Nonresonant Transitions Research Articles

Quantum Phase Control of Entanglement

A method of phase control of entanglement in two-qubit systems is proposed. We show that by changing a relative phase of the pulses that drive the transitions in a two-qubit system with closed-loop couplings, one can control entanglement at will. The method relies on adiabatic dynamics via time-delayed pulse sequences and can be implemented with both resonant and nonresonant transitions.

MINIMIZATION OF NONRESONANT EFFECTS IN A SCALABLE ISING SPIN QUANTUM COMPUTER

The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies. It is shown that these errors oscillate with changing gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.

Spectral dependence of coherent backscattering of light in a narrow-resonance atomic system

We report a combined theoretical and experimental study of the spectral and polarization dependence of near resonant radiation coherently backscattered from an ultracold gas of 85Rb atoms. Measurements in an approximately 6 MHz range about the 5s^{2}S_{1/2}- 5p^{2}P_{3/2}, F=3 - F'=4 hyperfine transition are compared with simulations based on a realistic model of the experimental atomic density distribution. In the simulations, the influence of heating of the atoms in the vapor, magnetization of the vapor, finite spectral bandwidth, and other nonresonant hyperfine transitions are considered. Good agreement is found between the simulations and measurements.

Theory of ultrafast non-resonant multi-photon transitions: basics and application to CpMn(CO) 3

Femtosecond laser pulse control experiments including non-resonant multiphoton transitions (NMT) are described theoretically. In order to apply optimal control theory for the computation of the pulse shape, an effective Schrödinger equation is derived. It contains effective coupling terms which account for any type of NMT processes. The general approach is applied to the two-photon non-resonant transition in the organometallic compound CpMn(CO) 3 which has been recently analyzed experimentally as well as theoretically in [C. Daniel et al. Science 299 (2003) 536]. The computations demonstrate that the whole methodology is ready to study a broad class of NMT experiments in the gaseous phase as well as in the condensed phase (upon generalization to a density matrix description).

Resonant interaction modified by the atomic environment

The dynamics of a resonant atom interacting with a quantum cavity field in the presence of many off-resonant atoms is studied. In the framework of the effective Hamiltonian approach we show that the results of elimination of non-resonant transitions are (a) a dynamical Stark shift of the field frequency, dependent on the populations of non-resonant atoms, (b) dependence of the coupling constant between the resonant atom and the field on the populations of non-resonant atoms, and (c) an effective dipole–dipole interaction between non-resonant atoms. Two effects (the coherent influence and dephasing) of the off-resonant environment on the dynamics of the resonant atom are discussed.

The “approach-induced” and collision-induced [formula omitted] transitions from low, vE=8–23, vibronic levels of the I 2(E) state

The dependences of the I 2( E0 g +,v E ,J E → I 2( X) D0 u +,v D ,J D ) transition rate constants on the vibrational v E, v D, rotational J E, J D quantum numbers, energy gaps, and Franck–Condon factors of the combined levels have been studied in the range v E=8–23. The extremely long-range near-resonance I 2( E,v E → I 2( X) D,v D ) process as well as nonresonant transitions, corresponding to the energy loss up to ΔE=240 cm −1 (approximately three quanta of vibrational energy), have been observed. Total cross-section of the latter is up to 12 times less than the maximum one of the extremely long-range transition. It has been shown that cross-sections of the processes are independent of initial J E number. The u↔g and ΔΩ=0 propensity rules are valid in the I 2( E) → I 2( X) I 2 (ion-pair states) transitions. The vibrational and rotational populations of the D state levels depend on v E and ΔE. Mechanism of the processes under study has been discussed. It has been shown that essentially nonresonant transitions occur after a mutual I 2(E) and I 2(X) capture in orbiting-controlled collision complex. Maybe, one has to take into account relativistic (magnetic) interactions for description of the extremely long-range transitions.

Perturbation theory for quantum computation with a large number of qubits

We describe a new and consistent perturbation theory for solid-state quantum computation with many qubits. The errors in the implementation of simple quantum logic operations caused by non-resonant transitions are estimated. We verify our perturbation approach using exact numerical solution for relatively small (L=10) number of qubits. A preferred range of parameters is found in which the errors in processing quantum information are small. Our results are needed for experimental testing of scalable solid-state quantum computers.

