Nonresonant Levels Research Articles

Adiabatic elimination in the presence of multiphoton transitions in atoms inside a cavity

Various approaches have been used in the literature for eliminating nonresonant levels in atomic systems and deriving effective Hamiltonians. Important among these are elimination techniques at the level of probability amplitudes, operator techniques to project the dynamics on to the subspace of resonant levels, Green’s function techniques, the James’ effective Hamiltonian approach, etc. None of the previous approaches is suitable for deriving effective Hamiltonians in intracavity situations. However, the James’ approach does work in the case of only two-photon transitions in a cavity. A generalization of the James’ approach works in the case of three-photon transitions in a cavity, but only under Raman-like resonant conditions. Another important approach for adiabatic elimination is based on an adaptation of the Markov approximation well-known in the theory of system–bath interactions. However, this approach has not been shown to work in intracavity situations. In this paper, we present a method of adiabatic elimination for atoms inside cavities in the presence of multiphoton transitions. We work in the Heisenberg picture, and our approach has the advantage that it allows one to derive effective Hamiltonians even when Raman-like resonance conditions do not hold.

Photoinduced diffusion molecular transport

We consider a Brownian photomotor, namely, the directed motion of a nanoparticle in an asymmetric periodic potential under the action of periodic rectangular resonant laser pulses which cause charge redistribution in the particle. Based on the kinetics for the photoinduced electron redistribution between two or three energy levels of the particle, the time dependence of its potential energy is derived and the average directed velocity is calculated in the high-temperature approximation (when the spatial amplitude of potential energy fluctuations is small relative to the thermal energy). The thus developed theory of photoinduced molecular transport appears applicable not only to conventional dichotomous Brownian motors (with only two possible potential profiles) but also to a much wider variety of molecular nanomachines. The distinction between the realistic time dependence of the potential energy and that for a dichotomous process (a step function) is represented in terms of relaxation times (they can differ on the time intervals of the dichotomous process). As shown, a Brownian photomotor has the maximum average directed velocity at (i) large laser pulse intensities (resulting in short relaxation times on laser-on intervals) and (ii) excited state lifetimes long enough to permit efficient photoexcitation but still much shorter than laser-off intervals. A Brownian photomotor with optimized parameters is exemplified by a cylindrically shaped semiconductor nanocluster which moves directly along a polar substrate due to periodically photoinduced dipole moment (caused by the repetitive excited electron transitions to a non-resonant level of the nanocylinder surface impurity).

Coherent control of population and pulse propagation beyond the rotating wave approximation

The dynamics of populations of the vibrational states in a NO molecule (one-photon absorption) and of the electronic states in a 4,4′-bis(dimethylamino) stilbene molecule (two-photon absorption) is studied versus the frequency, intensity and shape of the laser pulse. We show that specially designed infrared laser pulses can build selective populations of certain vibrational states. A detuning of light frequency from the vibrational resonance qualitatively changes the dynamics of populations. It is found out that the populations of the nonresonant levels follow the pulse shape adiabatically if the detuning significantly exceeds the inverse characteristic time of the change of the pulse. Depopulation of the nonresonant vibrational states leads to a high population of the resonant state at the end of the pulse. Complete breakdown of the standard rotating wave approximation for a two-photon absorption process is observed even for a rather small intensity of the laser pulse. An analytical solution for the interaction of a pulse with a three-level system beyond the rotating wave approximation is obtained, and it is in close agreement with the strict numerical solution of the amplitude equations. Special attention is paid to the population dynamics of randomly oriented molecules. The orientational disorder as well as the vibrations limit the coherent population transfer. Calculations show the strong role of the anisotropy of photoexcitation in the coherent control of populations which can affect the anisotropy of photobleaching.

Asymmetric line shape and Fano interference in the transport of electrons through a multilevel quantum dot in the Coulomb blockade regime

We investigate the resonant transmission of electrons through a multilevel quantum in the Coulomb blockade regime. We show that the quantum interference between the path through the resonant level and the paths via other (nonresonant) levels results in the Fano asymmetry of the transmission peaks. The Fano parameter q is expressed in terms of the level spacing and the dot-lead coupling. The Coulomb blockade provides another origin of asymmetry for the resonances of the conductance due to the asymmetric occupation about a resonant point. Physical ingredients that influence these two mechanisms of the asymmetry are discussed.

Excitation transfer cross sections for levels of the Ne2p53dconfiguration

We have measured electron-impact optical emission cross sections for selected resonance and nearby nonresonant levels of the neon ${2p}^{5}3d$ configuration at pressures from 2 to 70 mTorr. The enhanced fluorescence observed from nonresonant levels at high pressures is consistent with excitation transfer from highly populated resonance levels of the ${2p}^{5}3d$ configuration. We measured excitation-transfer cross sections of $540\ifmmode\pm\else\textpm\fi{}80 {\mathrm{\AA{}}}^{2},$ $1600\ifmmode\pm\else\textpm\fi{}500 {\mathrm{\AA{}}}^{2}$, and $1100\ifmmode\pm\else\textpm\fi{}200 {\mathrm{\AA{}}}^{2}$ for transfer from the ${3d}_{5}\ensuremath{\rightarrow}{3d}_{6},$ ${3s}_{1}^{\ensuremath{'}}\ensuremath{\rightarrow}{3s}_{1}^{\ensuremath{''}},$ and ${3s}_{1}^{\ensuremath{'}}\ensuremath{\rightarrow}{3s}_{1}^{}$, respectively.

