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Numerical and analytical investigation of the shape of Autler-Townes doublets in resonance ionization

Ayoub Ait Elarabi

Published Apr 24, 2024• 0 citations
OpenAlex

Abstract

Understanding the behavior of quantum systems under external perturbations is fundamental in quantum mechanics and has numerous applications in fields such as spectroscopy and quantum computing. In this thesis, we investigate the phenomenon of Autler-Townes doublets in hydrogen atoms numerically, focusing on a three-level model. Autler-Townes doublets arise when a two-level quantum system, such as a hydrogen atom, is subjected to an external electromagnetic field, leading to the splitting of spectral lines due to the Autler-Townes effect. The study involves formulating and solving the population amplitude equations describing the time evolution of the hydrogen atom’s probability amplitudes under the influence of external fields. We employ the Range-Kutta method in MATLAB to numerically solve these equations and analyze the shape and characteristics of Autler-Townes doublets. Our simulations explore the influence of various parameters such as field strength and frequency on the doublet structure. Additionally, our research compares the numerical results obtained from the simulation with the three-level model solutions, providing insights into the dynamic interference and understanding the physical reasons for the modulations in the spectrum. Our findings not only contribute to the understanding of Autler-Townes doublets in hydrogen atoms but also shed light on potential applications in quantum technologies and spectroscopic techniques.

Related papers

On the Dynamics of the Autler-Townes effect

Arnoldas Seputis

In this thesis the effect of Autler-Townes splitting is revisited and the dynamics of a 2- and 3-level quantum systems, exhibiting this effect, is studied. This effect is a special case of the Stark effect, where the spectral lines of an atom are modified due to an external driving electromagnetic field. Two different articles, describing the Autler-Townes splitting, are studied, where one solves the time-dependent equations of the semi-classical model and the other studies the time-independent Hamiltonian for the system, which is described completely quantum mechanically. In our work, we proceed by employing the semi-classical model but transforming the Hamiltonian into a time-independent form, which makes the model easier to study. Subsequently, we also study the atom as an open quantum system and investigate the effect that the decay of an atom to a vacuum field has on the Autler-Townes splitting. Throughout the thesis, we present the density matrices, and hence the time-evolution of the dynamics, in the Bloch-vector description in an attempt to understand the geometrical nature of the dynamics and, in effect, the Autler-Townes phenomenon.

•Jan 1, 2020•0 citations

Benchmark of few-level quantum theory vs ab initio numerical solutions for the strong-field Autler–Townes effect in photoionization of hydrogen

Daniel Younis, Joseph H. Eberly

Abstract The temporal and spectral consequences of an intermediate resonance en route to photoionization are investigated theoretically in two ways: by solving few-level model equations and by ab initio numerical solution of the time-dependent Schrödinger equation, in both cases for hydrogen in three dimensions. The model consists of atomic states resonantly field-dressed in a three-level reduction of the hydrogen atom that consists of the 2p–3d (Balmer) transition and one energetically-distant continuum state. The model’s level occupation probabilities are derived from three Schrödinger amplitude equations and are benchmarked against an ab initio numerical solution for the hydrogen electron’s wavefunction under the same field. We examine contrasts between the results of the two approaches with a particular focus on Autler–Townes doublets that appear in the photoelectron spectrum.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 30, 2022•7 citations

Spectral phase control of an ultrashort pulse for exploring the Autler-Townes effect in hydrogen atomic ionization through a resonant state

An Yang, Wen-Quan Jing, Bingshuang Zhang +3 more

We present a bound-continuum ionization model combined with numerical simulations to investigate the asymmetric features of Autler-Townes (AT) splitting in the ionization spectra of hydrogen atoms, induced by a spectrally phase-modulated ultrashort pulse. This model incorporates a resonance-enhanced two-photon ionization process, enabling transitions from the ground electronic state to the continuum state via the first excited electronic state through the absorption of two photons. By comparing our model predictions with exact numerical simulations based on time-dependent electronic wave-packet calculations, we demonstrate that the characteristics of the AT doublets, shaped by the spectral phase, emerge from the competing effects of selective population of dressed states and the transition amplitude to the continuum. In addition, through a perturbative analysis of the photoelectronic spectrum and the application of the Magnus expansion, we reveal a correlation between the number of AT fringes, resonant states, and pulse area, while drawing insights from bound states. This work enhances our understanding of how the spectral phase can be utilized to explore bound-state effects in ultrafast ionization dynamics.

Physical Review A•Nov 24, 2025•7 citations

Autler–Townes quadruplet spectroscopy

Bilal Farooq

We suggest an atomic scheme of Autler–Townes quadruplet spectroscopy by extending the concepts of Autler–Townes doublet and triplet spectroscopy. The present scheme is analyzed in detail with the help of a state vector approach to calculate its emission spectrum. By applying rotating wave and Weisskopf–Wigner approximations to our proposed scheme, we have successfully attained a simple analytical expression of the spectrum interpreting the basic mechanism involved in the process of quantum interference. All the spectroscopic parameters, like the locations of dark lines and the locations and widths of all the peaks, are presented in analytical form. These analyses provide a better understanding of the phenomenon of the Autler–Townes quadruplet spectrum.