Modeling an inhomogeneous optically thick laser induced plasma: a simplified theoretical approach

A simplified theoretical approach is developed for an optically thick inhomogeneous laser induced plasma. The model describes the time evolution of the plasma continuum and specific atomic emission after the laser pulse has terminated and interaction with a target material has ended. Local thermodynamic equilibrium is assumed allowing the application of the collision-dominated plasma model and standard statistical distributions. Calculations are performed for a two-component Si/N system. The model input parameters are the number of plasma species (or plasma pressure) and the ratio of atomic constituents. Functions are introduced which describe the evolution of temperature and size of the plasma. All model inputs are experimentally measurable. The model outputs are spatial and temporal distributions of atom, ion and electron number densities, evolution of an atomic line profile and optical thickness and the resulting absolute intensity of plasma emission in the vicinity of a strong non-resonance atomic transition. Practical applications of the model include prediction of temperature, electron density and the dominating broadening mechanism. The model can also be used to choose the optimal line for quantitative analysis.

Population transfer through coupled continua

The population transfer in a $\ensuremath{\Lambda}$-like system, with intermediate states belonging to the continuous spectrum, is investigated in the case in which continuum-continuum and nonresonant transitions must be taken into account. The two phenomena are shown to essentially influence the dynamics of the system, in particular the final populations of the discrete states. The transfer probability can be increased if the two components of the pulse are shifted in time in a counterintuitive way, but unlike in the typical case of STIRAP, it is an oscillating function of the time delay.

The approach-induced I 2( [formula omitted]) transitions, M=He, Ar, I 2, N 2, CF 4

The dependencies of rate constant of the intramolecular I 2( E0 g + → M D0 u + ) approach-induced transition, M=He, Ar, I 2, N 2, CF 4, on the vibrational v E, v D, rotational J E, J D numbers, energy gaps, and Franck–Condon factors of the combined levels have been studied at nearly single-collision conditions by the OODR method. It has been shown that the observed approach-induced intramolecular transitions (AIIT) are nonresonant, correspond to loss of 100–700 cm −1 or gain of 160 cm −1 energy. For M≠CF 4 their cross-sections are independent of initial J E≈50–110 number and up to 60 (M=He) times less than maximum cross-section of the extremely long-range nearly resonant I 2( E,v E ↔ I 2( X) D,v D ) AIIT [Chem. Phys. 242 (1999) 263]. The nonresonant transition corresponding to loss of up to 160 cm −1 energy was found out for M=I 2, as well, but its cross-section is approximately nine times less than the maximum cross-section of the nearly resonant I 2( E,v E ↔ I 2( X) D,v D ) processes. The u↔g and ΔΩ=0 propensity rules are valid in the I 2( E)+M→I 2 (ion-pair states) + M AIIT. The vibrational and rotational distributions of the D state levels depend on the M nature. The J E dependence of the AIIT rate constant in the M=CF 4 case has been found out. For J E=110 rate constant is close to that of resonance approach-induced one, and the single rovibronic v D, J D≈110 level corresponding to loss of about 1290 cm −1 energy is populated. It has been shown that the data observed in this work and Chem. Phys. 242 (1999) 263 can be qualitatively explained in the framework of model of collision (approach) with large impact parameter.

Atomic motion in a two-mode laser field

A modified perturbation theory is developed for the calculation of the time-dependent wave function describing the propagation of an atom in a two-mode laser field. With the mode frequencies nearly equal, a first approximation is obtained that reproduces and extends known results, for both resonant and nonresonant transitions. This lowest-order solution sums terms that describe the absorption of a photon from one mode and emission into the other, leaving the total number of photons unchanged and shifting the momentum of the atom accordingly. Corrections are generated by expansion of a resolvent from which the nearly degenerate states have been projected out. These approximate solutions are used to construct asymptotic states in a formulation of atom-atom scattering in the two-mode field. In close analogy with the soft-photon approximation, a ``soft-pair'' approximation is developed based on the dominance of those asymptotic interactions in which the transfer of energy from the field to the atom is small, allowing one to relate the scattering amplitude in the presence of the field to the field-free amplitude. When the atomic ground state and an excited state are closely coupled by the field, the asymptotic wave function can have mixed parity allowing for long-range contributions to the effective potential. In addition to an enhancement of forward-scattering probabilities, this leads to a threshold anomaly that is analyzed here, in the resonant case, with the aid of a modified effective-range theory.

