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Register a new userThe Wigner time delay for laser induced tunnel-ionization via the electron propagator
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Recent attoclock experiments using the attsecond angular streaking technique enabled the measurement of the tunneling time delay during laser induced strong field ionization. Theoretically the tunneling time delay is commonly modelled by the Wigner time delay concept which is derived from the derivative of the electron wave function phase with respect to energy. Here, we present an alternative method for the calculation of the Wigner time delay by using the fixed energy propagator. The developed formalism is applied to the nonrelativistic as well as to the relativistic regime of the tunnel-ionization process from a zero-range potential, where in the latter regime the propagator can be given by means of the proper-time method.
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More than 100 years after its discovery and its explanation in the energy domain, the duration of the photoelectric effect is still heavily studied. The emission time of a photoelectron can be quantified by the Wigner time delay. Experiments addressing this time delay for single-photon ionization became feasible during the last 10 years. A missing piece, which has not been studied, so far, is the Wigner time delay for strong-field ionization of molecules. Here we show experimental data on the Wigner time delay for tunnel ionization of $H_{2}$ molecules and demonstrate its dependence on the emission direction of the electron with respect to the molecular axis. We find, that the observed changes in the Wigner time delay can be quantitatively explained by elongated/shortened travel paths of the electrons that are due to spatial shifts of the electrons birth position after tunneling. This introduces an intuitive perspective towards the Wigner time delay in strong-field ionization.
Several recent attoclock experiments have investigated the fundamental question of a quantum mechanically induced time delay in tunneling ionization via extremely precise photoelectron momentum spectroscopy. The interpretations of those attoclock experimental results were controversially discussed, because the entanglement of the laser and Coulomb field did not allow for theoretical treatments without undisputed approximations. The method of semiclassical propagation matched with the tunneled wavefunction, the quasistatic Wigner theory, the analytical R-matrix theory, the backpropagation method, and the under-the-barrier recollision theory are the leading conceptual approaches put forward to treat this problem, however, with seemingly conflicting conclusions on the existence of a tunneling time delay. To resolve the contradicting conclusions of the different approaches, we consider a very simple tunneling scenario which is not plagued with complications stemming from the Coulomb potential of the atomic core, avoids consequent controversial approximations and, therefore, allows us to unequivocally identify the origin of the tunneling time delay as well as to confirm it with the backpropagation method being most known for predicting vanishing tunneling time.
We investigate specific features in the Wigner time behavior for slow electron elastic scattering by shallow potential wells. We considered two types of potentials wells, the small changes in the parameters of which lead to arising bound states in the well. It appeared that the time delay for attractive potential wells with no bound levels always has a positive value for small electron energies and changes sign after level arising in the well. At the moment of arising the times delay has a jump. The value of this jump is as more as less is the difference in the potential well depth from its critical value. The values of times delay strongly depend on geometrical sizes of potential wells.
The average dwell time of an electron in a potential barrier formed by an external electric field and the potential of a helium atom is evaluated within a semi classical one-dimensional tunneling approach. The tunneling electron is considered to interact with a nuclear charge screened by the electron in the helium ion. It is found that screening leads to smaller average dwell times of the tunneling electron. The dissipative effect of the environment on the tunneling electron is taken into account within a semiclassical model involving a velocity dependent frictional force and is found to change the average dwell time significantly.
High-harmonics generation spectroscopy is a promising tool for resolving electron dynamics and structure in atomic and molecular systems. This scheme, commonly described by the strong field approximation, requires a deep insight into the basic mechanism that leads to the harmonics generation. Recently, we have demonstrated the ability to resolve the first stage of the process -- field induced tunnel ionization -- by adding a weak perturbation to the strong fundamental field. Here we generalize this approach and show that the assumptions behind the strong field approximation are valid over a wide range of tunnel ionization conditions. Performing a systematic study -- modifying the fundamental wavelength, intensity and atomic system -- we observed a good agreement with quantum path analysis over a range of Keldysh parameters. The generality of this scheme opens new perspectives in high harmonics spectroscopy, holding the potential of probing large, complex molecular systems.
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