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Optimization of the ionization time of an atom with tailored laser pulses: a theoretical study

David Kammerlander, Alberto Castro, Miguel A. L. Marques

Published May 22, 2018• 1 citation
OpenAlex

Abstract

How fast can a laser pulse ionize an atom? We address this question by considering pulses that carry a fixed time-integrated energy per-area, and finding those that achieve the double requirement of maximizing the ionization that they induce, while having the shortest duration. We formulate this double-objective quantum optimal control problem by making use of the Pareto approach to multi-objective optimization, and the differential evolution genetic algorithm. The goal is to find out how a precise time-profiling of ultra-fast, large-bandwidth pulses may speed up the ionization process. We work on a simple one-dimensional model of hydrogen-like atoms (the Pöschl-Teller potential) that allows to tune the number of bound states that play a role in the ionization dynamics. We show how the detailed shape of the pulse accelerates the ionization, and how the presence or absence of bound states influences the velocity of the process.

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Optimizing an Electron's Path to Ionization Using a Genetic Algorithm

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A Rydberg atom is an atom with a highly excited and weakly bound valence electron. A widespread method of studying quantum mechanics with Rydberg atoms is to ionize the electron and measure its arrival time. We use a Genetic Algorithm (GA) to control the electron's path to ionization. The Rydberg electron's energy levels are strongly shifted by the presence of an electric field. The energy levels shift and curve, but never cross. At an avoided crossing the electron can jump from one level to the next. By engineering the electric field's time dependence, we thereby control the path to ionization. A GA is an optimization method modeled on natural selection. We use a GA to evolve electric field pulses to achieve a target path to ionization. Our algorithm initially generates random members of a population and then assigns each member a fitness score based on how well they achieve our target solution. We use elitism to pass the best members of the population directly into the next generation. We use tournament style selection to choose fit members to mate and pass their genes to the next generation. We then mutate the offspring to provide genetic diversity to our population. We present our results on the effects of varying GA parameters and modifying the GA to better model the experiment.

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Experimentally, we would like to demonstrate the process of selective field ionization of electrons as evidence of quantum control in a system of ultracold rubidium-85 Rydberg atoms. In order to accomplish this, an electric field pulse which is optimized to take an initial Rydberg electron state and produce the desired ionization spectra is necessary. We utilize techniques from artificial intelligence to develop a genetic algorithm for the optimization process. Our algorithm is computationally tested on an artificially constructed quantum system consisting of four energy states. In evaluating the viability of any given field pulse, we calculate the probability of an electron being found in a given state at a certain maximum field value by numerically evolving the electron’s wave function over time.

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A Rydberg atom has a highly excited valence electron which is weakly bound and far from the nucleus. These atoms have exaggerated properties that make them attractive candidates for quantum computation and studies of fundamental quantum mechanics. A widely used method for measuring the energy level of the outer electron is to ionize it with an electric field pulse and send it to a detector where the resulting spectrum is measured. However, this technique fails to resolve energy levels that are closely spaced. The electron’s path to ionization branches several hundreds of times, causing neighboring energy levels to overlap. By using an engineered electric field pulse, we can manipulate which branches the electron follows. To design our electric field pulse, we created a genetic algorithm. A genetic algorithm is an optimization process analogous to biological evolution. Our algorithm creates a random population of electric field pulses, evaluates the fitness of the field pulses, and allows the fittest members of the population to mate and create a new generation. We present results of our simulations.

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Resonant pulse excitation leading to ionization

Jay R. Ackerhalt

Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time $t$, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the $N$-level atom is discussed.

