arXiv subjects

Lars Bojer Madsen

Publications and source records attributed to Lars Bojer Madsen.

At least 73 records · Page 4Linked to original sources

arXiv2016

Time-dependent restricted-active-space self-consistent-field theory for bosonic many-body systems

We describe the time-dependent restricted-active-space self-consistent-field (TD-RASSCF) method for a system of interacting bosons. We provide the theory of the method and discuss its numerical implementation. The method provides a general wavefunction based approach to solve the time-dependent and time-independent Schrödinger equation for a system of bosons. It is based on the time-dependent variational principle to optimize at each instant of time a set of time-dependent coefficients and time-dependent orbitals used to describe the total wavefunction. Including the concept of a restricted-active-space, the exponential growth of the configurational space, resulting from all possible distributions of $N$ bosons in $M$ orbitals, can be controlled trough a specific excitation scheme. We show, by illustrative time-independent and time-dependent examples, that the method provides an accurate description of the system with a substantially smaller configurational space than the one required in the multi-configurational time-dependent Hartree method for bosons (MCTDHB). The TD-RASSCF method can also tackle problems beyond the reach of the MCTDHB method when a large number of orbitals are required.

quant-ph↗

arXiv2016

Non-Sequential Double Recombination High Harmonic Generation in Molecular-like Systems

We present a study of non-sequential double recombination (NSDR) high harmonic generation (HHG) in a molecular-like system. Using a Coulomb-corrected three-step model we are able to classically describe the observed NSDR HHG cutoffs precisely for all internuclear distances showing an intrinsic dependence on the location of the nuclei in the NSDR HHG process originating partly from the strong electron correlation in the NSDR HHG process. This dependence modifies the classically allowed return energies which in return changes the cutoffs observed in the HHG spectra. We also observe that the NSDR HHG signal changes its character for internuclear distances of $R\gtrsim 8-9$ a.u. which is proposed to stem from a change in the charge transfer dynamics within the molecule. For large internuclear distances of $R\gtrsim 13$ a.u. we observe a clear signature of the point of emission for the first electron emitted in the NSDR HHG signal and we also see signs of molecular exchange paths contributing to the HHG spectrum for these internuclear distances.

physics.atom-ph↗

arXiv2016

Laser-induced dissociative ionization of H$_{2}$ from the near-infrared to the mid-infrared regime

We apply the Monte Carlo Wave Packet (MCWP) approach to investigate the kinetic energy release (KER) spectra of the protons following double ionization in H$_{2}$ when interacting with laser pulses with central wavelengths ranging from the near-IR (800 nm) to the mid-IR (6400 nm) regions and with durations of 3-21 laser cycles. We uncover the physical origins of the peaks in the nuclear KER spectra and ascribe them to mechanisms such as ionization following a resonant dipole transition, charge-resonance-enhanced ionization (CREI) and ionization in the dissociative limit of large internuclear distances. For relatively large pulse durations, i.e., for 15 or more laser cycles at 3200 nm and 10 or more at 6400 nm, it is possible for the nuclear wave packet in H$_{2}^{+}$ to reach very large separations. Ionization of this part of the wave packet results in peaks in the KER spectra with very low energies. These peaks give direct information about the dissociative energy in the $2pσ_{u}$ potential energy curve of H$_{2}^{+}$ at the one- and three-photon resonances between the $2pσ_{u}$ and $1sσ_{g}$ curves in H$_{2}^{+}$. With the MCWP approach, we perform a trajectory analysis of the contributions to the KER peaks and identify the dominant ionization pathways. Finally, we consider a pump-probe scheme by applying two delayed pulses to track the nuclear dynamics in a time-resolved setting. Low-energy peaks appear for large delays and these are used to obtain the $2pσ_{u}$ dissociative energy values at the one-photon resonance between the $2pσ_{u}$ and $1sσ_{g}$ curves in H$_{2}^{+}$ for different wavelengths.

physics.atom-ph↗

arXiv2016

Torsional and rotational coupling in non-rigid molecules

We analyze theoretically the interplay between the torsional and the rotational motion of an aligned biphenyl-like molecule. To do so, we consider a transition between two electronic states with different internal torsional potentials, induced by means of a resonant laser pulse. The change in the internal torsional potential provokes the motion of the torsional wavepacket in the excited electronic state, modifying the structure of the molecule, and hence, its inertia tensor. We find that this process has a strong impact on the rotational wave function, displaying different behavior depending on the electronic states involved and their associated torsional potentials. We describe the dynamics of the system by considering the degree of alignment and the expectations values of the angular momentum operators for the overall rotation of the molecule.

