Landau-Zener Model Research Articles

Observation of the geometric amplitude factor in an optical system

By manipulating the discrete optical levels inside an optical resonator, we obtain a classical realization of a twisted Landau-Zener model. We experimentally demonstrate the geometric amplitude factor in the transition amplitude that arises for this model. We consider in particular the region of parameter space addressed in the original study of the geometric amplitude factor by M. V. Berry [7].

Theory of ion-pair formation in Rydberg-atom-ground-state-atom collisions at thermal energies.

We develop the distorted-wave and adiabatic theories of the ion-pair formation in collisions of a Rydberg atom ${\mathit{A}}^{\mathrm{*}\mathrm{*}}$ with a ground-state atom B at thermal collision velocities. The e-B interaction is modeled by a zero-range potential. Both theories give results that are in qualitative agreement with the standard Landau-Zener model, although their prediction for m-changing transitions is different, where m is the projection of the angular momentum. To incorporate these transitions into the adiabatic theory, we take into account the rotation of the internuclear axis before and after a nonadiabatic transition. The m-averaged cross sections are substantially higher than those following from the standard Landau-Zener model, and the distorted-wave results are slightly higher than the adiabatic results with the internuclear-axis rotation taken into account. We apply our results to a description of the McLaughlin and Duquette experiment on ${\mathrm{Ca}}^{+}$-${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ pair formation. The calculated n dependence of the rate for the ion-pair formation is too flat as compared to the experimental observations and does not agree with known values of the electron affinity of Ca. We discuss other possible mechanisms responsible for the ion-pair formation in this process. \textcopyright{} 1996 The American Physical Society.

Transfer-excitation processes in collisions of N3+ ions with H2, He, Ne, and Ar targets.

High-resolution translational energy-gain spectra for single-electron capture by ${\mathrm{N}}^{3+}$ ions from ${\mathrm{H}}_{2}$, He, Ne, and Ar have been measured experimentally at laboratory impact energies of 6, 9, 12, and 15 keV. For ${\mathrm{N}}^{3+}$-He and Ne collisions, transfer excitation into the 2s2${\mathit{p}}^{2}$ state of ${\mathrm{N}}^{2+}$ is significantly populated, while in ${\mathrm{N}}^{3+}$-${\mathrm{H}}_{2}$ collisions, transfer excitation into the 2s2${\mathit{p}}^{22}$P state dominates at low energies. In ${\mathrm{N}}^{3+}$-Ar collisions, pure single-electron capture into 3s is selectively populated. In all the collision systems studied here, contributions from processes commencing with a long-lived metastable state of ${\mathrm{N}}^{3+}$(2s${(}^{2}$S)2${\mathit{p}}^{3}$P) are detected. The translational energy-gain spectra are interpreted qualitatively in terms of the reaction windows, which are calculated using the single-crossing Landau-Zener model and the extended version of the classical over-the-barrier model. Total cross sections for single-electron capture for ${\mathrm{N}}^{3+}$ ions colliding with He and ${\mathrm{H}}_{2}$ are also measured and compared with available measurements and theoretical calculations. \textcopyright{} 1996 The American Physical Society.

Landau-Zener model: Effects of finite coupling duration.

We present the generalization of the Landau-Zener model for a constant coupling of a finite duration. The exact evolution matrix is expressed in terms of sums of by-products of parabolic cylinder functions estimated at the turn-on time and at the turn-off time of the coupling. Various approximations in terms of simpler functions are derived and applied to several physically distinct cases. They allow us to study the dependence of the transition probability on the interaction parameters: coupling strength, coupling duration, and detuning slope. Furthermore, the analytic approximations reveal the effects of the finite coupling duration as well as those caused by adding a constant detuning shift, absence of a level crossing, turn-on time or turn-off time near the crossing (``half crossing''), turn-on time and turn-off time near the crossing (``nonsubstantial crossing''). The results are used to obtain analytic approximations to the time evolution in the original Landau-Zener model. Furthermore, following related studies on other models, we define the Landau-Zener class of models that, along with the finite Landau-Zener model presented in this work, contains an infinite number of members that give the same transition probability. Comparison of this class to the Allen-Eberly class shows that the two classes contain members with the same coupling but different detuning chirps as well as members with the same chirp but different couplings. The former case reveals chirp effects while the latter demonstrates shape effects. \textcopyright{} 1996 The American Physical Society.

