We study the nonlinear transient effects similar to self-induced transparency and adiabatic following for a moving Rydberg atom undergoing a two-photon transition in an ideal cavity having a spatial field distribution for an uncorrelated two-mode coherent state. A comparative study is made of the case where an atom is undergoing a one-photon transition in a single-mode coherent field.

The energy levels of diamagnetic hydrogen as a function of two independent parameters, magnetic field strength $B,$ and angular momentum $m,$ are examined. Avoided crossings appear between these energy levels as either parameter is varied while the other is held fixed. These avoided crossings are directly related to degeneracies (Fermi resonances) occurring at zeroth order in perturbation theory. The mathematical basis of these degeneracies are the square-root branch points that connect the energy levels. It is found that the locations of avoided crossings in either constant-$B$ or constant-$m$ spectra can be predicted by visually scanning the locations of these branch points in the complex-δ plane, where $\delta =1/(2+2\mathrm{}|m|)$ is the perturbation parameter used in this research.

We discuss various theoretical issues that arise when one extends the conventional stimulated Raman adiabatic passage, involving a pump pulse preceded by a Stokes pulse, to situations in which the pump interaction involves a two-photon transition. As in the simpler cases, it is possible to obtain complete population transfer between an initial state and a targeted final state, if certain general conditions on the pulses are met. We point out important considerations, associated with dynamic Stark shifts and multiphoton ionization, which make successful population transfer more difficult in the multiphoton extension. We illustrate these problems and requirements by considering specific examples of excitation in metastable helium.

When one extends the conventional stimulated Raman adiabatic passage method of population transfer; involving a pump pulse preceded by a Stokes pulse, to situations in which the pump (or pump and Stokes) interaction involves a two-photon transition, there occur unavoidable dynamic Stark shifts which prevent maintenance of the relevant resonance conditions. Such shifts can prevent the desired population transfer. We show, through numerical modeling and analytic considerations, that the detrimental effects of dynamic shifts can be compensated by a suitable choice of (static) detunings of the carrier frequencies of the two pulses, so that population transfer can be achieved. We present simple analytic expressions for bounding the range of detunings for which population transfer can occur, and we present numerical results supporting the simple picture of the two-step linewidth. We illustrate these remarks by considering specific examples.

The steady-state populations, the fluorescent intensity-intensity correlation function, and the resonance fluorescence and absorption spectra of a two-level atom bichromatically driven by a strong, coherent field and a weak, stochastic field with tunable carrier frequency and wide bandwidth are investigated analytically. Surprisingly, the population is inverted if the stochastic field is appropriately detuned from the coherent field, which is assumed resonant with the atomic transition. The resonance fluorescence spectrum still displays a three-peaked structure, but with linewidths and heights that depend upon the frequency and bandwidth of the stochastic field as well as the intensities of both fields. Asymmetric fluorescence spectra are found when the coherent field is detuned from the atomic resonance frequency. The intensity-intensity correlation function varies dramatically with the carrier frequency of the stochastic field. For appropriate choices of the parameters, the fluorescent emission of the atom is antibunched for all time. The absorption spectral features also deviate significantly from those of the monochromatically driven atom. By appropriately tuning the stochastic field, one finds that a sharp peak (absorption) or hole (gain) can occur at line center and the probe beam can be amplified at either the lower-frequency Rabi sideband or the higher-frequency sideband and the inversionless gain can be enhanced.

The dependence of the width of the coherent population trapping (CPT) resonance on the atomic interaction time is studied theoretically. The optical Bloch equations are solved for the Hanle/CPT schemes corresponding to the open $F_g\to F_e$ transitions of the sodium $D_1$ line interacting with linearly polarized laser light. The mechanism producing the narrowing of the Hanle/CPT resonance is examined, the role of the population losses is pointed out, and the law describing the narrowing of the width of the resonance with the interaction time is determined. Our results are compared with the Hanle/CPT linewidth dependence on the interaction time occurring for a closed optical transition.