Physical Review A•Jan 1, 1978•19 citations
How fast can a laser pulse ionize an atom? We address this question by considering pulses that carry a fixed time-integrated energy per-area, and finding those that achieve the double requirement of maximizing the ionization that they induce, while having the shortest duration. We formulate this double-objective quantum optimal control problem by making use of the Pareto approach to multi-objective optimization, and the differential evolution genetic algorithm. The goal is to find out how a precise time-profiling of ultra-fast, large-bandwidth pulses may speed up the ionization process. We work on a simple one-dimensional model of hydrogen-like atoms (the Pöschl-Teller potential) that allows to tune the number of bound states that play a role in the ionization dynamics. We show how the detailed shape of the pulse accelerates the ionization, and how the presence or absence of bound states influences the velocity of the process.
We report a good agreement between the shapes of tailored pulses obtained theoretically and experimentally by using the optimal-control theory and the closed-loop learning technique to maximize the ionization yield in NaK. The theoretical pulse shapes are found to be robust regarding the choice of the initial guess. We assign the leading features of the pulse shapes to processes underlying the optimal control and reveal the mechanism which involves an electronic transition followed by a direct two-photon process and sequential one-photon processes at later times. We show that the optimal control not only serves for maximizing the desired yield but also as a tool for the analysis and the identification of the responsible processes.
A Rydberg atom is an atom with a highly excited and weakly bound valence electron. A widespread method of studying quantum mechanics with Rydberg atoms is to ionize the electron and measure its arrival time. We use a Genetic Algorithm (GA) to control the electron's path to ionization. The Rydberg electron's energy levels are strongly shifted by the presence of an electric field. The energy levels shift and curve, but never cross. At an avoided crossing the electron can jump from one level to the next. By engineering the electric field's time dependence, we thereby control the path to ionization. A GA is an optimization method modeled on natural selection. We use a GA to evolve electric field pulses to achieve a target path to ionization. Our algorithm initially generates random members of a population and then assigns each member a fitness score based on how well they achieve our target solution. We use elitism to pass the best members of the population directly into the next generation. We use tournament style selection to choose fit members to mate and pass their genes to the next generation. We then mutate the offspring to provide genetic diversity to our population. We present our results on the effects of varying GA parameters and modifying the GA to better model the experiment.
Experimentally, we would like to demonstrate the process of selective field ionization of electrons as evidence of quantum control in a system of ultracold rubidium-85 Rydberg atoms. In order to accomplish this, an electric field pulse which is optimized to take an initial Rydberg electron state and produce the desired ionization spectra is necessary. We utilize techniques from artificial intelligence to develop a genetic algorithm for the optimization process. Our algorithm is computationally tested on an artificially constructed quantum system consisting of four energy states. In evaluating the viability of any given field pulse, we calculate the probability of an electron being found in a given state at a certain maximum field value by numerically evolving the electron’s wave function over time.
A Rydberg atom has a highly excited valence electron which is weakly bound and far from the nucleus. These atoms have exaggerated properties that make them attractive candidates for quantum computation and studies of fundamental quantum mechanics. A widely used method for measuring the energy level of the outer electron is to ionize it with an electric field pulse and send it to a detector where the resulting spectrum is measured. However, this technique fails to resolve energy levels that are closely spaced. The electron’s path to ionization branches several hundreds of times, causing neighboring energy levels to overlap. By using an engineered electric field pulse, we can manipulate which branches the electron follows. To design our electric field pulse, we created a genetic algorithm. A genetic algorithm is an optimization process analogous to biological evolution. Our algorithm creates a random population of electric field pulses, evaluates the fitness of the field pulses, and allows the fittest members of the population to mate and create a new generation. We present results of our simulations.
Laser excitation of a two-level atom is analytically studied for arbitrary pulse shape, area, and energy. The ionization mechanism is modeled as a homogeneous width $\ensuremath{\gamma}$ of the atomic excited state. A transformation of the optical Bloch equations allows the dynamics to be completely described by a single equation for the area of the pulse at time ttt, $\ensuremath{\Phi}(t)$. Analytic solutions for the total bound population for a wide variety of pulse shapes can be found in two regions: $\ensuremath{\Phi}(t)\ensuremath{\approx}sin\ensuremath{\Phi}(t)$ and $\ensuremath{\Omega}(t)>\ensuremath{\gamma}$, where $\ensuremath{\Omega}(t)$ is the resonance Rabi frequency. The generalization of the two-level atom results to the NNN-level atom is discussed.