High-harmonic spectroscopy of impulsively aligned 1,3-cyclohexadiene: Signatures of attosecond charge migration.

High-harmonic spectroscopy is an all-optical technique with inherent attosecond temporal resolution that has been successfully employed to reconstruct charge migration, electron-tunneling dynamics, and conical-intersection dynamics. Here, we demonstrate the extension of two key components of high-harmonic spectroscopy, i.e., impulsive alignment and measurements with multiple driving wavelengths to 1,3-cyclohexadiene and benzene. In the case of 1,3-cyclohexadiene, we find that the temporal sequence of maximal and minimal emitted high-harmonic intensities as a function of the delay between the alignment and probe pulses inverts between 25 and 30 eV and again between 35 and 40 eV when an 800-nm driver is used, but no inversions are observed with a 1420-nm driver. This observation is explained by the wavelength-dependent interference of emission from multiple molecular orbitals (HOMO to HOMO-3), as demonstrated by calculations based on the weak-field asymptotic theory and accurate photorecombination matrix elements. These results indicate that attosecond charge migration takes place in the 1,3-cyclohexadiene cation and can potentially be reconstructed with the help of additional measurements. Our experiments also demonstrate a pathway toward studying photochemical reactions in the molecular frame of 1,3-cyclohexadiene.

Entanglement of orbital angular momentum in non-sequential double ionization.

Entanglement has a capacity to enhance imaging procedures, but this remains unexplored for attosecond imaging. Here, we elucidate that possibility, addressing orbital angular momentum (OAM) entanglement in ultrafast processes. In the correlated process non-sequential double ionization (NSDI) we demonstrate robust photoelectron entanglement. In contrast to commonly considered continuous variables, the discrete OAM allows for a simpler interpretation, computation, and measurement of entanglement. The logarithmic negativity reveals that the entanglement is robust to incoherence and an entanglement witness minimizes the number of measurements to detect the entanglement, both quantities are related to OAM coherence terms. We quantify the entanglement for a range of targets and field parameters to find the most entangled photoelectron pairs. This methodology provides a general way to use OAM to quantify and measure entanglement, well-suited to attosecond processes, and can be exploited to enhance imaging capabilities through correlated measurements, or for generation of OAM-entangled electrons.

Asymmetric Dissociative Tunneling Ionization of Tetrafluoromethane in ω - 2ω Intense Laser Fields.

Dissociative ionization of tetrafluoromethane (CF4) in linearly polarized ω-2ω ultrashort intense laser fields (1.4 × 1014 W/cm2, 800 and 400 nm) has been investigated by three-dimensional momentum ion imaging. The spatial distribution of C F 3 + produced by CF4 → C F 3 + + F + e- exhibited a clear asymmetry with respect to the laser polarization direction. The degree of the asymmetry varies by the relative phase of the ω and 2ω laser fields, showing that 1) the breaking of the four equivalent C-F bonds can be manipulated by the laser pulse shape and 2) the C-F bond directed along the larger amplitude side of the ω-2ω electric fields tends to be broken. Weak-field asymptotic theory (WFAT) shows that the tunneling ionization from the 4t 2 second highest-occupied molecular orbital (HOMO-1) surpasses that from the 1t 1 HOMO. This predicts the enhancement of the tunneling ionization with electric fields pointing from F to C, in the direction opposite to that observed for the asymmetric fragment ejection. Possible mechanisms involved in the asymmetric dissociative ionization, such as post-ionization interactions, are discussed.

Excitation spectra of systems of indistinguishable particles by the autocorrelation function technique: Circumventing the exponential scaling for bosons.