Robust disturbance cancellation in an active dynamic vibration absorber system

Two controllers for an active dynamic vibration absorber are designed to reduce the vibration to zero at specified frequencies and to non-resonant levels at the others. One of them contains a disturbance observer and asymptotically realizes a feedforward control of disturbance cancellation. It preserves the regulation property independent of perturbations in the primary system, but is sensitive to those in the absorber system. The other incorporates a disturbance model into its feedback loop. It preserves the regulation property in the presence of perturbations in both the primary and absorber systems. The designed controllers are studied experimentally.

Electronic state distribution of Xe+* formed by excitation transfer from Ne(3P0,2) to Xe+(2P3/2) at thermal energy

The Ne(3P00,2)+Xe+(5p5 2P01/2,3/2) excitation–transfer reaction has been studied by observing ultraviolet and visible emissions from Xe+* in a Ne flowing afterglow. The relative contribution of Xe+(2P03/2) and Xe+(2P01/2) to the excitation of Xe+* was examined by changing the [Xe+(2P01/2)]/[Xe+(2P03/2)] ratio with the addition of CH4 as a remover of the upper spin–orbit component. Since the intensity distribution of Xe+* lines was independent of the [Xe+(2P01/2)]/[Xe+(2P03/2)] ratio, it was concluded that the contribution of the Ne(3P00,2)+Xe+(2P01/2) reaction was insignificant. The Ne(3P00,2)+Xe+(2P03/2) reaction initially populates nine Xe+(6p,6p′,7s,6) levels in the 13.86–16.60 eV range. The favored product levels are 6p′ 2D03/2,5/2 and 7s 4P5/2 in the 16.36–16.43 eV range and 6p 4P05/2 at 13.88 eV, which are 0.2–0.3 and 2.7 eV below the entrance Ne(3P02)+Xe+(2P03/2) channel, respectively. The former near-resonant levels are excited by either direct curve crossings between attractive entrance potentials and flat exit ones or multiple curve crossings through a strongly attractive Ne−+Xe2+ ionic potential, while the latter nonresonant level is probably formed through the Ne−+Xe2+ ionic potential.

Design of Active Dynamic Vibration Absorber Systems with Multiple Absorption Frequencies.

An active dynamic vibration absorber is fabricated to reduce the vibration of the primary system to zero at specified frequencies and to nonresonant levels at the other frequencies. Its controller is designed based on the internal model principle ; accordingly, it incorporates a model of multiple-frequency disturbance into its feedback loop. The performance of the system obtained is experimentally studied using a vibration absorber with an electromagnetic servomechanism. The experiment succeeds in removing the vibration at up to four specified frequencies.

Robust Solutions to the Regulator Problem in an Active Dynamic Vibration Absorber System

Two controllers for an active dynamic vibration absorber are designed to reduce the vibration to zero at a specified frequency and to non-resonant levels at the other frequencies. One of them contains a disturbance observer and realizes asymptotically a feedforward control of disturbance cancellation. It preserves the regulation property independent of small perturbations in the primary system, but is sensitive to those in the absorber system. The other controller incorporates a disturbance model into its feedback loop. It preserves the regulation property in the presence of small perturbations in both the primary and absorber system parameters.

Control system design of a dynamic vibration absorber with an electromagnetic servomechanism

The control system of an active dynamic vibration absorber has been designed using the theory of output regulation with internal stability. The aim of the control system is to reduce the vibration of the controlled object equipped with the absorber to zero at a specified frequency and to a non-resonant level at other frequencies. Experimental data are provided for an active absorber system with an electromagnetic servomechanism. The absorber system consists of a lever generating an inertial reaction, two electromagnets driving the lever, sensors and a digital controller. The results emphasise the effectiveness of the proposed control method.

Output Regulation in an Active Dynamic Vibration Absorber System with an Electromagnetic Servomechanism.

The control system of an active dynamic vibration absorber with an electromagnetic servomechanism, is designed based on the theory of output regulation with internal stability. The absorber system consists of a lever generating an inertial reaction, two electromagnets driving the lever, sensors and a controller. The object of the control is twofold. First, it is to reduce the vibration of the primary system equipped with the absorber to a nonresonant level in the whole range of frequencies. Second, it is to reduce the vibration to zero at a specified frequency. It is shown that the latter property is preserved in the face of small parameter variations in the primary system, but is not preserved when the parameters in the absorber system are perturbed. Experimental results emphasize the effectiveness of the proposed control method, and support the analytical predictions well.

