Non-linear non-local molecular electrodynamics with nano-optical fields

Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory

The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.

Monitoring aromatic ring-currents in Mg-porphyrin by time-resolved circular dichroism

Time-resolved circular dichroism signals (TRCD) in the X-ray regime can directly probe the magnitude and the direction of ring currents in molecules. The electronic ring currents in Mg-porphyrin, generated by a coherent superposition of electronic states induced by a circularly polarized UV pulse, are tracked by a time-delayed circularly polarized attosecond X-ray pulse. The signals are calculated using the minimal coupling Hamiltonian, which directly makes use of transition current densities. The TRCD signals obtained from the left and right circularly polarized light pump have opposite signs, revealing the direction of the ring current. Molecular aromaticity and its role in photochemical reactions such as ring opening or closure can be studied using this technique.

Stimulated X-ray Raman Imaging of Conical Intersections

The conical intersection dynamics of thiophenol is studied theoretically using the stimulated X-ray Raman imaging (SXRI) technique. SXRI employs a hard X-ray narrowband/broadband hybrid probe field and provides a real-time and real-space image of the passage through conical intersections. The signal, calculated using the minimal-coupling radiation/matter Hamiltonian, carries the phase information, and the real-space image of the transition charge density can be reconstructed by its Fourier transform. The two conical intersections (S₂/S₁ (1¹ππ*/¹πσ*) and S₁/S₀ (¹πσ*/S₀)) can be distinguished and identified by the diffraction patterns in the level crossing regimes.

Stimulated X-ray Raman and Absorption Spectroscopy of Iron-Sulfur Dimers

Iron-sulfur complexes play an important role in biological processes such as metabolic electron transport. A detailed understanding of the mechanism of long-range electron transfer requires knowledge of the electronic structure of the complexes, which has traditionally been challenging to obtain, either by theory or by experiment, but the situation has begun to change with advances in quantum chemical methods and intense free electron laser light sources. We compute the spectra for stimulated X-ray Raman spectroscopy (SXRS) and absorption spectroscopy of homovalent and mixed-valence [2Fe-2S] complexes, using the ab initio density matrix renormalization group algorithm. The simulated spectra show clear signatures of the theoretically predicted dense low-lying excited states within the d-d manifold. Furthermore, the difference in spectral intensity between the absorption-active and Raman-active states provides a potential mechanism to selectively excite states by a proper tuning of the excitation pump, to access the electronic dynamics within this manifold.

Probing Molecular Chirality by Orbital-Angular-Momentum-Carrying X-ray Pulses

A twisted X-ray beam with orbital angular momentum is employed in a theoretical study to probe molecular chirality. A nonlocal response description of the matter-field coupling is adopted to account for the field short wavelength and the structured spatial profile. We use the minimal-coupling Hamiltonian, which implicitly takes into account the multipole contributions to all orders. The combined interactions of the spin and orbital angular momentum of the X-ray beam give rise to circular-helical dichroism signals, which are stronger than ordinary circular dichroism signals, and may serve as a useful tool for the study of molecular chirality in the X-ray regime.

Monitoring Spontaneous Charge-Density Fluctuations by Single-Molecule Diffraction of Quantum Light

Homodyne X-ray diffraction signals produced by classical light and classical detectors are given by the modulus square of the charge density in momentum space |σ(q)|², missing its phase, which is required in order to invert the signal to real space. We show that quantum detection of the radiation field yields a linear diffraction pattern that reveals σ(q) itself, including the phase. We further show that repeated diffraction measurements with variable delays constitute a novel multidimensional measure of spontaneous charge-density fluctuations. Classical diffraction, in contrast, only reveals a subclass of even-order correlation functions. Simulations of two-dimensional signals obtained by two diffraction events are presented for the amino acid cysteine.

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.

Perspective: Quantum Hamiltonians for optical interactions

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Quantum transition probabilities during a perturbing pulse: Differences between the nonadiabatic results and Fermi's golden rule forms

For a perturbed quantum system initially in the ground state, the coefficient c_k(t) of excited state k in the time-dependent wave function separates into adiabatic and nonadiabatic terms. The adiabatic term a_k(t) accounts for the adjustment of the original ground state to form the new ground state of the instantaneous Hamiltonian H(t), by incorporating excited states of the unperturbed Hamiltonian H₀ without transitions; a_k(t) follows the adiabatic theorem of Born and Fock. The nonadiabatic term b_k(t) describes excitation into another quantum state k; b_k(t) is obtained as an integral containing the time derivative of the perturbation. The true transition probability is given by b_k(t) ², as first stated by Landau and Lifshitz. In this work, we contrast b_k(t) ² and c_k(t) ². The latter is the norm-square of the entire excited-state coefficient which is used for the transition probability within Fermi's golden rule. Calculations are performed for a perturbing pulse consisting of a cosine or sine wave in a Gaussian envelope. When the transition frequency ω_k0 is on resonance with the frequency ω of the cosine wave, b_k(t) ² and c_k(t) ² rise almost monotonically to the same final value; the two are intertwined, but they are out of phase with each other. Off resonance (when ω_k0 ≠ ω), b_k(t) ² and c_k(t) ² differ significantly during the pulse. They oscillate out of phase and reach different maxima but then fall off to equal final values after the pulse has ended, when a_k(t) ≡ 0. If ω_k0 < ω, b_k(t) ² generally exceeds c_k(t) ², while the opposite is true when ω_k0 > ω. While the transition probability is rising, the midpoints between successive maxima and minima fit Gaussian functions of the form a exp[-b(t - d)²]. To our knowledge, this is the first analysis of nonadiabatic transition probabilities during a perturbing pulse.

Non-local real-space analysis of chiral optical signals

A spatially non-local response tensor description of linear chiral signals such as circular dichroism is developed.

A spatially non-local response tensor description of linear chiral signals such as circular dichroism is developed. By working directly with the vector potential rather that the electric and magnetic fields, we recast the signals in terms of correlation functions of charge and current densities and avoid the tedious expansion in multipoles.