We consider the autocorrelation function technique for obtaining excitation spectra for indistinguishable particles. The interacting particles are described by coherent superpositions of configurations built from time-dependent spin-orbitals. The fermionic or bosonic character of the particles is taken into account by considering Slater determinants or permanents, respectively. The approach involves the calculation of overlaps between nonorthonormal Slater determinants for fermions and permanents for bosons. Efficient methods already exist for fermions. In the case of bosons, the evaluation of permanents generally scales exponentially with system size. We present an efficient approach for bosons for calculating the excitation spectrum, which circumvents this scaling. The approach is illustrated and validated by comparison with an analytical model for interacting bosons, for a system with a number of bosons so large that the autocorrelation technique could not be applied without the present development.

Effects of core space and excitation levels on ground-state correlation and photoionization dynamics of Be and Ne.

We explore the effects of correlation on the ground-state energies and on photoionization dynamics in atomic Be and Ne. We apply the time-dependent restricted-active-space self-consistent-field method for several excitation schemes and active orbital spaces with and without a dynamic core to address the effects systematically at different levels of approximation. For the ground-state many-electron wave functions, we compare the correlation energies with entropic measures of entanglement. A larger magnitude of the correlation energy does not always correspond to a larger value of the considered entanglement measures. To evaluate the impact of correlation in a process involving continua, we consider photoionization by attosecond pulses. The photoelectron spectra may be significantly affected by including a dynamical core.

Structure factors for tunneling ionization rates of molecules: General grid-based methodology and convergence studies.

We present a general methodology for evaluating structure factors defining the orientation dependence of tunneling ionization rates of molecules, which is a key process in strong-field physics. The method is implemented at the Hartree-Fock level of electronic structure theory and is based on an integral-equation approach to the weak-field asymptotic theory of tunneling ionization, which expresses the structure factor in terms of an integral involving the ionizing orbital and a known analytical function. The evaluation of the required integrals is done by three-dimensional quadrature which allows calculations using conventional quantum chemistry software packages. This extends the applications of the weak-field asymptotic theory to polyatomic molecules of almost arbitrary size. The method is tested by comparison with previous results and illustrated by calculating structure factors for the two degenerate highest occupied molecular orbitals (HOMOs) of benzene and for the HOMO and HOMO-1 of naphthalene.

Signatures of a Conical Intersection in Attosecond Transient Absorption Spectroscopy.

We characterize attosecond transient absorption spectroscopy (ATAS) in molecules with coupled nuclear and electronic dynamics in the vicinity of a conical intersection between adiabatic potential energy surfaces. With respect to ATAS, the nonadiabatic vibronic coupling strength can be divided into weak, intermediate, and strong, and the characteristics of spectra belonging to each of these domains are discussed. The results can guide the analysis of ATAS experiments in molecules with conical intersections.

Entangled Quantum Dynamics of Many-Body Systems using Bohmian Trajectories.

Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational tool to simulate quantum systems consisting of many particles, a very demanding computational task. In this paper, we present a novel ab-initio approach to solve the many-body problem for bosonic systems by evolving a system of one-particle wavefunctions representing pilot waves that guide the Bohmian trajectories of the quantum particles. In this approach, quantum entanglement effects arise due to the interactions between different configurations of Bohmian particles evolving simultaneously. The method is used to study the breathing dynamics and ground state properties in a system of interacting bosons.

Illuminating Molecular Symmetries with Bicircular High-Order-Harmonic Generation.

We present a general theory of bicircular high-order-harmonic generation 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.

Role of Multi-Electron Effects in the Asymmetry of Strong-Field Ionization and Fragmentation of Polar Molecules: The Methyl Halide Series.

