medium varies with the proportions of heptane and toluene, the chemical environment of the dye molecules always remains the same. The modifications of the optical properties of the dye molecules can then be solely attributed to the effect of surrounding dielectric medium on the electromagnetic field. As predicted by the theory, the amplitude of the luminescence spectrum of a given type of dye molecules increases with the refractive index of the microemulsion while the amplitude of the absorption spectrum remains almost unchanged. The various experimental results are also used to evaluate the radiative lifetimes of the dye molecules in the various microemulsions using three different approaches: (i) from the luminescence decay times using a Fermi’s golden rule description of the spontaneous emission process taking into account the variations with the surrounding dielectric medium of both the local electromagnetic field and the density of available photon modes, (ii) from the variation of the intensity of luminescence as a function of the luminescence decay time, and (iii) from the absorption spectra using a modified Einstein relation between absorption and emission. An excellent agreement between the three methods is found for sulforhodamine 101. For sulforhodamine B, there are discrepancies between the values obtained from the luminescence and absorption measurements.

We present a theoretical study of the effects of mismatching wavelengths for the coupling and probe fields in Doppler-broadened media for the three basic energy level configurations commonly used to realize electromagnetically induced transparency (EIT). Three wavelength regimes are considered: mismatched wavelengths for which the coupling frequency is greater than the probe frequency, matched wavelengths for which the coupling and probe frequencies are equal, and mismatched wavelengths for which the probe frequency is greater than the coupling frequency. The transparency that may be induced in these regimes is compared for the cascade-, Λ-, and Vee-type systems. We show that in the first mismatched regime $({\lambda }_c<{\lambda }_p)$ EIT is possible in all schemes and is in fact stronger than in the matched case. It is also demonstrated that for the second mismatched regime $({\lambda }_c>{\lambda }_p)$ EIT can be realized most readily in the Vee-type configuration in the presence of Doppler broadening. These predictions are explained by considering the absorption as a function of both the probe field detuning and the atomic velocity.

Continuous-wave (cw) optical gain of $1.3\times {10}^{-2}\hspace{0.5em}{\mathrm{cm}}^{-1}$ is obtained on a probe transition in a driven, three-level, V-type atomic system. The atoms exhibit no population inversion between the probe excited state and the dressed ground states of the combined atom-drive Hamiltonian. This gain without population inversion is interpreted as direct evidence of quantum interference, arising from coherences established in the atom by the applied optical fields. Agreement with a simple four-level theoretical model is excellent.

We describe the dynamical behavior of both class A and class B lasers in terms of a Lyapunov potential. For class A lasers we use the potential to analyze both deterministic and stochastic dynamics. In the stochastic case it is found that the phase of the electric field drifts with time in the steady state. For class B lasers, the potential obtained is valid in the absence of noise. In this case, a general expression relating the period of the relaxation oscillations to the potential is found. We have included in this expression the terms corresponding to the gain saturation and the mean value of the spontaneously emitted power, which were not considered previously. The validity of this expression is also discussed and a semiempirical relation giving the period of the relaxation oscillations far from the stationary state is proposed and checked against numerical simulations.

To meet recent experimental advances, we generalize the intuitively appealing nonorthogonal-mode theory of excess quantum noise by introducing a Maxwell-Bloch description of the gain medium. The resulting equations extend the nonorthogonal-mode approach beyond the class A linear-gain regime providing a general starting point for theoretical descriptions of excess quantum noise. As an illustration of our theory, we derive rate equations describing excess quantum noise in class B lasers and obtain the non-Lorentzian spectrum due to the coloring of excess noise in class A lasers accounting for gain saturation.