non-Hermitian Floquet Theory Research Articles

Dynamical interference of H and H2+ in one-photon ionization

The non-Hermitian Floquet theory is applied to systematically calculate both the ac-Stark shift $\ensuremath{\delta}$ and the decay rate $\ensuremath{\gamma}$ for hydrogen atoms and hydrogen molecular ions, when placed in a high-frequency laser field with an intensity ranging from the perturbation to the stabilization region. This allows us to trace the appearance of dynamical interference in ionization. We find that both the stabilization and the dynamical interference are easier to achieve at a frequency close to the ionization threshold. For the molecular case, the effects of nuclear motion are discussed based on the Born-Oppenheimer approximation. Although the dynamical interference condition $\ensuremath{\delta}g\sqrt{\ensuremath{\pi}}\ensuremath{\gamma}$ seems to be satisfied at a low frequency for a fixed-nuclei ${{\mathrm{H}}_{2}}^{+}$ in the perturbation region, the effects of the nuclear motion are shown to destroy the interference patterns in this region. Meanwhile, for the sake of confirmation, the photoelectron energy distributions are calculated by solving the time-dependent Schr\odinger equation for the parameters where the dynamical interference is predicted by the non-Hermitian Floquet theory.

Adiabatic Floquet model for the optical response in femtosecond filaments

The standard model of femtosecond filamentation is based on phenomenological assumptions which suggest that the ionization-induced carriers can be treated as a homogeneous, uncorrelated plasma according to the Drude model, while the nonlinear response of the bound carriers is responsible for the all-optical Kerr effect. Here, we demonstrate that the additional plasma generated at a multiphoton resonance dominates the saturation of the nonlinear refractive index. Since resonances are not captured by the standard model, we propose a modification of the latter in which ionization enhancements can be accounted for by an ionization rate obtained from non-Hermitian Floquet theory. In the adiabatic regime of long pulse envelopes, this augmented standard model is in excellent agreement with direct quantum mechanical simulations. Since our proposal maintains the structure of the standard model, it can be easily incorporated into existing codes for the numerical simulation of femtosecond filaments.

Coherent light-driven electron transport through polycyclic aromatic hydrocarbon: laser frequency, field intensity, and polarization angle dependence.

A laser field is a potential control tool for operating ultrafast electronic devices due to a wide variety of options such as field strength, frequency, and polarization. To investigate these variables upon electron transport through a single-molecule device, we simulate a phenyl-acetylene macrocycle (PAM) within a linear-polarized laser field using single-particle Green's functions combined with the non-Hermitian Floquet theory. In the absence of the laser field, the PAM behaves as a perfect insulator due to destructive quantum interference. In the weak-field regime, field-amplitude power laws for one-, two-, and three-photon assisted tunneling are evident in the computational results. The study reveals a range of experimentally feasible field strengths for the observation of picoampere current caused by photon assisted tunneling. In addition, we find that the light-driven current is proportional to the cosine square of the polarization angle, and molecular electronic structure is revealed by the current-frequency characteristics. The origin of these behaviors is established using non-Hermitian Floquet perturbation analysis. The computations show that PAM-based optoelectronic switches have robust large on-off switching ratios under weak-field operating conditions, which are not sensitive to asymmetric molecule-lead couplings.

Light-driven electron transport through a molecular junction based on cross-conjugated systems.

This work explores light-driven electron transport through cross-conjugated molecules with different numbers of alkenyl groups. In the framework of coherent quantum transport, the analysis uses single-particle Green's functions together with non-Hermitian Floquet theory. With realistic parameters stemming from spectroscopy, the simulations show that measurable current (∼10(-11) A) caused by photon-assisted tunneling should be observed in a weak driving field (∼2 × 10(5) V/cm). Current-field intensity characteristics give one-photon and two-photon field amplitude power laws. The gap between the molecular orbital and the Fermi level of the electrodes is revealed by current-field frequency characteristics. Due to generalized parity symmetry, the cross-conjugated molecules with odd and even numbers of alkenyl groups exhibit completely different current-polarization characteristics, which may provide an advantageous feature in nanoelectronic applications.

Resonances induced in H atoms by the high-intensity 800 nm laser field

A hydrogen atom exposed to a linearly polarized laser field with a wavelength of 800 nm and intensity varying from 1013 to 1014 W cm−2 is studied using non-perturbative non-Hermitian Floquet theory. The rate of ionization is calculated and the resonant enhancements are analysed by determining the composition of the ground and resonant-state wave functions. A map of resonant-state quasienergies is presented. The electronic density of the quasi-energy ground state versus the electron coordinate is analysed too. We conclude that the decay of an atom in a low intensity non-resonant laser field occurs from the asymptotically distant part of the ground state. For a higher intensity, the ionization proceeds using the mechanism of interchanging the character of the ground state with a radiatively coupled excited state(s). The process of electron emission is governed by the excited-bound-state part of the resonance wave function. With an increase of intensity, the electron is ionized at smaller distances from the nucleus.

Hydrogen atom in 2s state in a laser field

The hydrogen atom in the 2s state exposed to a linearly polarized laser field is studied by using the non-perturbative non-Hermitian Floquet theory. The electronic density of the quasi-energy H(2s) state versus the electron coordinate is analyzed. We conclude that the decay of an atom in a low-intensity non-resonant laser field occurs from the asymptotically distant part of the initial state. On the other hand, the process of electron emission in a resonant laser field is governed by the excited-bound-statepart of the resonance wave function. With an increase in the intensity and by increasing the degree of excitation of the initial state not too high, the electron is ionized at smaller distances from the nucleus.