physics.chem-ph↗

arXiv2016

The Integral Screened Configuration Interaction Method

We present the formulation and implementation of the Integral-Screened Configuration-Interaction method (ISCI). The ISCI is a minimal-operational count integral-driven direct Configuration-Interaction (CI) method with a simple and rigorous integral screening (IS). With a novel derivation of the CI equations we show that the time consuming $σ$-vector calculation is separable up to an overall sign and that this separability can lead to a rigorous IS. The rigorous IS leads to linear scaling in the $σ$-vector step for large systems but can also lead to near linear scaling for smaller systems for the standard CISD, CISDT and CISDTQ methods, where the exponent for the scaling is 1.27, 1.48 and 1.98, respectively, even while retaining an accuracy of $10^{-14}$ or less in the energy. In the ISCI the non-relativistic CI problem can be broken into 42 generalized-matrix-vector products in the $σ$-vector calculation, which can be separately optimized. Due to the IS the ISCI can use dramatically larger orbital spaces combined with large CI expansions, on a single cpu, as compared with traditional CI methods. Further, it offers an intrinsic possibility for parallelization on modern computing architectures. We show examples of how IS leads to linear or near linear scaling with respect to the size of the simulation box in calculations on the Beryllium atom.

physics.chem-ph↗

arXiv2016

Illuminating Molecular Symmetries with Bicircular High-Order-Harmonic Generation

We present a complete theory of bicircular high-order-harmonic emission from N-fold rotationally symmetric molecules. Using a rotating frame of reference we predict the complete structure of the high-order-harmonic spectra for arbitrary driving frequency ratios and show how molecular symmetries can be directly identified from the harmonic signal. Our findings reveal that a characteristic fingerprint of rotational molecular symmetries can be universally observed in the ultrafast response of molecules to strong bicircular fields.

physics.atom-ph↗

arXiv2016

Characterization of Molecular Breakup by Very Intense Femtosecond XUV Laser Pulses

We study the breakup of $\text{H}_2^+$ exposed to super-intense, femtosecond laser pulses with frequencies greater than that corresponding to the ionization potential. By solving the time-dependent Schrödinger equation in an extensive field parameter range, it is revealed that highly nonresonant dissociation channels can dominate over ionization. By considering field-dressed Born-Oppenheimer potential energy curves in the reference frame following a free electron in the field, we propose a simple physical model that characterizes this dissociation mechanism. The model is used to predict control of vibrational excitation, magnitude of the dissociation yields, and nuclear kinetic energy release spectra. Finally, the joint energy spectrum for the ionization process illustrates the energy sharing between the electron and the nuclei and the correlation between ionization and dissociation processes.

physics.atom-ph↗

arXiv2016

Same Period Emission and Recombination in Non-Sequential Double Recombination High-Harmonic Generation in H$_2$

Non-sequential double recombination (NSDR) high-order harmonic generation (HHG) is studied in a molecular system. We observe a unique molecular two-electron effect with a characteristic cutoff in the HHG spectrum at higher energies than what was previously seen for NSDR HHG in atoms. The effect is corroborated with a classical model where it is found that the effect is sensitive to the molecular potential and originates from same period emission and recombination (SPEaR) of two electrons. The effect persists for intermediate nuclear distances of $R \gtrsim 8.0$ a.u.

physics.atom-ph↗

arXiv2016

Exterior time scaling with stiffness-free Lanczos time propagator: formulation and application to atoms interacting with strong mid-infrared lasers

Aiming at efficient numerical treatment of tunneling ionization of atoms and molecules by mid-infrared (IR) lasers, exterior time scaling (ETS) theory is formulated as a generalization of the time-scaled coordinate approach. The key idea of ETS is the division of the spatial volume into a small region around the nucleus and its outside; the radial coordinates are time scaled only in the outer region. The continuum components of photoelectron wave packets are prevented from reaching the edge of the spatial simulation volume, enabling the long-time evolution of wave packets with a relatively small number of basis functions without concerns of electron reflections. On the other hand, the bound-state components are free from shrinking toward the origin because of non-time scaling in the inner region. Hence, the equations of motion in ETS are less stiff than the ones in the original time-scaled coordinate approach in which the shrinking bound states make the equations of motion seriously stiff. For numerical implementation of ETS, the working equations are derived in terms of finite-element discrete-variable-representation functions. Furthermore, the stiffness-free Lanczos time propagator is introduced to remove any persistent stiffness in the treatment of mid-IR lasers due to the involvement of hundreds of angular-momentum states. The test calculations for atomic hydrogen interacting with linearly polarized mid-IR pulses demonstrate the accuracy and numerical efficiency of the new scheme, and exhibit its special capability if there is no recollision with the parent ion. Hence, ETS will show its true potential for the detailed analysis of photoelectron wave packet dynamics in circularly or near-circularly polarized mid-IR fields.

