arXiv subjects

Piotr Gniewek

Publications and source records attributed to Piotr Gniewek.

6 recordsLinked to original sources

arXiv2024

Photodissociation spectra of single trapped CaOH+ molecular ions

Molecular ions that are generated by chemical reactions with trapped atomic ions can serve as an accessible testbed for developing molecular quantum technologies. On the other hand, they are also a hindrance to scaling up quantum computers based on atomic ions as unavoidable reactions with background gas destroy the information carriers. Here, we investigate the single- and two-photon dissociation processes of single $\text{CaOH}^+$ molecular ions co-trapped in $\text{Ca}^+$ ion crystals using a femtosecond laser system. We report the photodissociation cross section spectra of $\text{CaOH}^+$ for single-photon processes at $λ=$245 - 275$\,$nm and for two-photon processes at $λ=$500 - 540$\,$nm. Measurements are interpreted with quantum-chemical calculations, which predict the photodissociation threshold for $\text{CaOH}^+\to \text{Ca}^++\text{OH}$ at 265$\,$nm. This result can serve as a basis for dissociation-based spectroscopy for studying the internal structure of $\text{CaOH}^+$. The result also gives a prescription for recycling $\text{Ca}^+$ ions in large-scale trapped $\text{Ca}^+$ quantum experiments from undesired $\text{CaOH}^+$ ions formed in the presence of background water vapor.

physics.atom-ph↗

arXiv2020

Symphony on Strong Field Approximation

This paper has been prepared by the Symphony collaboration (University of Warsaw, Uniwersytet Jagielloński, DESY/CNR and ICFO) on the occasion of the 25th anniversary of the "simple man's models" which underlie most of the phenomena that occur when intense ultrashort laser pulses interact with matter. The phenomena in question include High-Harmonic Generation, Above-Threshold Ionization, and Non-Sequential Multielectron Ionization. "Simple man's models" provide, both an intuitive basis for understanding the numerical solutions of the time-dependent Schrödinger equation, and the motivation for the powerful analytic approximations generally known as the Strong Field Approximation (SFA). In this paper we first review the SFA in the form developed by us in the last 25 years. In this approach SFA is a method to solve the TDSE using a systematic perturbation theory in a part of the Hamiltonian describing continuum-continuum transitions in the presence of the laser field. In this review we focus on recent applications of SFA to HHG, ATI and NSMI from multi-electron atoms and from multi-atom. The main novel part of the presented theory concerns generalizations of SFA to: (i) time-dependent treatment of two-electron atoms, allowing for studies of an interplay between Electron Impact Ionization (EII) and Resonant Excitation with Subsequent Ionization (RESI); (ii) time-dependent treatment in the single active electron (SAE) approximation of "large" molecules and targets which are themselves undergoing dynamics during the HHG or ATI process. In particular, we formulate the general expressions for the case of arbitrary molecules, combining input from quantum chemistry and quantum dynamics. We formulate also theory of time-dependent separable molecular potentials to model analytically the dynamics of realistic electronic wave packets for molecules in strong laser fields.

quant-ph↗

arXiv2016

Determination of the exchange interaction energy from the polarization expansion of the wave function

The exchange contribution to the energy of the hydrogen atom interacting with a proton is calculated from the polarization expansion of the wave function using the conventional surface-integral formula and two formulas involving volume integrals: the formula of the symmetry-adapted perturbation theory (SAPT) and the variational formula recommended by us. At large internuclear distances $R$, all three formulas yield the correct expression $-(2/e)Re^{-R}$, but approximate it with very different convergence rates. In the case of the SAPT formula, the convergence is geometric with the error falling as $3^{-K}$, where $K$ is the order of the applied polarization expansion. The error of the surface-integral formula decreases exponentially as $a^K/(K+1)!$, where $a=\ln2 -\tfrac{1}{2}$. The variational formula performs best, its error decays as $K^{1/2} [a^{ K}/(K+1)!]^2$. These convergence rates are much faster than those resulting from approximating the wave function through the multipole expansion. This shows the efficiency of the partial resummation of the multipole series effected by the polarization expansion. Our results demonstrate also the benefits of incorporating the variational principle into the perturbation theory of molecular interactions.