We present ion time-of-flight data showing strong-field ionization of iodine molecules up to ${\mathrm{I}}_2^{13+}$ using 33-fsec laser pulses. Every even molecular charge state shows an charge asymmetric dissociation channel $({\mathrm{I}}_2^{2n+}\to {\mathrm{I}}^{\mathrm{}(n+1\mathrm{})+}+{\mathrm{I}}^{\left(n-1\right)+})$ with a significant branching ratio (15–30 %) in addition to the symmetric dissociation channel $({\mathrm{I}}_2^{2n+}\to {\mathrm{I}}^{n+}+{\mathrm{I}}^{n+})$ showing the general nature of this process. Furthermore, all charge states are formed at internuclear separations less than the critical separation for electron localization and enhanced ionization ${(R}_c).\mathrm{}$ One channel, in particular, ${\mathrm{I}}_2^{10+}\to {\mathrm{I}}^{6+}+{\mathrm{I}}^{4+},$ represents a direct electronic excitation by nonresonant strong-field interaction to a state 20.9 eV above the ground state $({\mathrm{I}}_2^{10+}\to {\mathrm{I}}^{5+}+{\mathrm{I}}^{5+}).\mathrm{}$ We show that the interaction of the dipole moment of the asymmetric charge distribution with the external field can account for this energy and the excitation mostly likely involves charge-transfer states. These results establish strong-field ionization of molecules as an efficient method for populating highly excited electronic states.

The interaction of a cold trapped ion with a strong laser field is studied in a configuration in which quasienergetic levels become important but heating of the system is unessential. Absorption spectroscopy of the quasienergetic states of a strongly confined and laser-driven trapped ion is analyzed by probing vibrational transitions. Calculations are carried out analytically by using the master equation in quasienergetic state representation. We consider a $\mathsf{V}$-level scheme for the ion with a resonant strong pump field and a weak probe field. The steady-state and time-evolution behavior of the system is discussed and the probe-field absorption spectrum for various initial population distributions of the motional state is calculated. It is found that the absorption spectrum displays vibrational sidebands with multipeak splitting due to the nonlinear dependence of the Rabi frequencies on both the Lamb-Dicke parameter and the trap occupation number. This multipeak splitting has interesting consequences and can be useful for the measurement of the initial trap number population distribution.

A uniform iteration method is presented for achieving quantum optimal control over any real objective with a positive semidefinite Hessian matrix. Theoretical analysis shows that this uniform algorithm exhibits quadratic and monotonic convergence. Numerical calculations verify that for this uniform algorithm, within a few steps, the optimized objective functional comes close to its converged limit. For some optimal control purposes, the objective itself is not required to be directly a physical observable, but it is only necessary that the objective have a suitable association with some desired physical observables. As an illustration of the algorithm, the control objective is chosen to achieve maximum population in a target state as well as minimum phase mismatch with the target state.

We present a generalized Floquet formulation of time-dependent current-density-functional theory for nonperturbative treatment of multiphoton processes of many-electron systems in intense monochromatic electric and magnetic fields. It is shown that the time-dependent Kohn-Sham-like equation can be transformed into an equivalent time-independent Floquet Hamiltonian matrix eigenvalue problem. A procedure is outlined for the determination of the dynamical properties in bound-bound multiphoton transitions. For the case of bound-free transitions, such as the multiphoton ionization processes, we introduce the notion of complex density and complex current and present a non-Hermitian Floquet formalism for the calculation of the complex quasienergies of individual spin orbitals and total many-electron systems.

We propose a method to laser-cool atoms based on stochastic cooling, first developed at CERN to cool antiprotons. Fluctuations in the momentum distribution will be detected in a pump-probe configuration with far-detuned lasers, and the appropriate correction kick will be accomplished with optical dipole potentials. Each stage of an iterative cooling process will involve measurement and feedback, with phase space remixing in between. We discuss possible applications of this method to magnetically trapped atoms and molecules.

When viewed from a rotating frame the ionization of a hydrogen atom in a circularly polarized microwave field is largely governed by Coriolis forces. Although simulations show that the ionization mechanism is chaotic, we find that ionization is governed by a linear resonance. Because the electron is fed into the resonance by chaotic scattering from the core the overall ionization process, when it occurs, is chaotic. Suppression of ionization by an applied magnetic field is shown to be possible: it is due to detuning of the linear resonance by the field.