Multiphoton ionization and multiphoton resonances in the tunneling regime

The rate of ionization of an atom of helium, argon, or hydrogen exposed to an intense monochromatic laser field and the quasienergy spectrum of their dressed states are studied for values of the Keldysh parameter between 1 and 0.6 and wavelengths between 390 and 1300 nm. The calculations are carried out within the non-Hermitian Floquet theory. Resonances with intermediate excited states significantly affect ionization from the dressed ground state at all the intensities and all the wavelengths considered. The dressed excited states responsible for these structures are large-${\ensuremath{\alpha}}_{0}$ states akin to the Kramers-Henneberger states of the high-frequency Floquet theory. Within the single-active-electron approximation, these large-${\ensuremath{\alpha}}_{0}$ states become species independent at sufficiently high intensity or sufficiently long wavelength. Apart for the resonance structures arising from multiphoton coupling with excited states, the ab initio Floquet ionization rate is in excellent agreement with the predictions of two different calculations in the strong field approximation, one based on a length-gauge formulation of this approximation and one based on a velocity-gauge formulation. The calculations also confirm the validity of the ${\ensuremath{\omega}}^{2}$ expansion as an alternative to the strong field approximation for taking into account the nonadiabaticity of the ionization process in intense low-frequency laser fields.

Shot-noise control in ac-driven nanoscale conductors

We derive within a time-dependent scattering formalism expressions for both the current through ac-driven nanoscale conductors and its fluctuations. The results for the time-dependent current, its time average, and, above all, the driven shot noise properties assume an explicit and serviceable form by relating the propagator to a non-Hermitian Floquet theory. The driven noise cannot be expressed in terms of transmission probabilities. The results are valid for a driving of arbitrary strength and frequency. The connection with commonly known approximation schemes such as the Tien-Gordon approach or a high-frequency approximation is elucidated together with a discussion of the corresponding validity regimes. Within this formalism, we study the coherent suppression of current and noise caused by properly chosen electromagnetic fields.

Current noise in ac-driven nanoscale conductors.

The theory for current fluctuations in ac-driven transport through nanoscale systems is put forward. By use of a generalized, non-Hermitian Floquet theory we derive novel explicit expressions for the time-averaged current and the zero-frequency component of the power spectrum of current fluctuations. A distinct suppression of both the zero-frequency noise and the dc current occurs for suitably tailored ac fields. The relative level of transport noise, being characterized by a Fano factor, can selectively be manipulated by ac sources; in particular, it exhibits both characteristic maxima and minima near current suppression.

Two-photon detachment of H−

A precision calculation of the two-photon detachment cross section for ${\mathrm{H}}^{\ensuremath{-}}$ is performed by means of a non-Hermitian Floquet theory. A highly accurate initial state wave function is used along with fully correlated saddle-point wave functions for the intermediate and final states. The cross section is investigated for energies below the $n=2$ and $n=3$ thresholds. The peak cross section predicted for the ${}^{1}D$ resonance is $3.10\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}49}$ ${\mathrm{cm}}^{4}$ sec at 10.873 2 eV. It represents an ab initio theoretical prediction in complete agreement with the experimental result of 3.2 $(+1.8,\ensuremath{-}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}49}$ ${\mathrm{cm}}^{4}$ sec at 10.873 2(27) eV.

Floquet analysis of laser-induced continuum structures

A semi-perturbative description of the resonance structures induced by strong laser fields is formulated within the framework of the non-Hermitian Floquet theory. Three cases are examined numerically, namely continuum structures induced by a two-colour embedding field, resonance enhancements in two-colour ionization and Stark-shift-induced resonances in a strong monochromatic field.

High-order perturbation expansion of non-Hermitian Floquet theory for multiphoton and above-threshold ionization processes

A high-order perturbation theory is presented for efficient and accurate computation of multiphoton and above-threshold ionization cross sections of atoms and molecules in weak to medium strength laser fields. The procedure is based on a Raleigh-Schrodinger perturbative expansion of the time-independent non-Hermitian Floquet Hamiltonian. The reduced Green function and generalized pseudospectral discretization techniques are extended to facilitate the calculation of complex quasienergy resonance states without the need of diagonaliz- ing the full Floquet Hamiltonian. Explicit expressions are presented for the determination of intensity- dependent total and partial rates and electron angular distributions. The theory is applied to a case study of multiphoton detachment of H 2 for a range of laser frequencies ~corresponding to the absorption of a minimum of two photons! and laser intensities from 10 7 to 10 12 W/cm 2 . It is found that a 16th-order perturbative Floquet procedure provides an excellent description of the two-photon-dominant detachment processes for laser inten- sity up to 2310 11 W/cm 2 . The predicted electron angular distributions are in good agreement with recent experimental data.

Theoretical study of the energy spectra of multiphoton above-threshold dissociation of H 2+ in intense laser fields

We present a new procedure for the determination of the kinetic energy spectra of molecules undergoing multiphoton above-threshold dissociation (ATD) in intense laser fields. The method is based on the extension of the non-Hermitian Floquet theory and an integral equation formulation of the partial rates. The non-Hermitian Floquet Hamiltonian is discretized by means of the complex-scaling generalized pseudospectral technique, and a back rotation procedure is introduced for extracting the partial widths from the total resonance wavefunctions. The method is applied to the study of the ATD energy spectra of H 2 + molecular ions in intense (775 nm) laser fields.