quant-ph↗

arXiv2016

Convergence properties of the multipole expansion of the exchange contribution to the interaction energy

The conventional surface integral formula $J_{\rm surf}[Φ]$ and an alternative volume integral formula $J_{\rm var}[Φ]$ are used to compute the asymptotic exchange splitting of the interaction energy of the hydrogen atom and a proton employing the primitive function $Φ$ in the form of its truncated multipole expansion. Closed-form formulas are obtained for the asymptotics of $J_{\rm surf}[Φ_N]$ and $J_{\rm var}[Φ_N]$, where $Φ_N$ is the multipole expansion of $Φ$ truncated after the $1/R^N$ term, $R$ being the internuclear separation. It is shown that the obtained sequences of approximations converge to the exact results with the rate corresponding to the convergence radius equal to 2 and 4 when the surface and the volume integral formulas are used, respectively. When the multipole expansion of a truncated, $K$th order polarization function is used to approximate the primitive function the convergence radius becomes equal to unity in the case of $J_{\textrm{var}}[Φ]$. At low order the observed convergence of $J_{\rm var}[Φ_N]$ is, however, geometric and switches to harmonic only at certain value of $N=N_c$ dependent on $K$. An equation for $N_c$ is derived which very well reproduces the observed $K$-dependent convergence pattern. The results shed new light on the convergence properties of the conventional SAPT expansion used in applications to many-electron diatomics.

physics.chem-ph↗

arXiv2015

Exchange splitting of the interaction energy and the multipole expansion of the wave function

The exchange splitting $J$ of the interaction energy of the hydrogen atom with a proton is calculated using the conventional surface-integral formula $J_{\textrm{surf}}[φ]$, the volume-integral formula of the symmetry-adapted perturbation theory $J_{\textrm{SAPT}}[φ]$, and a variational volume-integral formula $J_{\textrm{var}}[φ]$. The calculations are based on the multipole expansion of the wave function $φ$, which is divergent for any internuclear distance $R$. Nevertheless, the resulting approximations to the leading coefficient $j_0$ in the large-$R$ asymptotic series $J(R) = 2 e^{-R-1} R ( j_0 + j_1 R^{-1} + j_2 R^{-2} +\cdots ) $ converge, with the rate corresponding to the convergence radii equal to 4, 2, and 1 when the $J_{\textrm{var}}[φ]$, $J_{\textrm{surf}}[φ]$, and $J_{\textrm{SAPT}}[φ]$ formulas are used, respectively. Additionally, we observe that also the higher $j_k$ coefficients are predicted correctly when the multipole expansion is used in the $J_{\textrm{var}}[φ]$ and $J_{\textrm{surf}}[φ]$ formulas. The SAPT formula $J_{\textrm{SAPT}}[φ]$ predicts correctly only the first two coefficients, $j_0$ and $j_1$, gives a wrong value of $j_2$, and diverges for higher $j_n$. Since the variational volume-integral formula can be easily generalized to many-electron systems and evaluated with standard basis-set techniques of quantum chemistry, it provides an alternative for the determination of the exchange splitting and the exchange contribution of the interaction potential in general.

physics.chem-ph↗

arXiv2015

Asymptotics of the exchange splitting energy for a diatomic molecular ion from a volume integral formula of symmetry-adapted perturbation theory

The exchange splitting energy $J$ of the lowest \emph{gerade} and \emph{ungerade} states of the H$_2^+$ molecular ion was calculated using a volume integral expression of symmetry-adapted perturbation theory and standard basis set techniques of quantum chemistry. The performance of the proposed expression was compared to the well known surface integral formula. Both formulas involve the primitive function which we calculated employing either the Hirschfelder-Silbey perturbation theory or the conventional Rayleigh-Schrödinger perturbation theory (the polarization expansion). Our calculations show that very accurate values of $J$ can be obtained using the proposed volume integral formula. When the Hirschfelder-Silbey primitive function is used in both formulas the volume formula gives much more accurate results than the surface integral expression. We also show that using the volume integral formula with the primitive function approximated by Rayleigh-Schrödinger perturbation theory, one correctly obtains only the first four terms in the asymptotic expansion of the exchange splitting energy.

quant-ph↗