Mechanisms of single-electron capture by the dichlorocarbene dication

The single-electron capture (SEC) by dichlorocarbene dications with eight different atomic and molecular target gases, CCl 2 (2+) + G → CCl 2 (+) + G(+), has been studied by product ion spectroscopy and ion kinetic energy spectroscopy. The experimental data have been interpreted in the framework of a theoretical model mat describes the charge exchange process. Exothermic charge exchange is handled within the Landau-Zener model, whereas endothermic charge exchange is described by the Demkov model. The calculated data reproduce qualitatively the essential features of the experimental results: (1) the appearance of a reaction window centered at an exothermicity in the 4-4.5-eV range, (2) the lower SEC cross sections for endothermic charge exchange, (3) the wider internal energy distributions obtained for CCl 2 (+) in the endothermic regime than in the exothermic one, which results in larger dissociation yields, (4) the excitation of molecular targets that accompany their ionization in the SEC process, and (5) the kinetic energy released on the CCl(+) + Cl fragments in dissociative SEC.

Charge transfer in collision of N2+and He

Abstract Charge transfer cross-sections in the collision of a doubly-charged nitrogen ion and a helium atom are evaluated with a close-coupling formalism. The charge transfer produces N+(3P), N+(1D) and He+ ions via the 2Σ+ and 2π molecular states of NHe2+. We describe a method for obtaining a particular diabatic representation from a set of adiabatic dipole moments. Comparison with Landau-Zener model calculations is made and the importance of inner couplings for the production of charge transfer states is demonstrated. Collisional rate coefficients are also obtained. At 104 K, the rate coefficient for charge transfer into the ground N+(3P) state is about 1·3 × 10−10 cm3 s−1 and for charge transfer into the metastable N+(1D) state 1·8 × 10−11 em3 s−1.

Observation of interference in transitions due to local geometric phases.

We present an optical implementation of a twisted Landau-Zener model for which local aspects of the geometric phase strongly influence the transition amplitude. The transition amplitude is influenced by an interference effect caused by the interplay between geometric and dynamic phases. \textcopyright{} 1996 The American Physical Society.

Excitation transfer in collisions of Kr{4p55p; 3D3} with N2 molecules

Cross sections for the excitation of the ν1 = 0 and 1 vibrational levels of the electronically excited N2(C,ν′) product state have been measured, for collision energies in the range 85 ⩽ E(meV) </ 115, using the short-lived laser-excited Kr{(4p)55p;3D3} atoms as projectile. The cross sections Qν′ = 10.0 A2 for ν′ = 0 and 7.2 A2 for ν′ = 1 for this slightly exothermic process are interpreted in terms of a Landau-Zener model, with the ionic Kr+ + N2− state as an intermediate which crosses both the initial and final state. The crossing parameters are in good agreement with the results obtained for the similar but strongly endothermic process for the Kr{(4p)55s;3P0,3P2} + N2 systems, investigated by Vredenbregt et al. [Chem. Phys. 145 (1990) 267] in the superthermal energy range.

Study on photochemistry of concerted [1, j] and [ i, j] sigmatropic rearrangements by the classical path method

In this article, a simple and generalized method is developed for investigating nonadiabatic transitions in photochemical sigmatropic rearrangements. To achieve a rapid computation for concerted sigmatropic rearrangements, the many-body treatment developed by Matsen and the Landau-Zener model have been employed to construct the potential energy surfaces for the reaction systems, and to process the nonadiabatic transition probabilities. The nonadiabatic coupling term is evaluated by neglecting the atomic orbital deformation with respect to the reaction coordinate, thus enabling the calculation of coupling terms to be carried out with the topology of the reaction system. It can be seen from the calculations of the nonadiabatic transition for [1,3], [1,4], [1,5], and [3,3] sigmatropic rearrangements that this treatment gives more detailed information than that from the Woodward-Hoffmann rule and the usual molecular theories. The ratio lnP(H) lnP(M) (H = Hückel, M = Mobius) predicts the stereoselectivity of photochemical [ i, j] sigmatropic rearrangements including cations, radicals and neutral molecules.

