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Journal of Physics B Atomic Molecular and Optical Physics

Ultra-fast spin dynamics in the 2s2p2configuration of C+studied by time-dependentR-matrix theory

Steven Hutchinson, Michael Lysaght, H. W. van der Hart

Published Oct 20, 2011• 5 citations
Publisher

Abstract

We employ time-dependent R-matrix theory to study ultra-fast dynamics in the doublet 2s2p(2) configuration of C+ for a total magnetic quantum number M = 1. In contrast to the dynamics observed for M = 0, ultra-fast dynamics for M = 1 is governed by spin dynamics in which the 2s electron acts as a flag rather than a spectator electron. Under the assumption that m(S) = 1/2, m(2s) = 1/2 allows spin dynamics involving the two 2p electrons, whereas m(2s) = -1/2 prevents spin dynamics of the two 2p electrons. For a pump-probe pulse scheme with (h) over bar omega(pump) = 10.9 eV and (h) over bar omega(probe) = 16.3 eV and both pulses six cycles long, little sign of spin dynamics is observed in the total ionization probability. Signs of spin dynamics can be observed, however, in the ejected-electron momentum distributions. We demonstrate that the ejected-electron momentum distributions can be used for unaligned targets to separate the contributions of initial M = 0 and M = 1 levels. This would, in principle, allow unaligned target ions to be used to obtain information on the different dynamics in the 2s2p(2) configuration for the M = 0 and M = 1 levels from a single experime

DOI
10.1088/0953-4075/44/21/215602

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We employ time-dependent R-matrix theory to study ultra-fast dynamics in the doublet 2s2p(2) configuration of C+ for a total magnetic quantum number M = 1. In contrast to the dynamics observed for M = 0, ultra-fast dynamics for M = 1 is governed by spin dynamics in which the 2s electron acts as a flag rather than a spectator electron. Under the assumption that m(S) = 1/2, m(2s) = 1/2 allows spin dynamics involving the two 2p electrons, whereas m(2s) = -1/2 prevents spin dynamics of the two 2p electrons. For a pump-probe pulse scheme with (h) over bar omega(pump) = 10.9 eV and (h) over bar omega(probe) = 16.3 eV and both pulses six cycles long, little sign of spin dynamics is observed in the total ionization probability. Signs of spin dynamics can be observed, however, in the ejected-electron momentum distributions. We demonstrate that the ejected-electron momentum distributions can be used for unaligned targets to separate the contributions of initial M = 0 and M = 1 levels. This would, in principle, allow unaligned target ions to be used to obtain information on the different dynamics in the 2s2p(2) configuration for the M = 0 and M = 1 levels from a single experime
The precession of orbital and spin angular momentum vectors has been observed in a pump-probe study of the 4P fine-structure states of atomic potassium. A femtosecond pump pulse prepared a coherent superposition of the two fine-structure components. A time-delayed probe pulse then ionized the system after it had been allowed to evolve freely. Oscillations recorded in the ion signal reflect the evolution of the orientation of the orbital and spin angular momentum due to spin-orbit coupling. This interpretation gives physical insight into the cause of the half-period phase shift observed when the relative polarizations of the laser pulses were changed from parallel to perpendicular. Finally, it is shown that these changes in the orientation of the spin momentum vector of the system can be utilized to produce highly spin-polarized free electrons on the femtosecond scale
Summary form only given. Femtosecond pulses were used to generate long-lived (/spl tau/>0.1 ns) quantum-entangled states involving the spins of many individual Mn/sup 2+/ ions in Cd/sub 1-x/Mn/sub x/Te. The experiments were performed on a single crystal of Cd/sub 0.98/Mn/sub 0.02/Te with a standard pump-probe setup in the Voigt reflection geometry. We used a mode-locked Ti:sapphire laser which provided /spl sim/ 95 fs pulses at a repetition rate of 85 MHz an average-power of 80 mW and focused to a 80-/spl mu/m-diameter spot. The intensity of the reflected probe pulse measures changes in the optical constants that depend on the expectation value of the total spin for the particular entangled state /spl Psi/ created by the pump. The signature for an entanglement between states |j) and |l) is the observation of oscillations of frequency n/spl Omega//sub 0/ where n=(n/sub j/-n/sub l/). We notice that the highest harmonic of /spl Omega//sub 0/ provides a lower bound for the number of magnetic ions N that are entangled. The entanglement process, relying on coupling to localized excitons, holds promise for quantum-gate operations.
Ultrafast spectroscopy with attosecond resolution has enabled the real time observation of ultrafast electron dynamics in atoms, molecules and solids. These experiments employ attosecond pulses or pulse trains and explore dynamical processes in a pump-probe scheme that is selectively sensitive to electronic state of matter via photoelectron or XUV absorption spectroscopy or that includes changes of the ionic state detected via photo-ion mass spectrometry. Here, we demonstrate how the implementation of combined photo-ion and absorption spectroscopy with attosecond resolution enables tracking the complex multidimensional excitation and decay cascade of an Auger auto-ionization process of a few femtoseconds in highly excited krypton. In tandem with theory, our study reveals the role of intermediate electronic states in the formation of multiply charged ions. Amplitude tuning of a dressing laser field addresses different groups of decay channels and allows exerting temporal and quantitative control over the ionization dynamics in rare gas atoms.
We consider a scenario where interacting electrons confined in quantum dots (QDs) are either too close to be resolved, or we do not wish to apply measurements that resolve them. Then, the physical observable is an electron spin only and the system state is fully described by the spin density matrix. Accounting for the spatial degrees of freedom, we examine to what extent a Hamiltonian description of the spin-only degrees of freedom is valid. We show that as long as there is no coupling between singlet and triplet states, this is indeed the case, but when there is such a coupling, there are open systems effects, i.e., the dynamics is nonunitary even without interaction with a true bath. Our primary focus is an investigation of nonunitary effects, based on exact master equations we derive for the spin density matrix in the Lindblad and time-convolutionless forms, and the implications for quantum computation. In particular, we demonstrate that the Heisenberg interaction does not affect the unitary part (apart from a Lamb shift) but does affect the nonunitary contributions to the time evolution of the spin density matrix. In a sequel paper, we present a detailed analysis of an example system of two quantum dots, including spin-orbit effects.
If another linearly polarized attosecond pulse (the probe pulse) centered at 100 eV doubly ionizes the helium atom in the mixed state as illustrated in the right graph of Figure 9.1, the ionization probability depends on the time delay between the pump and the probe pulses. The probability is higher when the two electrons are located near each other, as depicted in Figure 9.2. Experimentally, one can measure the doubly ionized helium ion (He2þ) signal as function of time delay between the probe pulse and the pump pulse. The He2þ yield as a function of the time delay would inform us how the electron separation changes with time. Hu and Collins’s simulation shows that the separation changes periodically with a 2 fs cycle, which can be observed with the attosecond pulses. The cycle is much larger than the 200 as corresponding to the energy difference between the ground state and the first excited state (1s2p) because other excited states are involved.
Using sequential strong-field double ionization in a pump–probe scheme we show through calculations how electronic dynamics can be prepared and imaged. Electronic dynamics may arise whenever multiple states of the ion are accessed in the ionization step. The dynamics in the cation influence the rate of the second ionization step and the momentum distribution of the ejected electron, allowing their detailed characterization. We show how the probe step is controlled through spatial propensities of the ionizing orbitals and the energy level structure of the dication. Both the final electronic state of the dication and the spin state of the ejected electron pair can be controlled through the time delay between the two ionizing pulses. We discuss how our results will extend to the preparation and measurement of attosecond electron dynamics.