We report angle- and momentum-resolved measurements of the dissociative ionization and Coulomb explosion of methyl halides (CH3F, CH3Cl, CH3Br, and CH3I) in intense phase-controlled two-color laser fields. At moderate laser intensities, we find that the emission asymmetry of low-energy CH3(+) fragments from the CH3(+) + X(+) (X = F, Cl, Br, or I) channel reflects the asymmetry of the highest occupied molecular orbital of the neutral molecule with important contributions from the Stark effect. This asymmetry is correctly predicted by the weak-field asymptotic theory, provided that the Stark effect on the ionization potentials is calculated using a nonperturbative multielectron approach. In the case of high laser intensities, we observe a reversal of the emission asymmetries for high-energy CH3(+) fragments, originating from the dissociation of CH3X(q+) with q ≥ 2. We propose ionization to electronically excited states to be at the origin of the reversed asymmetries. We also report the measurements of the emission asymmetry of H3(+), which is found to be identical to that of the low-energy CH3(+) fragments measured at moderate laser intensities. All observed fragmentation channels are assigned with the help of CCSD(T) calculations. Our results provide a benchmark for theories of strong-field processes and demonstrate the importance of multielectron effects in new aspects of the molecular response to intense laser fields.

Characterization of Molecular Breakup by Very Intense Femtosecond XUV Laser Pulses.

We study the breakup of H2+ exposed to superintense, 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.

Dynamic stark control of torsional motion by a pair of laser pulses.

The torsional motion of a molecule composed of two substituted benzene rings, linked by a single bond, is coherently controlled by a pair of strong (3×10^{13} W cm^{-2}), nonresonant (800 nm) 200-fs-long laser pulses-both linearly polarized perpendicular to the single-bond axis. If the second pulse is sent at the time when the two benzene rings rotate toward (away from) each other the amplitude of the torsion is strongly enhanced (reduced). The torsional motion persists for more than 150 ps corresponding to approximately 120 torsional oscillations. Our calculations show that the key to control is the strong transient modification of the natural torsional potential by the laser-induced dynamic Stark effect.

Time-dependent restricted-active-space self-consistent-field singles method for many-electron dynamics.

The time-dependent restricted-active-space self-consistent-field singles (TD-RASSCF-S) method is presented for investigating TD many-electron dynamics in atoms and molecules. Adopting the SCF notion from the muticonfigurational TD Hartree-Fock (MCTDHF) method and the RAS scheme (single-orbital excitation concept) from the TD configuration-interaction singles (TDCIS) method, the TD-RASSCF-S method can be regarded as a hybrid of them. We prove that, for closed-shell Ne-electron systems, the TD-RASSCF-S wave function can be fully converged using only Ne/2 + 1 ⩽ M ⩽ Ne spatial orbitals. Importantly, based on the TD variational principle, the converged TD-RASSCF-S wave function with M = Ne is more accurate than the TDCIS wave function. The accuracy of the TD-RASSCF-S approach over the TDCIS is illustrated by the calculation of high-order harmonic generation spectra for one-dimensional models of atomic helium, beryllium, and carbon in an intense laser pulse. The electronic dynamics during the process is investigated by analyzing the behavior of electron density and orbitals. The TD-RASSCF-S method is accurate, numerically tractable, and applicable for large systems beyond the capability of the MCTDHF method.

Retardation effects and the Born-Oppenheimer approximation: theory of tunneling ionization of molecules revisited.

We show that retardation in adjusting an electronic state to an instantaneous internuclear configuration caused by the finiteness of the electron's velocity breaks the validity of the Born-Oppenheimer (BO) approximation at large electron-nuclei distances. This applies even to the ground state. As a result, the BO approximation in the theory of tunneling ionization of molecules breaks down at sufficiently weak fields. We also show that to account for nuclear motion the weak-field asymptotic expansion for the tunneling ionization rate must be restructured. The predictions for the rate using the BO approximation and the asymptotic expansion are compared with numerical results for a one-dimensional three-body system modeling a diatomic molecule, with both electronic and nuclear motions treated exactly.

Molecular-frame 3D photoelectron momentum distributions by tomographic reconstruction.

Naphthalene molecules are fixed in space by a laser field and rotated, in 2° steps, over 180°. For each orientation, they are ionized by an intense, circularly polarized femtosecond laser pulse, and the 2D projection of the photoelectron momentum distribution is recorded. The molecular-frame 3D momentum distribution is obtained by tomographic reconstruction from all 90 projections. It reveals an anisotropic electron distribution, angularly shifted in the polarization plane, that is not accessible by the 2D momentum images. Our theoretical analysis shows that the magnitude of the angular shift is very sensitive to the exact form of the laser-modified molecular potential.