The guiding of atoms by laser light is investigated for atoms inside a long hollow cylinder with a rectangular cross section of subwavelength dimensions $a\times b.\mathrm{}$ The cavity modes are quantized, allowing the position-dependent spontaneous emission rate to be evaluated for an electric dipole inside the cylinder. Useful limits of the spontaneous rate are derived. In particular, results appropriate for the parallel-plate case are recovered when side a of the rectangular cross section becomes large, while side b is kept fixed. In the limit of the small cross section, especially when both a and b are less than λ (the atom electric dipole transition wavelength), the spontaneous emission process is possible only via a few cavity modes. If a cavity mode is now excited with sufficient intensity, the atoms become subject to a transverse dipole potential and an axial dissipative force, both of which vary across the cylinder and are also functions of the atom axial velocity. The dipole potential is responsible for the transverse trapping (and hence the channeling) of atoms at specific regions of the cross section, while the dissipative force controls the axial motion of the channeled atoms. The conditions facilitating atom guiding are explored using typical parameters for sodium atoms in rectangular cylinders of subwavelength dimensions.

We study the classical and quantum dynamics of a Fermi accelerator realized by an atom bouncing off a modulated atomic mirror. We find that in a window of the modulation amplitude, dynamical localization occurs in both position and momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett. 74, 4972 (1995)] shows that this system can be implemented experimentally.

We report an observation of a change in the energy spectrum of a matter wave due to fast modulation in time. The experiment, carried out with slow neutrons, achieved pulse widths of 33 n, and has been analyzed using time-dependent optics based on the nonrelativistic Schrödinger equation. A good fit to the data is obtained. The modulation of a matter wave in time leads to a characteristic energy spread. These phenomena can be seen as a consequence of the time-energy uncertainty relation. In our case, the amplitude modulation is done by a rapid periodic opening and closing of a slit. In the time domain this causes a so-called “diffraction in time.” In this work we demonstrate the operation of a time-of-flight spectrometer (FOTOF), and achieve an energy resolution of 20 neV, which to our knowledge represents a new limit for a TOF with slow neutrons.

We investigate a matter wave amplifier model which is capable of enhancing an external input atomic wave signal. This amplifier makes use of a cavity QED interaction with a trapped Bose-Einstein condensate. We examine the atomic wave equations and describe the gain performance.

We determine the critical temperature of parabolically trapped hard-sphere bosons via path-integral quantum Monte Carlo calculations of the condensate fraction and the specific heat. Contrary to previous predictions, the critical temperature of the weakly interacting gas remains roughly constant with respect to increases in the hard-sphere diameter, and is approximately equal to the critical temperature for ideal bosons. As the hard-sphere diameter is increased further, the critical temperature eventually begins to decrease. We give an explanation for the discrepancy between previous results and those presented here.

An atom-field geometry is chosen in which an atomic beam traverses a field interaction zone consisting of three fields, one having frequency $\Omega =2\mathrm{}\pi c/\lambda$ propagating in the $\mathbf{ẑ}$ direction and the other two having frequencies $\Omega +{\delta }_1$ and $\Omega +{\delta }_2$ propagating in the $-\mathbf{ẑ}$ direction. For $n_1{\delta }_1{+n}_2{\delta }_2=0\mathrm{}$ and $|{\delta }_1|T,|{\delta }_2|T\gg 1,$ where $n_1$ and $n_2$ are positive integers and T is the pulse duration in the atomic rest frame, the atom-field interaction results in the creation of atom amplitude and phase gratings having period $\lambda /\left[{2(n}_1{+n}_2\right)].$ In this manner, one can use optical fields having wavelength λ to produce atom gratings having periodicity much less than λ.

A path-integral quantum Monte Carlo method is used to calculate finite temperature properties of up to 1000 hard-core bosons in a two-dimensional isotropic harmonic-oscillator potential. If the interatomic repulsions are sufficiently short range, an abrupt increase in the condensate fraction and a hump in the specific heat occur close to the critical temperature of ideal bosons. The critical temperature and the condensate fraction are in general lowered by an increase in the hard-core radius a. If a is decreased below a certain level, the condensate fraction becomes indistinguishable from the corresponding value of the ideal bosons. For up to 1000 particles, this occurs when ${\ln }^{-1}{(1/na}^2)\lesssim 0.1,$ where n is the average particle density.

The properties of vortex states in a Bose-Einstein-condensed cloud of atoms are considered at zero temperature. Using both analytical and numerical methods, we solve the time-dependent Gross-Pitaevskii equation for the case when a cloud of atoms containing a vortex is released from a trap. In two dimensions we find the simple result that the time dependence of the cloud radius is given by $(1+{\omega }^2{t}^2{)}^{1/2},$ where $\omega$ is the trap frequency. We calculate and compare the expansion of the vortex core and the cloud radius for different numbers of particles and interaction strengths, in both two and three dimensions, and discuss the circumstances under which vortex states may be observed experimentally.