We examine time ordering effects in strongly, suddenly perturbed two-state quantum systems (kicked qubits) by comparing results with time ordering to results without time ordering. Simple analytic expressions are given for state occupation amplitudes and probabilities for singly and multiply kicked qubits. We investigate the limit of no time ordering, which can differ in different representations.

Analytic solutions are developed for two-state systems (e.g. qubits) strongly perturbed by a series of rapidly changing pulses, called 'kicks'. The evolution matrix may be expressed as a time ordered product of evolution matrices for single kicks. Single, double, and triple kicks are explicitly considered, and the onset of observability of time ordering is examined. The effects of different order of kicks on the dynamics of the system are studied and compared with effects of time ordering in general. To determine the range of validity of this approach, the effect of using pulses of finite widths for 2s − 2p transitions in atomic hydrogen is examined numerically.

Cross sections for ionization with excitation and for double excitation in helium are evaluated in a full second Born calculation. These full second Born calculations are compared to calculations in the independent electron approximation, where spatial correlation between the electrons is removed. Comparison is also made to calculations in the independent time approximation, where time correlation between the electrons is removed. The two-electron transitions considered here are caused by interactions with incident protons and electrons with velocities ranging between 2 and 10 au. Good agreement is found between our full calculations and experiment, except for the lowest velocities, where higher Born terms are expected to be significant. Spatial electron correlation, arising from internal electron-electron interactions, and time correlation, arising from time ordering of the external interactions, can both give rise to observable effects. Our method may be used for photon impact.

Time connection between electrons in dynamic atomic systems is considered. We describe time correlation in terms of the Dyson time ordering operator T. In this paper we decompose T into an uncorrelated term T unc , plus a correlated term T cor ϭTϪT unc , which interconnects the time-dependent external interactions. We show that time correlation between electrons requires both T cor and spatial electron-electron correlation. Two examples are analyzed. In transfer ionization the time correlation operator incoherently changes the shape of an electron-electron Thomas peak. In double excitation the influence of T cor in amplitudes for coherently interfering pathways changes resonance intensities and profiles.Understanding time correlation between electrons requires connecting the concept of spatial correlation with time. Spatial correlation arises from the Coulomb interactions between electrons ͓1-3͔. Without this correlation the electrons are independent in both space and time, i.e., they do not mix with one another in space and they evolve independently in time ͓3͔. In this paper we address time correlation between electrons, namely, how electrons communicate about time. We show that both temporal correlation of external interactions and spatial correlation between electrons are required for time correlation between electrons.Cross sections of multielectron atoms dynamically interacting with both matter and light have been widely studied for many years ͓4-6͔. In the last decade studies of multiple electron transitions have lead to more detailed understanding of correlated dynamic reaction mechanisms ͓3,7-10͔. Now, new experimental techniques ͓10-12͔ are providing data in unprecedented detail, which can be used to test in greater depth new descriptions of collision dynamics. Thus, both a conceptual and an observational basis is now available for more explicit studies of how time works in quantum multiparticle dynamics. In this paper we analyze two atomic processes in which time correlation between electrons affects reaction cross sections. The first case is a kinematic peak in a reaction in which electron transfer and ionization both occur. In this case time correlated and time uncorrelated amplitudes add incoherently. The second case is double electron excitation where coherent reaction pathways interfere. In the second case time correlation between electrons produces a large effect on both the shape and intensity of a double excitation resonance.Time dependence is imposed on a quantum system ͓13-16͔ by an external time-dependent interaction V I (t). The general expression for the probability amplitude, a f i (t) ϭ͗ f ͉U I (t,t i )͉i͘, for scattering of one or more electrons from ͉i͘ at time t i to ͉ f ͘ at time t may be described most conveniently in the interaction representation ͓3,5͔ using the evolution operator U I (t,tЈ), which satisfies i ‫ץ‬U I ͑ t,tЈ͒/‫ץ‬tϭV I ͑ t ͒U I ͑ t,tЈ͒, ͑1͒with the initial condition lim t→Ϫϱ U I (t,Ϫϱ)ϭÎ. The formal solution for the evolution operator may be expressed as a time orde...

We consider the time evolution of the occupation probabilities for the 2s − 2p transition in a hydrogen atom interacting with an external field, V (t). A two-state model and a dipole approximation are used. In the case of degenerate energy levels an analytical solution of the time-dependent Shrödinger equation for the probability amplitudes exists. The form of the solution allows one to choose the ratio of the field amplitude to its frequency that leads to temporal trapping of electrons in specific states. The analytic solution is valid when the separation of the energy levels is small compared to the energy of the interacting radiation.