Kh. Kh. Shakov

Analytic description of population transfer in a degenerate n-level atom

Analytic expressions have been found for transition probabilities in a degenerate n-level atom interacting with a strong external field that gives a common time dependence to all of the transition matrix elements. Except for solving a simple nth-order equation to determine eigenvalues of dressed states, the method is entirely analytic. These expressions may be used to control electron populations in degenerate n-level atoms. Examples are given for n = 2 and 3.

Spatial and temporal correlation in dynamic, multi-electron quantum systems

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 ordering in kicked qubits

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.

Population control of 2s-2p transitions in hydrogen

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 Schroedinger 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.

Time ordering in multi-electron dynamics

Time ordering of interactions in dynamic quantum multi-electron systems provides a constraint that interconnects the time evolution of different electrons. In energy space, time ordering appears as the principal value contribution from the Green function, which corresponds to the asymptotic condition that specifies whether the system has outgoing (or possibly incoming) scattered waves. We report evidence of effects of time correlation found by comparing calculations to recent spectropolarimetric data.

Time Ordering Dynamics in Ionization‐Excitation of Helium to HeII (2p) Magnetic Sublevels Using Extreme Ultraviolet Spectropolarimetry

Time ordering of interactions in dynamic quantum multi‐electron systems provides a constraint that connects the time evolution of different electrons in ion‐atom collisions. When spatial correlation between electrons is combined with time ordering, the time evolution operators for different electrons become correlated. We report in this study evidence for quantum time correlation between electrons by comparing full second‐Born calculations, which include both spatial and temporal electron correlation, to recent magnetic sublevel cross section measurements corresponding to simultaneous ionization‐excitation of He (1s2) 1So to He+ (2p) 2Po levels by proton impact. The experimental substates cross sections σ0 and σ1 for ML =0, ±1 are determined by combining corresponding total extreme ultraviolet (EUV) cross sections with our recent polarization fraction measurements. Such results have important applications for the understanding of quantum phenomena like time entanglement.

How do electrons communicate about time

We show that time correlation between electrons requires that the Dyson time ordering operator, T, differs from its uncorrelated value and spatial electron-electron correlation be present. In this paper we decompose T into an uncorrelated term, Tunc, plus a correlated term, Tcor=T∼Tunc, which leads to time correlation in time dependent external interactions. Effects of time correlation between electrons can be observed. Two examples are presented. In transfer ionization the time correlation operator incoherently changes the shape of an electron-electron Thomas peak. In double excitation the influence of Tcor in amplitudes for coherently interfering pathways changes resonance intensities and profiles.