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Engineering Electron Superpositions Using a Magnetic Field

Zoe A. Rowley, Bianca R. Gualtieri

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

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. The discrete energy levels of Rydberg atoms are shifted in the presence of an electric field by the Stark effect and are similarly shifted due to a magnetic field by the Zeeman effect. These effects couple the energy levels together, creating avoiding crossings. At these avoided crossings, an electron in one energy level can jump to the other. Our goal is to be able to use these avoided crossings to put the electron in a superposition state of both energy levels. In order to achieve this we created new software that enables us to calculate the energy levels of an electron in both a magnetic and an electric field. We present energy level maps visualizing the results of the Stark and Zeeman effects.

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A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.

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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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Abstract A spectroscopic study of Rydberg states of helium ( n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ( n = 30, B ≤ 120 mT and F = 0–78 V cm −1 ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ( n = 45, B = 277 mT and F = 0–8 V cm −1 ). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin–orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m l values and pronounced m l -mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg–Stark deceleration.

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Stark–Zeeman and Blokhintsev Spectra of Rydberg Atoms

Andrei Letunov, Valerii S. Lisitsa

The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.

Journal of Experimental and Theoretical Physics•Nov 1, 2020•2 citations
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. The discrete energy levels of Rydberg atoms are shifted in the presence of an electric field by the Stark effect and are similarly shifted due to a magnetic field by the Zeeman effect. These effects couple the energy levels together, creating avoiding crossings. At these avoided crossings, an electron in one energy level can jump to the other. Our goal is to be able to use these avoided crossings to put the electron in a superposition state of both energy levels. In order to achieve this we created new software that enables us to calculate the energy levels of an electron in both a magnetic and an electric field. We present energy level maps visualizing the results of the Stark and Zeeman effects.
A spectroscopic study of Rydberg states of helium (n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear (n = 30, B ≤ 120 mT and F = 0-78 V cm⁻¹), and (ii) the diamagnetic term is dominant and the Stark effect is linear (n = 45, B = 277 mT and F = 0-8 V cm⁻¹). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin-orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m ₗ values and pronounced m ₁-mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg-Stark deceleration.
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.
Abstract A spectroscopic study of Rydberg states of helium ( n = 30 and 45) in magnetic, electric and combined magnetic and electric fields with arbitrary relative orientations of the field vectors is presented. The emphasis is on two special cases where (i) the diamagnetic term is negligible and both paramagnetic Zeeman and Stark effects are linear ( n = 30, B ≤ 120 mT and F = 0–78 V cm −1 ), and (ii) the diamagnetic term is dominant and the Stark effect is linear ( n = 45, B = 277 mT and F = 0–8 V cm −1 ). Both cases correspond to regimes where the interactions induced by the electric and magnetic fields are much weaker than the Coulomb interaction, but much stronger than the spin–orbit interaction. The experimental spectra are compared to spectra calculated by determining the eigenvalues of the Hamiltonian matrix describing helium Rydberg states in the external fields. The spectra and the calculated energy-level diagrams in external fields reveal avoided crossings between levels of different m l values and pronounced m l -mixing effects at all angles between the electric- and magnetic-field vectors other than 0. These observations are discussed in the context of the development of a method to generate dense samples of cold atoms and molecules in a magnetic trap following Rydberg–Stark deceleration.
On one side, atom-chip experiments have demonstrated to be a versatile tool to study quantum physics in cold atoms systems. On the other side, Rydberg atoms have exaggerated properties that makes them good candidates to study quantum information and quantum simulations protocols. In this thesis both system are put together with the aim to study Rydberg physics (in particular atom-atom interaction) in an atom-chip experiment. Due to the exaggerated properties of Rydberg atoms they are very sensitive to electric fields. Thus, the combination of Rydberg atoms with surfaces can be challenging. Therefore a detailed characterization of the mentioned stray electric fields via the analysis of Stark-Zeeman maps is crucial. We employ two-photon Rydberg Stark spectroscopy of a micron-sized cloud of magnetically trapped ultracold rubidium atoms to characterize the electric fields near our atom-chip. Once we characterized the local electric fields we were able to study in more detail the effect of Rydberg excitation in the ultracold cloud of atoms. For instance we observed the formation of ultralong-range Rydberg molecules in our system. In these molecules a ground state atom is weakly bound to the Rydberg electron. We also attempted to observe the effect of Rydberg blockade in the system by looking at the characteristics of Rydberg spectra. Finally we studied the possibility of inducing rf transitions within a Rydberg state manifold in order to enhance our detection method and populate states that are not accessible directly with a two-photon laser transition.
Rydberg excitons are semiconductor analogues to Rydberg atoms, where one electron is promoted to an energy level of large principal quantum number η and which behave in a manner similar to hydrogen. Their huge spatial extent results in giant dipole moments and interaction effects, which can be used to create nonlinearities at the single excitation level. In contrast to hydrogen, the effective masses and Rydberg energies involved are moderately small, so that in contrast to Rydberg atoms the high field limit of Rydberg physics can be studied using fields strengths that can be realized in the lab. Here we investigate the effects of external magnetic fields of up to 7T on Rydberg excitons both in Faraday and Voigt geometry. In both cases complicated splitting patterns emerge. We investigate the differences between the two geometries and highlight spectroscopic features that are especially easy to access using them. We show that the large number of resonances in the spectrum renders a microscopic treatment of each individual resonance implausible. We instead demonstrate general effects introduced by the field like avoided crossings and discuss alternative approaches to the level structure in terms of collective descriptions.
The problem of Rydberg atomic spectra in crossed electric F and magnetic B fields (combined Stark–Zeeman effects), as well as an oscillating electric field are under consideration. The main problem is the great array of radiative transitions between the Rydberg atomic states. The different versions of semiclassical approaches are applied for the solution of the problem. New approximate selection rules are established to simplify the matrix elements of radiative transitions, making it possible to reduce the complex expressions of Gordon’s hypergeometric series to the trivial trigonometric functions. Simple analytical formulas for the dipole matrix elements of a Rydberg hydrogen-like atom in external crossed electric and magnetic fields for Hnα are obtained. The specific calculations are presented for n = 10 to 9 transition both for parallel and perpendicular orientations of F–B fields. The result of Blokhintsev for a single Stark component in oscillating field is generalized for the array of radiative transitions between Rydberg atomic states. Such spectra with large values of modulation index are compared with static ones.