quant-ph↗

arXiv2016

Theory of dissociative tunneling ionization

We present a theoretical study of the dissociative tunneling ionization process. Analytic expressions for the nuclear kinetic energy distribution of the ionization rates are derived. A particularly simple expression for the spectrum is found by using the Born-Oppenheimer (BO) approximation in conjunction with the reflection principle. These spectra are compared to exact non-BO ab initio spectra obtained through model calculations with a quantum mechanical treatment of both the electronic and nuclear degrees freedom. In the regime where the BO approximation is applicable imaging of the BO nuclear wave function is demonstrated to be possible through reverse use of the reflection principle, when accounting appropriately for the electronic ionization rate. A qualitative difference between the exact and BO wave functions in the asymptotic region of large electronic distances is shown. Additionally the behavior of the wave function across the turning line is seen to be reminiscent of light refraction. For weak fields, where the BO approximation does not apply, the weak-field asymptotic theory describes the spectrum accurately.

physics.atom-ph↗

arXiv2016

Inter- and intracycle interference effects in strong-field dissociative ionization

We theoretically study dissociative ionization of H$_2^+$ exposed to strong linearly polarized few-cycle visible, near-infrared and midinfrared laser pulses. We find rich energy-sharing structures in the combined electron and nuclear kinetic energy spectra with features that are a priori at odds with simple energy conservation arguments. We explain the structures as interferences between wave packets released during different optical cycles, and during the same optical cycle, respectively. Both inter- and intracycle interference structures are clearly visible in the joint energy spectra. The shapes of the interference structures depend on the dynamics leading to the double continuum, and carry sub-femtosecond information.

physics.atom-ph↗

arXiv2016

A Rotating-Frame Perspective on High-Harmonic Generation of Circularly Polarized Light

We employ a rotating frame of reference to elucidate high-harmonic generation of circularly polarized light by bicircular driving fields. In particular, we show how the experimentally observed circular components of the high-harmonic spectrum can be directly related to the corresponding quantities in the rotating frame. Supported by numerical simulations of the time-dependent Schrödinger equation, we deduce an optimal strategy for maximizing the cutoff in the high-harmonic plateau while keeping the two circular components of the emitted light spectrally distinct. Moreover, we show how the rotating-frame picture can be more generally employed for elliptical drivers. Finally, we point out how circular and elliptical driving fields show a near-duality to static electric and static magnetic fields in a rotating-frame description. This demonstrates how high-harmonic generation of circularly polarized light under static electromagnetic fields can be emulated in practice even at static field strengths beyond current experimental capabilities.

physics.atom-ph↗

arXiv2015

Light-Induced Structures in Attosecond Transient Absorption Spectroscopy of Molecules

The nature of light-induced structures in attosecond transient absorption spectroscopy of molecular systems is investigated theoretically. It is shown how nuclear dynamics affect these structures. We find that a theoretical three-surface model captures the main characteristics in the calculated spectra. Based on this model, nuclear dynamics is divided into different categories, each category having unique signatures in the absorption spectra. Finally, we discuss the possibility for experimental observation of light-induced structures in molecules.

physics.atom-ph↗

arXiv2015

Nuclear-Motion Effects in Attosecond Transient Absorption Spectroscopy of Molecules

We investigate the characteristic effects of nuclear motion on attosecond transient absorption spectra in molecules by calculating the spectrum for different model systems. Two models of the hydrogen molecular ion are considered: one where the internuclear separation is fixed, and one where the nuclei are free to vibrate. The spectra for the fixed nuclei model are similar to atomic spectra reported elsewhere, while the spectra obtained in the model including nuclear motion are very different and dominated by extremely broad absorption features. These broad absorption features are analyzed and their relation to molecular dissociation investigated. The study of the hydrogen molecular ion validates an approach based on the Born-Oppenheimer approximation and a finite electronic basis. This latter approach is then used to study the three-dimensional hydrogen molecule including nuclear vibration. The spectrum obtained from H$_2$ is compared to the result of a fixed-nuclei calculation. In the attosecond transient absorption spectra of H$_2$ including nuclear motion we find a rich absorption structure corresponding to population of different vibrational states in the molecule, while the fixed-nuclei spectra again are very similar to atomic spectra. We find that light-induced structures at well-defined energies reported in atomic systems are also present in our fixed nuclei molecular spectra, but suppressed in the ${\text{H}_2}^+$ and H$_2$ spectra with moving nuclei. We show that the signatures of light-induced structures are closely related to the nuclear dynamics of the system through the shapes and relative arrangement of the Born-Oppenheimer potential energy curves.

