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arXiv:1908.09052 · Journal of Physics B Atomic Molecular and Optical Physics

Perturbed field ionization for improved state selectivity

Vincent C. Gregoric, Jason J. Bennett, Bianca R. Gualtieri, Hannah Hastings, Ankitha Kannad, Zhimin Cheryl Liu, Maia R. Rabinowitz, Zoe A. Rowley, Miao Wang, Lauren Yoast, Thomas J. Carroll, Michael W. Noel

Published Jan 27, 2020• 4 citations
arXivHTMLPDF

Abstract

Abstract Selective field ionization (SFI) is used to determine the state or distribution of states to which a Rydberg atom is excited. By evolving a small perturbation to the ramped electric field using a genetic algorithm, the shape of the time-resolved ionization signal can be controlled. This allows for the separation of signals from pairs of states that would be indistinguishable with unperturbed SFI. Measurements and calculations are presented that demonstrate this technique and shed light on how the perturbation directs the pathway of the electron to ionization. Pseudocode for the genetic algorithm is provided. Using the improved resolution afforded by this technique, quantitative measurements of the 36 p 3 / 2 + 36 p 3 / 2 → 36 s 1 / 2 + 37 s 1 / 2 dipole–dipole interaction are made.

DOI
10.1088/1361-6455/ab707a

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•Jan 1, 2018•0 citations
Abstract Selective field ionization (SFI) is used to determine the state or distribution of states to which a Rydberg atom is excited. By evolving a small perturbation to the ramped electric field using a genetic algorithm, the shape of the time-resolved ionization signal can be controlled. This allows for the separation of signals from pairs of states that would be indistinguishable with unperturbed SFI. Measurements and calculations are presented that demonstrate this technique and shed light on how the perturbation directs the pathway of the electron to ionization. Pseudocode for the genetic algorithm is provided. Using the improved resolution afforded by this technique, quantitative measurements of the 36 p 3 / 2 + 36 p 3 / 2 → 36 s 1 / 2 + 37 s 1 / 2 dipole–dipole interaction are made.
Quantum control of the pathway along which a Rydberg electron field ionizes is experimentally and computationally demonstrated. Selective field ionization is typically done with a slowly rising electric field pulse. The (1/n∗)4{(1/{n}^{*})}^{4}(1/n∗)4 scaling of the classical ionization threshold leads to a rough mapping between arrival time of the electron signal and principal quantum number of the Rydberg electron. This is complicated by the many avoided level crossings that the electron must traverse on the way to ionization, which in general leads to broadening of the time-resolved field ionization signal. In order to control the ionization pathway, thus directing the signal to the desired arrival time, a perturbing electric field produced by an arbitrary wave-form generator is added to a slowly rising electric field. A genetic algorithm evolves the perturbing field in an effort to achieve the target time-resolved field ionization signal.
The electron signals from the field ionization of two closely spaced Rydberg states of rubidium-85 are separated using quantum control. In selective field ionization, the state distribution of a collection of Rydberg atoms is measured by ionizing the atoms with a ramped electric field. Generally, atoms in higher energy states ionize at lower fields, so ionized electrons which are detected earlier in time can be correlated with higher energy Rydberg states. However, the resolution of this technique is limited by the Stark effect. As the electric field is increased, the electron encounters numerous avoided Stark level crossings which split the amplitude among many states, thus broadening the time-resolved ionization signal. Previously, a genetic algorithm has been used to control the signal shape of a single Rydberg state. The present work extends this technique to separate the signals from the 34s34s34s and 33p33p33p states of rubidium-85, which are overlapped when using a simple field ramp as in selective field ionization.
Quantum control of the pathway along which a Rydberg electron field ionizes is demonstrated. Selective field ionization is typically done with a slowly rising electric field pulse. The (1/n∗)4(1/n^*)^4(1/n∗)4 scaling of the classical ionization threshold leads to a rough mapping between arrival time of the electron signal and principal quantum number of the Rydberg electron. This is complicated by the many avoided level crossings that the electron must traverse on the way to ionization, which in general leads to broadening of the time-resolved field ionization signal. In order to control the ionization pathway, thus directing the signal to the desired arrival time, a perturbing electric field produced by an arbitrary waveform generator is added to a slowly rising electric field. A genetic algorithm evolves the perturbing field in an effort to achieve the target time-resolved field ionization signal.
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.
Rydberg atoms, which have a highly excited outer electron, are easily manipulated by electric fields. Using a magneto-optical trap, we cool Rubidium atoms to a few hundred millionths of a Kelvin above absolute zero and then excite to Rydberg states. Our first project looks at the dipole-dipole interactions of two atoms starting in the 33p state and ending in the 34s and 33s states. The standard technique is to apply an increasing electric field that ionizes the Rydberg electron and sends it to a detector, but unfortunately the signals overlap. A genetic algorithm is used to separate the signals by controlling the ionization pathway. In order to understand how a Rydberg atom ionizes we need to build a model. The current model, which uses a semi-empirical formula, neglects important quantum phase information. In our second project we are building a computational model that includes continuum states along with discrete states. We present progress on a new model which takes into account the differences in normalization for continuum and discrete states.