MOIL: A program for simulations of macromolecules

A package of computer programs for molecular dynamics simulations-MOIL-is described. A flexible data structure enables the study of macromolecules with potentials consistent with the AMBER/OPLS force field. The supplied parameter set has proteins in mind. In addition to ‘wide spread’ applications such as energy, energy minimization, normal modes, dynamics and free energy calculations code is also provided to pursue less common applications. This includes reaction path calculations (in condensed phases), uses of the mean field approach for enhanced sampling (LES-locally enhanced sampling) and calculations of curve crossing using the Landau-Zener model. A brief review of the overall program is provided. A few modules are discussed in considerable detail.

Suppression of ultracold ground-state hyperfine-changing collisions with laser light.

Using laser light tuned to a repulsive molecular potential, we have been able to suppress inelastic ground-state hyperfine-changing collisions between ultracold {sup 87}Rb atoms. Adiabatic excitation to the repulsive curve alters the atomic trajectories and prevents the atoms from approaching close enough for the hyperfine change to occur. Experimental results show suppressions up to {similar_to}50% and are in reasonable agreement with a simple Landau-Zener model. Our ability to control collisional trap loss processes may have important implications for the achievement of high densities in laser cooled samples.

Quantum interference in microwave multiphoton transitions.

We observe interference in the resonant microwave multiphoton transition probability between the 21s state and the 19,3 Stark state of K in a static field as a function of the duration and intensity of a microwave pulse at 9 GHz. The 19,3 state adiabatically connects to the 19f state in zero field. The ac Stark effect shifts the 21s state through a multiphoton resonance with the 19,3 Stark state during both the rising and falling edges of the microwave pulse. The transitions that occur during each traversal of the resonance lead to an interference in the net transition probability as a function of the relative phase accumulated by each state during the pulse. We measure both the frequency of the interference oscillations for different detunings from resonance and the amplitude of the fringes for different degrees of pulse asymmetry. The latter results are in complete agreement with the predictions of a Landau-Zener model for the resonance transitions.

Differential cross sections for single-electron capture processes by low-energy multiply charged ions

Doubly differential cross sections, in energy and angle, for state-selective single-electron capture by Ne 3+, Ne 4+ ions from Ne, and Ne 6+ ions from He have been measured at laboratory impact energies between 60 and 600 eV and scattering angles between 0° and 5°. The measurements show that the angular distributions of the reaction channels with large energy-gain values are shifted towards larger scattering angles as would be expected. The energy-gain spectra are interpreted qualitatively in terms of the reaction window, which are calculated using the single-crossing Landau-Zener model.

Cross section for the mutual neutralization reaction H2++H-, calculated in a multiple-crossing Landau-Zener approximation.

A multiple-crossing Landau-Zener model is applied to calculate mutual neutralization cross sections for the reactions ${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{H}}_{2}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ as a function of the principal quantum number n of the resulting H atom. For low-energy collisions (E\ensuremath{\le}10 eV), the total cross section for ${\mathrm{H}}_{2}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ is a factor of 8 larger than the one for ${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$. The cross section for the process including ${\mathrm{H}}_{2}^{+}$, in which the H atom is excited to the quantum state n (2\ensuremath{\le}n\ensuremath{\le}8), has a nonmonotonic behavior as a function of the atomic quantum state. Comparison of the calculated results with newly received experimental data is made.

Selectivity with respect to the orbital polarization in the energy-pooling process with sodium atoms

Cross sections sigma (m1m2)nl for the energy pooling processes in the collision between two excited sodium atoms are calculated for the case when the partners are prepared in the 3p-excited states with the definite orbital momentum projections m1 and m2. As a result of the process one of the colliding atoms comes to the ground state and the other partner is excited to nl state with nl=5s, 4d, 4f. The collision velocity is equal to or higher than thermal. The Landau-Zener-locking model (LZ-locking) is developed: the sudden change of the type of the coupling between the electron orbital momentum and the internuclear axis (the locking approximation) is combined with the multicrossing Landau-Zener model. The validity of the LZ-locking model is analysed. The results show strong cross section dependence on the initial quantum numbers m1 and m2, especially in the 5s channel.