Canadian Journal of Physics•Jul 2, 2013•0 citations

Phase control of the Autler-Townes doublet in multistate systems

Tim Bayer, Kevin Eickhoff, D. Köhnke +1 more

The resonant dynamic Stark effect, observed in the Autler-Townes (AT) splitting, plays a central role in ultrafast strong-field physics. Recent experiments have demonstrated the phase control of the AT doublet in atomic resonance-enhanced multiphoton ionization using intense resonant shaped femtosecond laser pulses [Bayer et al., Adv. Chem. Phys. 159, 235 (2016)]. Based on a two-state model, we showed that the underlying control mechanism is the selective population of dressed states (SPODS). In this work, we use a numerical model to calculate the photoelectron momentum distribution (PMD) based on the ab initio solution of the two-dimensional (2D) time-dependent Schr\"odinger equation (TDSE) to obtain a more complete physical picture of the nonperturbative control of the AT doublet. The 2D-TDSE model reproduces the ultrafast switching among the AT components while also revealing deviations from the signatures predicted by the two-state model. These deviations are attributed to the influence of additional intermediate states. To rationalize our observations, we propose a refined five-state model that includes all significantly populated bound states from the full calculation and accurately reproduces the 2D PMD. Based on the validated five-state model, we conduct a dressed-state analysis which provides a clear physical picture of the SPODS mechanism in a multistate system and sheds light on the role of the intermediate states in strong-field control.

Physical Review A•Sep 22, 2023•18 citations

Autler–Townes multiplet spectroscopy

Fazal Ghafoor

The Autler–Townes doublet and triplet spectroscopy are well known in the literature. Here, atomic systems for quartuplet, quintuplet emission spectroscopy and their linkages with the sodium atom are investigated for display of the corresponding spectra. We explore the involved fundamental processes of quantum interference in these systems by examining the Laplace transform of the corresponding state-vector subjected to steady coherent illumination in the rotating wave approximation and Weisskopf–Wigner treatment of spontaneous emission as a simplest probability loss. In the quartuplet (quintuplet), four (five) fields interact appropriately and resonantly with the five-level (six-level) atom. The spectral profile of the single decaying level, upon interaction with three (four) other levels, splits into four (five) destructively interfering dressed states generating three (four) dark lines in the spectrum. These dark lines divide the spectrum into four (five) spectral components (bright lines) whose widths are effectively controlled by the relative strength of the laser fields and the relative width of a single decaying level. The idea is also extended to higher-ordered spectroscopy. The apparent disadvantage of these schemes is the successive increase in the number of laser fields required for the strongly interactive atomic states. However, these complexities are naturally inherited and are the beauty of these atomic systems. They provide the foundations for the basic mechanisms of the quantum interference involved in the higher-ordered multiplet spectroscopy.