physics.atom-ph↗

arXiv2015

Dissociative ionization of H2+ using intense femtosecond XUV laser pulses

The dissociative ionization of H2+ interacting with intense, femtosecond extreme-ultraviolet laser pulses is investigated theoretically. This is done by numerical propagation of the time-dependent Schrödinger equation for a colinear one-dimensional model of H2+, with electronic and nuclear motion treated exactly within the limitations of the model. The joint-energy spectra (JES) are extracted for the fragmented electron and nuclei by means of the t-SURFF method. The dynamic interference effect, which was first observed in one-electron atomic systems, is in the present work observed for H2+, emerging as interference patterns in the JES. The photoelectron spectrum and the nuclear energy spectrum is obtained by integration of the JES. Without the JES, the photoelectron spectrum itself is shown to be inadequate for the observation of the dynamic interference effect. The resulting JES are analyzed in terms of two models. In one model the wave function is expanded in terms of the "essential" states of the system, consisting of the ground state and the continuum states. In the second model the photoelectron spectra from fixed nuclei calculations are used to reproduce the JES using simple reflection arguments. The range of validity of these models is discussed and it is shown that the continuum-continuum couplings and the consideration of the population of excited vibrational states are crucial for understanding the structures of the JES.

physics.atom-ph↗

arXiv2014

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

We present a wave-function based method to solve the time-dependent many-electron Schrödinger equation (TDSE) with special emphasis on strong-field ionization phenomena. The theory builds on the configuration-interaction (CI) approach supplemented by the generalized-active-space (GAS) concept from quantum chemistry. The latter allows for a controllable reduction in the number of configurations in the CI expansion by imposing restrictions on the active orbital space. The method is similar to the recently formulated time-dependent restricted-active-space (TD-RAS) CI method [D. Hochstuhl, and M. Bonitz, Phys. Rev. A 86, 053424 (2012)]. We present details of our implementation and address convergence properties with respect to the active spaces and the associated account of electron correlation in both ground state and excitation scenarios. We apply the TD-GASCI theory to strong-field ionization of polar diatomic molecules and illustrate how the method allows us to uncover a strong correlation-induced shift of the preferred direction of emission of photoelectrons.

quant-ph↗

arXiv2014

Dissociation and dissociative ionization of H2+ using the time-dependent surface flux method

The time-dependent surface flux method developed for the description of electronic spectra [L. Tao and A. Scrinzi, New J. Phys. 14, 013021 (2012); A. Scrinzi, New J. Phys. 14, 085008 (2012)] is extended to treat dissociation and dissociative ionization processes of H2+ interacting with strong laser pulses. By dividing the simulation volume into proper spatial regions associated with the individual reaction channels and monitoring the probability flux, the joint energy spectrum for the dissociative ionization process and the energy spectrum for dissociation is obtained. The methodology is illustrated by solving the time-dependent Schrödinger equation (TDSE) for a collinear one-dimensional model of H2+ with electronic and nuclear motions treated exactly and validated by comparison with published results for dissociative ionization. The results for dissociation are qualitatively explained by analysis based on dressed diabatic Floquet potential energy curves, and the method is used to investigate the breakdown of the two-surface model.

physics.atom-ph↗

arXiv2014

Time-dependent restricted-active-space self-consistent-field theory for laser-driven many-electron dynamics. II. Extended formulation and numerical analysis

The time-dependent restricted-active-space self-consistent-field (TD-RASSCF) method is formulated based on the TD variational principle. In analogy with the configuration-interaction singles (CIS), singles-and-doubles (CISD), singles-doubles-and-triples (CISDT) methods in quantum chemistry, the TD-RASSCF-S, -SD, and -SDT methods are introduced as extensions of the TD-RASSCF dou- bles (-D) method [Phys. Rev. A 87, 062511 (2013)]. Based on an analysis of the numerical cost and test calculations for one-dimensional (1D) models of atomic helium, beryllium, and carbon, it is shown that the TD-RASSCF-S and -D methods are computationally feasible for systems with many electrons and more accurate than the TD Hartree-Fock (TDHF) and TDCIS methods. In addition to the discussion of methodology, an analysis of electron dynamics in the high-order harmonic generation (HHG) process is presented. For the 1D beryllium atom, a state-resolved analysis of the HHG spectrum based on the time-independent HF orbitals shows that while only single-orbital excitations are needed in the region below the cutoff, single- and double-orbital excitations are es- sential beyond, where accordingly the single-active-electron (SAE) approximation and the TDCIS method break down. On the other hand, the TD-RASSCF-S and -D methods accurately describe the multi-orbital excitation processes throughout the entire region of the HHG spectrum. For the 1D carbon atom, our calculations show that multi-orbital excitations are essential in the HHG process even below the cutoff. Hence, in this test system a very accurate treatment of electron correlation is required. The TD-RASSCF-S and -D approaches meet this demand, while the SAE approximation and the TDCIS method are inadequate.

quant-ph↗