Crossover from tunneling to multiphoton ionization of atoms

We present a theory illuminating the cross-over from strong-field tunnelling ionization to weak-field multiphoton ionization in the interaction of a classical laser field with a hydrogen atom. A simple formula is derived in which the ionization amplitude appears as a product of two separate amplitudes. The first describes the initial polarization of the atom by virtual multiphoton absorption and the second the subsequent tunnelling out of the polarized atom. Tunnelling directly from the ground state and multiphoton absorption without tunnelling appear naturally as the limits of the theory

Subcycle time-resolved nondipole dynamics in tunneling ionization

The electron nondipole dynamics in tunneling ionization in an elliptically polarized laser field is investigated theoretically using a relativistic Coulomb-corrected strong-field approximation (SFA) based on the eikonal approximation of the Klein-Gordon equation. We calculate attoclock angle-resolved light-front momentum distributions at different ellipticities of the laser field in quasistatic and nonadiabatic regimes and analyze them with an improved Simpleman model. The nondipole correlations between longitudinal and transverse momentum components are examined. Deviations of the photoelectron momentum distribution calculated via SFA with respect to the available experimental results as well as with the improved Simpleman model are discussed and interpreted in terms of nonadiabatic as well as Coulomb effects in the continuum and under-the-barrier. The favorable prospects of an experimental observation are discussed

Tunneling ionization in ultrashort laser pulses: Edge effect and remedy

Tunneling ionization of an atom in ultrashort laser pulses is considered. When the driving laser pulse is switched-on and -off with a steep slope, the photoelectron momentum distribution (PMD) shows an edge-effect because of the photoelectron diffraction by the time-slit of the pulse. The trivial diffraction pattern of the edge effect consisting of fast oscillations in the PMD disguises in the deep nonadiabatic regime the physically more interesting features in the spectrum which originate from the photoelectron dynamics. We point out the precise conditions how to avoid this scenario experimentally and if unavoidable in theory we put forward an efficient method to remove the edge-effect in the PMD. This allows to highlight the nonadiabatic dynamical features of the PMD, which is indispensable for their further investigation in complex computationally demanding scenarios. The method is firstly demonstrated on a one-dimensional problem, and further applied in three-dimensions for the attoclock. The method is validated by a comparison of analytical results via the strong-field approximation with numerical solutions of the time-dependent Schr\"odinger equation

Role of reflections in the generation of a time delay in strong-field ionization

The problem of time delay in tunneling ionization is revisited. The origin of time delay at the tunnel exit is analysed, underlining the two faces of the concept of the tunnelling time delay: the time delay around the tunnel exit and the asymptotic time delay at a detector. We show that the former time delay, in the sense of a delay in the peak of the wavefunction, exists as a matter of principle and arises due to the sub-barrier interference of the reflected and transmitted components of the tunneling electronic wavepacket. We exemplify this by describing the tunnelling ionization of an electron bound by a short-range potential within the strong field approximation in a "deep tunnelling" regime. If sub-barrier reflections are extracted from this wavefunction, then the time delay of the peak is shown to vanish. Thus, we assert that the disturbance of the tunnelling wavepacket by the reflection from the surface of the barrier causes a time delay in the neighbourhood of the tunnel exit

Relativistic strong-field ionization of hydrogen-like atomic systems in constant crossed electromagnetic fields

Relativistic strong-field ionization of hydrogen-like atoms or ions in a constant crossed electromagnetic field is studied. The transition amplitude is formulated within the strong-field approximation in G\"oppert-Mayer gauge, with initial and final electron states being described by the corresponding Dirac-Coulomb and Dirac-Volkov wave functions, respectively. Coulomb corrections to the electron motion during tunneling are taken into account by adjusting an established method to the present situation. Total and energy-differential ionization rates are calculated and compared with predictions from other theories in a wide range of atomic numbers and applied field strengths.Comment: 9 pages, 4 figure

Strong-field ionization via a high-order Coulomb-corrected strong-field approximation

Signatures of the Coulomb corrections in the photoelectron momentum distribution during laser-induced ionization of atoms or ions in tunneling and multiphoton regimes are investigated analytically in the case of an one-dimensional problem. High-order Coulomb corrected strong-field approximation is applied, where the exact continuum state in the S-matrix is approximated by the eikonal Coulomb-Volkov state including the second-order corrections to the eikonal. Although, without high-order corrections our theory coincides with the known analytical R-matrix (ARM) theory, we propose a simplified procedure for the matrix element derivation. Rather than matching the eikonal Coulomb-Volkov wave function with the bound state as in the ARM-theory to remove the Coulomb singularity, we calculate the matrix element via the saddle-point integration method as by time as well as by coordinate, and in this way avoiding the Coulomb singularity. The momentum shift in the photoelectron momentum distribution with respect to the ARM-theory due to high-order corrections is analyzed for tunneling and multiphoton regimes. The relation of the quantum corrections to the tunneling delay time is discusse

Exact Asymptotic Behaviour of Fermion Correlation Functions in the Massive Thirring Model

We obtain an exact asymptotic expression for the two-point fermion correlation functions in the massive Thirring model (MTM) and show that, for $\beta^2=8\pi$, they reproduce the exactly known corresponding functions of the massless theory, explicitly confirming the irrelevance of the mass term at this point. This result is obtained by using the Coulomb gas representation of the fermionic MTM correlators in the bipolar coordinate system.Comment: To appear in J. Phys. A: Math. Gen. 12 page

Reconciling Conflicting Approaches for the Tunneling Time Delay in Strong Field Ionization

Several recent attoclock experiments have investigated the fundamentalquestion of a quantum mechanically induced time delay in tunneling ionizationvia extremely precise photoelectron momentum spectroscopy. The interpretationsof those attoclock experimental results were controversially discussed, becausethe entanglement of the laser and Coulomb field did not allow for theoreticaltreatments without undisputed approximations. The method of semiclassicalpropagation matched with the tunneled wavefunction, the quasistatic Wignertheory, the analytical R-matrix theory, the backpropagation method, and theunder-the-barrier recollision theory are the leading conceptual approaches putforward to treat this problem, however, with seemingly conflicting conclusionson the existence of a tunneling time delay. To resolve the contradictingconclusions of the different approaches, we consider a very simple tunnelingscenario which is not plagued with complications stemming from the Coulombpotential of the atomic core, avoids consequent controversial approximationsand, therefore, allows us to unequivocally identify the origin of the tunnelingtime delay.<br