Four-photon coherent resonant propagation and transient wave mixing: Application to the mercury atom.

Density-matrix formalism is applied to construct a model for third- and fifth-harmonic generation in a four-photon resonant medium. The transition rates and coherent superposition of states associated with the resonant levels are treated rigorously, while the adiabatic following approximation is used to calculate the contribution of all nonresonant levels to the interaction. Expressions for the quadratic and quartic Stark shift and multiphoton ionization emerge naturally from the theory. At the power level required for appreciable four-photon absorption, the intensity-dependent Stark shift and ionization become overwhelming and limit the efficiency of harmonic generation. Because of the Stark shift, an intense pulse suffers a ``self-detuning'' effect and propagates through the resonant medium with minimal absorption. The interference of the phase-dependent Raman scattering with the multiphoton transition is found to be responsible for the vanishing of ionization in the presence of the generated third-harmonic field, an effect which was observed in earlier experiments.

Cooperative fluorescence by three-level atoms in a strong excitation field

When a system of two-level atoms interacts with a very intense field, the phenomena associated with superradiance do not appear in the fluorescent radiation. The question has been raised, "Can pumping by an intense field inhibit the occurrence of superradiance in the fluorescence of a system of three-level atoms to the third (nonresonant) level?" In this paper, we calculate the fluorescence spectrum of 2 three-level atoms. We find that superradiance, while absent in that part of the radiation corresponding to resonance fluoresence, is present in the radiation to the nonresonant level.

ChemInform Abstract: MULTIPLE PHASE‐COHERENT LASER PULSES IN OPTICAL SPECTROSCOPY. I. THE TECHNIQUE AND EXPERIMENTAL APPLICATIONS

In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy. In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels. It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid. Exact calculations show, e.g., that a two‐pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180° pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes. The role of pulse phase is extensively analyzed. Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters. The experimental results are based on an extension of the acousto‐optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail e t a l., Chem. Phys. Lett. 4 8, 256 (1977); Orlowski e t a l., ibid. 5 4, 197 (1978)]. The relative merits of fluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences. Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions. In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.

PassiveQ-switching in lasers with saturable absorbers: Improved treatment of a four-level model

We consider a four-level model of laser with saturable absorber which describes the interaction of a single radiation mode with two resonant rotational levels and with two sets of nonresonant levels of both the lasing and the absorbing medium. We eliminate adiabatically the variables of the resonant levels and investigate the occurrence of repetitive passiveQ-switching. Our results are compareda) with previous treatments in which either no adiabatic elimination is performed or equal relaxation rates are assumed for the nonresonant levels of the amplifier, andb) with experimental results for CO2 lasers with gaseous intracavity absorbers.

Multiple phase-coherent laser pulses in optical spectroscopy. I. The technique and experimental applications

In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy. In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels. It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid. Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180° pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes. The role of pulse phase is extensively analyzed. Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters. The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem. Phys. Lett. 48, 256 (1977); Orlowski et al., ibid. 54, 197 (1978)]. The relative merits of fluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences. Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions. In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.

Experimental lifetimes of some levels belonging to the3p5nd (n=4,5,6,7)configurations of Ar I

Lifetimes of twenty-three nonresonant levels belonging to the $3{p}^{5}\mathrm{nd} (n=4,5,6,7)$ configurations of Ar I have been measured. The single-photon delayed-coincidence method has been used to obtain the lifetime values given in the present work. As far as we know, no previous experimental results exist for sixteen of these levels. The experimental error was in the range from 1 to 10%. Our results have been compared with other experimental values and with our calculations performed in $\mathrm{jK}$ coupling and Coulomb approximation and with the intermediate-coupling results given in the literature.

The theory of the optical Autler-Townes effect in sodium

Feneuille and Schweighofer (1975) have used a three-level model to discuss the observation of the Autler-Townes effect in a two-step resonance experiment. A numerical investigation is presented in which the effect of the neighbouring non-resonant hyperfine levels is taken into account. Firstly all the levels are treated as non-degenerate, and then degeneracy is allowed for. It is found that both the inclusion of the neighbouring states and allowance for their degeneracy cause a large change in the expected upper-state population, especially at high light intensities. It is concluded that the resonant three-level model is a poor model in this situation.

Nonlinear Optical Processes by Van der Waals Interaction during Collision

We describe an optical process where off-diagonal optical excitation of a first atomic species is coupled during collision to a second species. This coupling leads to new types of nonlinear optical processes, and allows large cross sections for inelastic collision between atoms with nonresonant energy levels.

Extension of the geometrical representation of the schrödinger equation for a two-state system to include the effect of non-resonant levels

For field intensities which are not too large or rapidly varying, weak excitation of non-resonant levels introduces a time dependent Stark shift of the resonant levels without affecting the total probability of the system being in the resonant levels. Some consequences of this for the theory of ultra-short pulse propagation in a resonant medium are considered.