Collinear Quantum Calculation of Transition-State Spectrum for the K + NaCl Reaction

Abstract The laser-induced reaction, K + NaCl + hν → KCl + Na*, has been studied quantum-mechanically, with consideration of only collinear geometries. Laser-dressed equations are numerically solved by the R-matrix propagation method. Quantum reaction probabilities are dominated by many resonances corresponding to the vibrational states of the reaction complex formed in the reaction. The results obtained are compared with surface hopping trajectory calculations. The trajectory surface hopping model fails in predicting the translational energy dependence of the reaction probabilities but a Landau–Zener model is qualitatively correct in the calculation of the laser wavelength dependence of the reaction probabilities. These results suggest that the dynamics of the laser-induced reaction can be divided into two independent processes; the ground state reaction K + NaCl → KCl + Na and the non-adiabatic transition from the laser-dressed ground state to the excited state.

Partial and total cross sections for single electron capture by Ar8+ from He in the 400-2400 eV energy range

Charge-exchange processes in 400-2400 eV Ar8+-He collisions are investigated: high energy resolution ion beam spectroscopy is performed with a recoil ion source (RIS) built in GANIL, total and partial cross sections for single-electron capture are measured using retarding field and energy gain techniques. Comparison with previous experimental results for total charge-exchange cross sections shows a rather good agreement and confirms the independence of these cross sections on the collision energy in the studied range. In contrast partial charge-exchange cross sections are shown to depend strongly on the collision energy. The experimental data are compared with theoretical results in the semi-classical impact parameter frame and with predictions made by other authors using the Landau-Zener model.

Observation of Landau-Zener dynamics in classical optical systems.

We report the observation of ``tunneling'' effects in a classical optical two-level system. In particular, we present experimental results for the optical implementations of the Landau-Zener model and of a hidden level-crossing model. The experimental results are in good agreement with theory for both the transition probability and the detailed time evolution of the wave function.

Atoms in strong fields and the quest for high intensity lasers

In recent years, novel techniques have been developed to achieve high laser field intensities by shortening the duration of the pulses after several stages of amplification (by first stretching and subsequently compressing mode-locked laser pulses). A laser system built according to these principles at Imperial College is described. It is capable of reaching powers of ∼ 1018 W cm−2 in pulse lengths of about 1 ps.The availability of field strengths 10 to 100 times as strong as the field experienced by the electron of the hydrogen atom in the first Bohr orbit opens up a new regime in the study of the interaction between light and matter. In particular, several effects, characteristic of very strong AC fields such as "above threshold ionisation" (ATI) high harmonic generation, etc are observed. Examples are given and their implications for atomic physics are discussed.Although such effects are novel and interesting in their own right, an important question which arises is the extent to which they may reveal new characteristics specific to the atom under study. Alternative possibilities are that most of the atomic features (correlations, shell structure, etc) are swamped by the effects of the strong field, or else that the atom is ionised before the strong field regime can even be reached. Some account of the controversies surrounding this question is given, and the importance of the dynamics is stressed.A theory is described which accounts for multiphoton excitation and ionisation by pulses of intense laser light in a generalised Landau-Zener model within a dressed atom basis of Floquet states. Different regimes of the interaction are classified, and a semi-classical limit is illustrated using action-angle plots of the Poincaré section. These reveal how excitation takes place across a separatrix between two modes of motion, and how the growth of chaotic trajectories near such a separatrix provides new paths leading to ionization. Our approach stresses the significance of the match between pulse rise time and the magnitude of the avoided crossings between dressed atom states for the atom or molecule concerned.

Experimental study of single-electron capture by low-energy Neq+ recoil ions (q=3-6) from He, Ne and Ar using translational energy spectroscopy

The translational energy spectroscopy technique has been used to study single-electron capture processes for collisions of slow Neq+ ions (q=3-6, where q is the projectile charge state), produced in a recoil ion source, with He, Ne and Ar at laboratory impact energies between 100 and 600 eV and scattering angles between 0 degrees and 6 degrees . The measurements show that the dominant reaction channels are due to capture into excited states of the projectile products and show a dependence on scattering angle. There is clear evidence of the presence of the first and second metastable states in the incident Ne3+ ion beam. A reasonable description of the dominant final states is obtained in terms of the reaction windows, which are calculated using the single-crossing Landau-Zener model. The measured differential cross sections show that the projectile products are distributed with maximum intensity near a scattering angle theta c which corresponds to capture at an impact parameter equal to the crossing radius.