Nonsequential Double Ionization with Polarization-gated Pulses

We investigate laser-induced nonsequential double ionization by a polarization-gated laser pulse, constructed employing two counter-rotating circularly polarized few cycle pulses with a time delay $T_{d}$. We address the problem within a classical framework, and mimic the behavior of the quantum-mechanical electronic wave packet by means of an ensemble of classical electron trajectories. These trajectories are initially weighted with the quasi-static tunneling rate, and with suitably chosen distributions for the momentum components parallel and perpendicular to the laser-field polarization, in the temporal region for which it is nearly linearly polarized. We show that, if the time delay $T_{d}$ is of the order of the pulse length, the electron-momentum distributions, as functions of the parallel momentum components, are highly asymmetric and dependent on the carrier-envelope (CE) phase. As this delay is decreased, this asymmetry gradually vanishes. We explain this behavior in terms of the available phase space, the quasi-static tunneling rate and the recollision rate for the first electron, for different sets of trajectories. Our results show that polarization-gating technique may provide an efficient way to study the NSDI dynamics in the single-cycle limit, without employing few-cycle pulses.Comment: 17 pages, 6 figure

Causality and quantum interference in time-delayed laser-induced nonsequential double ionization

We perform a detailed analysis of the importance of causality within the strong-field approximation and the steepest-descent framework for the recollision-excitation with subsequent tunneling ionization (RESI) pathway in laser-induced nonsequential double ionization (NSDI). In this time-delayed pathway, an electron returns to its parent ion and, by recolliding with the core, gives part of its kinetic energy to excite a second electron at a time t′. The second electron then reaches the continuum at a later time t by tunneling ionization. We show that, if t′ and t are complex, the condition that recollision of the first electron occurs before tunnel ionization of the second electron translates into boundary conditions for the steepest-descent contours and thus puts constraints on the saddles to be taken when computing the RESI transition amplitudes. We also show that this generalized causality condition has a dramatic effect on the shapes of the RESI electron momentum distributions for few-cycle laser pulses. Physically, causality determines how the dominant sets of orbits of an electron returning to its parent ion can be combined with the dominant orbits of a second electron tunneling from an excited state. All features encountered are analyzed in terms of such orbits and their quantum interference

Classical and quantum-mechanical treatments of nonsequential double ionization with few-cycle laser pulses

We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron with its parent ion. The problem is treated classically, using an ensemble model, and quantum-mechanically, within the strong-field and uniform saddle-point approximations. In the latter case, the results are interpreted in terms of "quantum orbits", which can be related to the trajectories of a classical electron in an electric field. We obtain highly asymmetric electron momentum distributions, which strongly depend on the absolute phase, i.e., on the phase difference between the pulse envelope and its carrier frequency. Around a particular value of this parameter, the distributions shift from the region of positive to that of negative momenta, or vice-versa, in a radical fashion. This behavior is investigated in detail for several driving-field parameters, and provides a very efficient method for measuring the absolute phase. Both models yield very similar distributions, which share the same physical explanation. There exist, however, minor discrepancies due to the fact that, beyond the region for which electron-impact ionization is classically allowed, the yields from the quantum mechanical computation decay exponentially, whereas their classical counterparts vanish.Comment: 12 pages revtex, 12 figures (eps files

Interference effects in above-threshold ionization from diatomic molecules: determining the internuclear separation

We calculate angle-resolved above-threshold ionization spectra for diatomic molecules in linearly polarized laser fields, employing the strong-field approximation. The interference structure resulting from the individual contributions of the different scattering scenarios is discussed in detail, with respect to the dependence on the internuclear distance and molecular orientation. We show that, in general, the contributions from the processes in which the electron is freed at one center and rescatters off the other obscure the interference maxima and minima obtained from single-center processes. However, around the boundary of the energy regions for which rescattering has a classical counterpart, such processes play a negligible role and very clear interference patterns are observed. In such energy regions, one is able to infer the internuclear distance from the energy difference between adjacent interference minima.Comment: 10 pages, 8 figures; discussions slightly modified and an additional figure inserted for clarit

Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime

We provide exact analytical solutions for a two-dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the model parameters, and has therefore a partially complex energy eigenspectrum, its time-dependent version has real energy expectation values at all times. In our solution procedure we compare the two equivalent approaches of directly solving the time-dependent Dyson equation with one employing the Lewis–Riesenfeld method of invariants. We conclude that the latter approach simplifies the solution procedure due to the fact that the invariants of the non-Hermitian and Hermitian system are related to each other in a pseudo-Hermitian fashion, which in turn does not hold for their corresponding time-dependent Hamiltonians. Thus constructing invariants and subsequently using the pseudo-Hermiticity relation between them allows to compute the Dyson map and to solve the Dyson equation indirectly. In this way one can bypass to solve nonlinear differential equations, such as the dissipative Ermakov–Pinney equation emerging in our and many other systems

Non-sequential double ionization below laser-intensity threshold: Anticorrelation of electrons without excitation of parent ion

Two-electron correlated spectra of non-sequential double ionization below laser-intensity threshold are known to exhibit back-to-back scattering of the electrons, viz., the anticorrelation of the electrons. Currently, the widely accepted interpretation of the anticorrelation is recollision-induced excitation of the ion plus subsequent field ionization of the second electron. We argue that another mechanism, namely simultaneous electron emission, when the time of return of the rescattered electron is equal to the time of liberation of the bounded electron (the ion has no time for excitation), can also explain the anticorrelation of the electrons in the deep below laser-intensity threshold regime. Our conclusion is based on the results of the numerical solution of the time-dependent Schr\"{o}dinger equation for a model system of two one-dimensional electrons as well as an adiabatic analytic model that allows for a closed-form solution.Comment: 6 pages and 3 figure

A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field

We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turns out to be unique with the sole assumption that the Dyson map is Hermitian. Finally we compute the magnetization of the chain in the z and x direction

Delta-Function Potential with a Complex Coupling

We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at E=-z^2/4. For \Re(z)<0, H has an eigenvalue at E=-z^2/4. For the case that \Re(z)>0, H has a real, positive, continuous spectrum that is free from spectral singularities. For this latter case, we construct an associated biorthonormal system and use it to perform a perturbative calculation of a positive-definite inner product that renders H self-adjoint. This allows us to address the intriguing question of the nonlocal aspects of the equivalent Hermitian Hamiltonian for the system. In particular, we compute the energy expectation values for various Gaussian wave packets to show that the non-Hermiticity effect diminishes rapidly outside an effective interaction region.Comment: Published version, 14 pages, 2 figure

PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields

The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construction of a new inner product employing a "quasi-fermion" algebra in momentum space where creation and annihilation operators are not related via Hermitian conjugation. For a special example, when the boundary fields lie on the imaginary axis, we show the spectral equivalence of the quasi-Hermitian XX spin-chain with a non-local fermion model, where long range hopping of the particles occurs as the non-Hermitian boundary fields increase in strength. The corresponding Hamiltonian interpolates between the open XX and the quantum group invariant XXZ model at the free fermion point. For an even number of sites the former is known to be related to a CFT with central charge c=1, while the latter has been connected to a logarithmic CFT with central charge c=-2. We discuss the underlying algebraic structures and show that for an odd number of sites the superalgebra symmetry U(gl(1|1)) can be extended from the unit circle along the imaginary axis. We relate the vanishing of one of its central elements to the appearance of Jordan blocks in the Hamiltonian.Comment: 37 pages, 5 figure