arXiv:1303.5182•Laser Physics•Feb 14, 2014•11 citations
Understanding the behavior of quantum systems under external perturbations is fundamental in quantum mechanics and has numerous applications in fields such as spectroscopy and quantum computing. In this thesis, we investigate the phenomenon of Autler-Townes doublets in hydrogen atoms numerically, focusing on a three-level model. Autler-Townes doublets arise when a two-level quantum system, such as a hydrogen atom, is subjected to an external electromagnetic field, leading to the splitting of spectral lines due to the Autler-Townes effect. The study involves formulating and solving the population amplitude equations describing the time evolution of the hydrogen atom’s probability amplitudes under the influence of external fields. We employ the Range-Kutta method in MATLAB to numerically solve these equations and analyze the shape and characteristics of Autler-Townes doublets. Our simulations explore the influence of various parameters such as field strength and frequency on the doublet structure. Additionally, our research compares the numerical results obtained from the simulation with the three-level model solutions, providing insights into the dynamic interference and understanding the physical reasons for the modulations in the spectrum. Our findings not only contribute to the understanding of Autler-Townes doublets in hydrogen atoms but also shed light on potential applications in quantum technologies and spectroscopic techniques.
In this thesis the effect of Autler-Townes splitting is revisited and the dynamics of a 2- and 3-level quantum systems, exhibiting this effect, is studied. This effect is a special case of the Stark effect, where the spectral lines of an atom are modified due to an external driving electromagnetic field. Two different articles, describing the Autler-Townes splitting, are studied, where one solves the time-dependent equations of the semi-classical model and the other studies the time-independent Hamiltonian for the system, which is described completely quantum mechanically. In our work, we proceed by employing the semi-classical model but transforming the Hamiltonian into a time-independent form, which makes the model easier to study. Subsequently, we also study the atom as an open quantum system and investigate the effect that the decay of an atom to a vacuum field has on the Autler-Townes splitting. Throughout the thesis, we present the density matrices, and hence the time-evolution of the dynamics, in the Bloch-vector description in an attempt to understand the geometrical nature of the dynamics and, in effect, the Autler-Townes phenomenon.
Abstract The temporal and spectral consequences of an intermediate resonance en route to photoionization are investigated theoretically in two ways: by solving few-level model equations and by ab initio numerical solution of the time-dependent Schrödinger equation, in both cases for hydrogen in three dimensions. The model consists of atomic states resonantly field-dressed in a three-level reduction of the hydrogen atom that consists of the 2p–3d (Balmer) transition and one energetically-distant continuum state. The model’s level occupation probabilities are derived from three Schrödinger amplitude equations and are benchmarked against an ab initio numerical solution for the hydrogen electron’s wavefunction under the same field. We examine contrasts between the results of the two approaches with a particular focus on Autler–Townes doublets that appear in the photoelectron spectrum.
We present a bound-continuum ionization model combined with numerical simulations to investigate the asymmetric features of Autler-Townes (AT) splitting in the ionization spectra of hydrogen atoms, induced by a spectrally phase-modulated ultrashort pulse. This model incorporates a resonance-enhanced two-photon ionization process, enabling transitions from the ground electronic state to the continuum state via the first excited electronic state through the absorption of two photons. By comparing our model predictions with exact numerical simulations based on time-dependent electronic wave-packet calculations, we demonstrate that the characteristics of the AT doublets, shaped by the spectral phase, emerge from the competing effects of selective population of dressed states and the transition amplitude to the continuum. In addition, through a perturbative analysis of the photoelectronic spectrum and the application of the Magnus expansion, we reveal a correlation between the number of AT fringes, resonant states, and pulse area, while drawing insights from bound states. This work enhances our understanding of how the spectral phase can be utilized to explore bound-state effects in ultrafast ionization dynamics.
We suggest an atomic scheme of Autler–Townes quadruplet spectroscopy by extending the concepts of Autler–Townes doublet and triplet spectroscopy. The present scheme is analyzed in detail with the help of a state vector approach to calculate its emission spectrum. By applying rotating wave and Weisskopf–Wigner approximations to our proposed scheme, we have successfully attained a simple analytical expression of the spectrum interpreting the basic mechanism involved in the process of quantum interference. All the spectroscopic parameters, like the locations of dark lines and the locations and widths of all the peaks, are presented in analytical form. These analyses provide a better understanding of the phenomenon of the Autler–Townes quadruplet spectrum.
The resonant dynamic Stark effect, observed in the Autler-Townes (AT) splitting, plays a central role in ultrafast strong-field physics. Recent experiments have demonstrated the phase control of the AT doublet in atomic resonance-enhanced multiphoton ionization using intense resonant shaped femtosecond laser pulses [Bayer et al., Adv. Chem. Phys. 159, 235 (2016)]. Based on a two-state model, we showed that the underlying control mechanism is the selective population of dressed states (SPODS). In this work, we use a numerical model to calculate the photoelectron momentum distribution (PMD) based on the ab initio solution of the two-dimensional (2D) time-dependent Schr\"odinger equation (TDSE) to obtain a more complete physical picture of the nonperturbative control of the AT doublet. The 2D-TDSE model reproduces the ultrafast switching among the AT components while also revealing deviations from the signatures predicted by the two-state model. These deviations are attributed to the influence of additional intermediate states. To rationalize our observations, we propose a refined five-state model that includes all significantly populated bound states from the full calculation and accurately reproduces the 2D PMD. Based on the validated five-state model, we conduct a dressed-state analysis which provides a clear physical picture of the SPODS mechanism in a multistate system and sheds light on the role of the intermediate states in strong-field control.
The Autler–Townes doublet and triplet spectroscopy are well known in the literature. Here, atomic systems for quartuplet, quintuplet emission spectroscopy and their linkages with the sodium atom are investigated for display of the corresponding spectra. We explore the involved fundamental processes of quantum interference in these systems by examining the Laplace transform of the corresponding state-vector subjected to steady coherent illumination in the rotating wave approximation and Weisskopf–Wigner treatment of spontaneous emission as a simplest probability loss. In the quartuplet (quintuplet), four (five) fields interact appropriately and resonantly with the five-level (six-level) atom. The spectral profile of the single decaying level, upon interaction with three (four) other levels, splits into four (five) destructively interfering dressed states generating three (four) dark lines in the spectrum. These dark lines divide the spectrum into four (five) spectral components (bright lines) whose widths are effectively controlled by the relative strength of the laser fields and the relative width of a single decaying level. The idea is also extended to higher-ordered spectroscopy. The apparent disadvantage of these schemes is the successive increase in the number of laser fields required for the strongly interactive atomic states. However, these complexities are naturally inherited and are the beauty of these atomic systems. They provide the foundations for the basic mechanisms of the quantum interference involved in the higher-ordered multiplet spectroscopy.