Dielectronic recombination satellite transitions in dense plasmas

Radiative and dielectronic recombination of multiply charged many-electron ions in high-temperature plasmas are usually treated as independent, non-interfering processes. A projection-operator and resolvent-operator approach has been developed to provide a fundamental, unified quantum-mechanical description of the combined electron–ion photo-recombination process. This ordinary Hilbert-space approach provides a valid description in low-density electron–ion beam interactions or in low-density plasmas. By means of the Hebrew University Lawrence Livermore Atomic Code (HULLAC), cross sections for photo-recombination of He-like ions through autoionizing states in Li-like ions have been obtained. For certain transitions, interference effects are predicted in the form of radiatively modified, asymmetric satellite cross-section profiles (or spectral line shapes). A density–matrix formulation has been developed for high-density plasmas, for which collisional and radiative relaxation processes can play an important role. Using Liouville-space projection-operator techniques, collisional and radiative relaxation processes (including cascades) are incorporated on an equal footing and in a self-consistent manner with autoionization and radiative emission. Both time-independent (resolvent-operator) and time-dependent (equation-of-motion) formulations are developed. The density–matrix approach provides a comprehensive description of the broadening of dielectronic satellite spectral lines due to autoionization processes, radiative transitions, electron–ion collisions, and electric and magnetic fields. We plan to adapt HULLAC so that the various elementary electron–ion collisional and radiative transition amplitudes can be used as input data in a generalized collisional-radiative model based on the density–matrix formulation. By means of the density–matrix approach, radiation processes involving resonant and non-resonant transitions in a diverse class of quantized electronic systems can be treated within the context of a single quantum statistical formulation.

On the consistency of spectroscopic ion density measurements

A comparison between two different quantitative spectroscopic measurements of the ion density of He-like carbon C4+ has been performed and used as a consistency check of a collisional-radiative model. The C4+ ion density was calculated from a zero-dimensional excitation and ionization balance for a resonant vacuum ultraviolet transition in Li-like carbon C3+. This was compared with a one-dimensional excitation balance for a non-resonant ultraviolet transition in C4+. At stable plasma conditions the two methods give consistent results.

Resonant Cherenkov emission of whistlers by a modulated electron beam

Emission of whistler waves through the Cherenkov resonance mechanism has been studied in a laboratory experiment modeling the interaction of a modulated electron beam with a magnetized plasma under conditions relevant to space experiments involving electron beam injection. The characteristics of the emission and the propagation of the radiated whistlers, and namely the features of their directive radiation patterns, have been controlled as a function of the beam and plasma parameters. This beam radiation process can be distinguished from another mechanism of wave emission, the nonresonant transition radiation from the beam injection point, owing to adequate choices of the physical conditions.

Whistler excitation by short current pulses in a magnetoplasma

In the frame of laboratory studies devoted to whistler excitation by a modulated electron beam injected in a magnetoplasma under conditions relevant to space experiments, fast processes have been investigated using the modulated electron beam as a train of short-time current pulses injected in the plasma. Single pulses of duration of the order of τ≃15 ns as well as unmodulated beams with sharp fronts (step functions with rise time of the order of τ≃10 ns) have been injected in the afterglow plasma with an energy of the order of 300 eV. Plasma responses to the fast perturbations are transported by whistler waves in the frequency range ωlh≪1/τ<ωc<ωp. Different types of responses have been evidenced and characterized, depending on the nature of the whistler excitation mechanism involved: Nonresonant transition radiation from the beam injection point and Cherenkov resonant emission. Both emissions could be distinguished one from each other owing to adequate choices of plasma parameters and observation conditions. The formation of wake fields associated with the propagating current pulses has also been observed for the first time in the whistler range. This study should shed light on the physical mechanisms connected with the injection of modulated and pulsed electron beams in space plasmas, as well as on fast processes induced in the whistler frequency range by the presence of suprathermal fluxes of electrons traveling in the ionospheric and magnetospheric plasmas.