Control and femtosecond time-resolved imaging of torsion in a chiral molecule.

We study how the combination of long and short laser pulses can be used to induce torsion in an axially chiral biphenyl derivative (3,5-difluoro-3',5'-dibromo-4'-cyanobiphenyl). A long, with respect to the molecular rotational periods, elliptically polarized laser pulse produces 3D alignment of the molecules, and a linearly polarized short pulse initiates torsion about the stereogenic axis. The torsional motion is monitored in real-time by measuring the dihedral angle using femtosecond time-resolved Coulomb explosion imaging. Within the first 4 picoseconds (ps), torsion occurs with a period of 1.25 ps and an amplitude of 3° in excellent agreement with theoretical calculations. At larger times, the quantum states of the molecules describing the torsional motion dephase and an almost isotropic distribution of the dihedral angle is measured. We demonstrate an original application of covariance analysis of two-dimensional ion images to reveal strong correlations between specific ejected ionic fragments from Coulomb explosion. This technique strengthens our interpretation of the experimental data.

Time-resolved photoelectron angular distributions from strong-field ionization of rotating naphthalene molecules.

A nanosecond laser pulse confines the spatial orientation of naphthalene in 1D or 3D while a femtosecond kick pulse initiates rotation of the molecular plane around the fixed long axis. Time-dependent photoelectron angular distributions (PADs), resulting from ionization by an intense femtosecond probe pulse, exhibit pronounced changes as the molecular plane rotates. Enhanced 3D alignment, occurring shortly after the kick pulse, provides strongly improved contrast in molecular-frame PADs. Calculations in the strong-field approximation show that the striking structures observed in the PADs originate from nodal planes in occupied valence orbitals.

Polarization effects in attosecond photoelectron spectroscopy.

We study the influence of polarization effects in streaking by combined atto- and femtosecond pulses. The polarization-induced terms alter the streaking spectrum. The conventional streaking spectrum, which maps to the vector potential of the femtosecond pulse, is modified by a contribution following the field instead. We show that polarization effects may lead to an apparent temporal shift that needs to be properly accounted for in the analysis. The effect may be isolated and studied by angle-resolved photoelectron spectroscopy from oriented polar molecules. We also show that polarization effects will lead to an apparent temporal shift of 50 as between photoelectrons from a 2p and 1s state in atomic hydrogen.

Monte carlo wave packet theory of dissociative double ionization.

Nuclear dynamics in strong-field double ionization processes is predicted using a stochastic Monte Carlo wave packet technique. Using input from electronic structure calculations and strong-field electron dynamics the description allows for field-dressed dynamics within a given molecule as well as transitions between several different charge states. The description is computationally efficient and applicable to a wide range of systems. As a proof of principle, theoretical nuclear kinetic energy release spectra for H2 (D2) in strong near-infrared laser pulses of 40 fs duration are compared to experiments and very good agreement is obtained.

Quantum gates and multiparticle entanglement by Rydberg excitation blockade and adiabatic passage.

We propose to apply stimulated adiabatic passage to transfer atoms from their ground state into Rydberg excited states. Atoms a few micrometers apart experience a dipole-dipole interaction among Rydberg states that is strong enough to shift the atomic resonance and inhibit excitation of more than a single atom. We show that the adiabatic passage in the presence of this interaction between two atoms leads to robust creation of maximally entangled states and to two-bit quantum gates. For many atoms, the excitation blockade leads to an effective implementation of collective-spin and Jaynes-Cummings-like Hamiltonians, and we show that the adiabatic passage can be used to generate collective J_{x}=0 eigenstates and Greenberger-Horne-Zeilinger states of tens of atoms.