Computation of Optical Properties for Quantized Electronic Systems

ABSTRACTA density-matrix description has been developed to treat relaxation (decoherence) phenomena during resonant and non-resonant radiative transitions of quantized electronic systems, including many-electron atoms and quantum-confinement systems (e. g., semiconductor microstructures). Radiative and collisional relaxation phenomena have been treated using Liouville-space proj ecti on-operator techniques. Both time-independent (resolvent-operator) and time-dependent (equation-of-motion) formulations have been developed. The self-energy operators that occur in these formulations can provide the fundamental basis for a self-consistent determination of the non-equilibrium and coherent electronic-state kinetics together with the homogeneous spectral-line shapes. This density-matrix description can be adapted for the computer simulation of electromagnetic processes. From first-principles electronic-structure calculations or from semi-empirical approaches, the parameters describing the elementary collisional and radiative interactions can be evaluated and organized into the basic data set for the application of the density-matrix description. The final product is a theoretical prediction for the linear or non-linear optical absorption or emission spectrum corresponding to a given set of values for the appropriate physical variables, such as temperatures, densities, and electric or magnetic field strengths.

Three-photon ionization of lithium

Abstract We study three-photon ionization of neutral lithium, in the presence of a strong laser light intensity of up to 15 GW cm −2 , involving the absorption of three photons combined in such a way that first we have one-photon resonant plus two-photon non-resonant ionization transitions, then the reverse case is studied. The resolvent operator formalism and projection operators are used in the calculations. An atomic central field model potential is used to generate orbital wavefunctions. We compare our calculations with previous calculations done by Chang and Poe [Phys. Rev. A 16 (1977) 606] for non-resonant three-photon ionization rates of lithium, with which we obtained a very good agreement.

Fast elastice−H(2s)scattering in laser fields

A numerical method for the evaluation of the Born{endash}Floquet amplitude for laser-assisted scattering is proposed for the case when a large basis set is required to achieve convergence. The method is applied to analyze the elastic scattering of fast electrons by the H(2s) state in a low-intensity laser field of varying frequency and to study the resonant scattering with increasing laser intensity. While the behavior of an atom in a resonant field of low intensity is determined by virtual transitions between resonant levels, at high intensity a great number of nonresonant virtual transitions may significantly influence laser-assisted processes. As a consequence, the attenuation of resonant effects could appear, as well as the {open_quotes}local{close_quotes} stabilization of the atom against ionization. {copyright} {ital 1997} {ital The American Physical Society}

Schrödinger's Equation as a Model Approach to Short Time-Scale Quantum Kinetics in a Semiconductor.

We present a new approach to quantum kinetics based on a Schr{umlt o}dinger{close_quote}s equation formalism. As an example we apply this method to a coupled electron-LO phonon system in a semiconductor. We demonstrate that it is possible to compute the full many-body wave function of the electron-phonon system for short times. The time-dependent electron probability distribution, extracted from the many-body wave function, illustrates the non-Markovian nature of the early time kinetics. The retarded onset of dissipation and kinetic energy overshoots are explained through virtual, nonresonant transitions. {copyright} {ital 1996 The American Physical Society.}

Surface and image-potential states on Pt(111) probed by two- and three-photon photoemission

The surface state and image-potential state (IPS) on Pt(111) have been studied by multi-photon photoemission spectroscopy. The intensity of two-photon photoemission by nanosecond laser pulses shows a resonant transition from the sp-derived surface state to the n = 1 IPS at 5.39 ± 0.03 eV. The three-photon photoelectron spectrum by femtosecond pulses shows two peaks: photoemission from the n = 1 IPS populated by nonresonant transitions and that from the surface state. The surface state is located at 0.19 ± 0.05 eV below the Fermi level and the n = 1 IPS at 0.78 ± 0.05 eV below the vacuum level.