For many purposes it is desirable to have an easily understandable and accurate picture of the atomic states. This is especially true for the highly excited states which exhibit features not present in the well known states hydrogen-like orbitals with usual values of the quantum numbers. It could be expected that such visualizations are readily available. Unfortunately, that is not the case. We illustrate the problems by showing several less fortunate earlier presentations in some scientifically most valuable works, and show more suitable visualizations for those cases. The selected cases are not chosen to criticize the authors' approach. Rather, we have taken these very important papers to underline the need for serious work with graphical representations which this work attempts to be a part of. In this text we discuss the problems encountered when visualizing Rydberg states, review some existing presentations and propose guidelines for applications. The focus of this work are so called Stark states and coherent elliptic states of Rydberg atoms. In the sections on elliptic states we show some quite novel geometric interpretations which should be very helpful in analysis of Rydberg state manipulations in external fields. Our demonstration examples involve only hydrogen-like states. However, the techniques and analysis are also relevant for Rydberg molecules and more complicated highly excited atomic and molecular systems.
For many purposes it is desirable to have an easily understandable and accurate picture of the atomic states. This is especially true for the highly excited states which exhibit features not present in the well known states hydrogen-like orbitals with usual values of the quantum numbers. It could be expected that such visualizations are readily available. Unfortunately, that is not the case. We illustrate the problems by showing several less fortunate earlier presentations in some scientifically most valuable works, and show more suitable visualizations for those cases. The selected cases are not chosen to criticize the authors' approach. Rather, we have taken these very important papers to underline the need for serious work with graphical representations which this work attempts to be a part of. In this text we discuss the problems encountered when visualizing Rydberg states, review some existing presentations and propose guidelines for applications. The focus of this work are so called Stark states and coherent elliptic states of Rydberg atoms. In the sections on elliptic states we show some quite novel geometric interpretations which should be very helpful in analysis of Rydberg state manipulations in external fields. Our demonstration examples involve only hydrogen-like states. However, the techniques and analysis are also relevant for Rydberg molecules and more complicated highly excited atomic and molecular systems.
Introduction Series of atomic spectral lines had been studied by emission from excited vapors even before Balmer described the regularity of the visible lines of hydrogen in 1884. However, direct excitation had been restricted to the few lowest-lying levels, particularly those accessible by electric dipole transitions from the ground state using classical light sources. The advent of tunable lasers in the 1970s changed such spectroscopic limitations enormonsly, allowing excitation to a very much larger number of states. Atoms in highly excited states, typically with principal quantum numbers n ≥ 10, are called Rydberg atoms. They are oversize, fragile states of significant intrinsic interest. They are very rare in nature because of their size and fragility, but they are found in interstellar space (H I regions). One of the best sources for comprehensive descriptions of Rydberg atoms and references to the literature describing their exploration is Ref. [120]. It describes their characteristic properties and behavior both classically and quantum mechanically, and especially their strongly enhanced interactions with external fields. The first thing to note is that Rydberg atoms are usually characterized by a single, highly excited electron while all the other electrons remain in their original states. Thus their properties are very nearly classical, and the atoms are much closer to the ideal hydrogen-like model of Chap. 7, along with appropriate quantum defects (see Chap. 10). The spectroscopy of such states is especially interesting because the active electron is much less perturbed by the other electrons in the atom than when it is in lower states. Moreover, there are some special circumstances in which the energy of a Rydberg state is degenerate with an atomic state having two electrons excited to lower levels, and such configurations yield further new information. Second, Rydberg atoms do not usually decay back to the ground state by emission of characteristic radiation, so their study is mediated by other techniques that reveal new and interesting properties. Such properties arise because Rydberg atoms have a huge dipole moment and very low binding energy resulting from the large average distance between the excited electron and the nucleus-plus-core of the rest of the atom with net charge e . Third, transitions between Rydberg states are quite different from those connecting to the ground state for at least three reasons.
Rydberg physics is the land of gentle giants—highly-excited electronic states where an electron is, on average, far from the nucleus. They are created with a lot of energy, have unusually large size and live relatively long. They are useful because they are extremely sensitive to their environment; so much so that a single photon of light can change the behaviour of not only one, but dozens or hundreds of them, over distances we can easily see under an optical microscope. Wherever Rydberg states are created—in atoms, molecules or solids—they all share common features that are exemplified by the physical description of highly-excited hydrogen atoms, with energy levels described by the Rydberg formula. In this ebook, we outline the universal properties of Rydberg systems and then present a selection of ideas that demonstrate their increasing relevance to applications, including sensing, the manipulation of light on the single photon level (quantum optics) and in engineering the interactions between individual quanta (quantum simulation).
Rydberg physics is the land of gentle giants—highly-excited electronic states where an electron is, on average, far from the nucleus. They are created with a lot of energy, have unusually large size and live relatively long. They are useful because they are extremely sensitive to their environment; so much so that a single photon of light can change the behaviour of not only one, but dozens or hundreds of them, over distances we can easily see under an optical microscope. Wherever Rydberg states are created—in atoms, molecules or solids—they all share common features that are exemplified by the physical description of highly-excited hydrogen atoms, with energy levels described by the Rydberg formula. In this ebook, we outline the universal properties of Rydberg systems and then present a selection of ideas that demonstrate their increasing relevance to applications, including sensing, the manipulation of light on the single photon level (quantum optics) and in engineering the interactions between individual quanta (quantum simulation).
Because of their unusual properties, Rydberg atoms, i.e., atoms with one electron occupying a highly excited orbit, have attracted the interest of many physicists. For example, due to their large size, such atoms are particularly sensitive to external fields. Fifty years ago, Segre and co-workers1 investigated the Stark effect and atomic diamagnetism of Rydberg states of alkalis with principal quantum numbers up to n = 30. During the last decade, Rydberg states have been studied extensively2 due to the availability of tunable laser radiation.
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called “common sense” based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
This introductory chapter presents the scope of this book: namely that the book is devoted to Rydberg (i.e., highly-excited) atoms and molecules They have striking distinctions to atoms and molecules in the ground or low-excited states. For Rydberg atoms, with the increase of the principal quantum number n, their characteristic size and the electric dipole moment scales as n 2 (which is why they are extremely sensitive to even weak electric fields and electromagnetic radiation) and their radiative lifetime scales as n 3. They strongly interact not only with an electric field, but also with each other: their dipole–dipole interaction scales as n 4/R 3 and their van der Waals interaction scales as n 11/R 6, where R is their separation from each other. In laboratory conditions experimentalists deal with Rydberg atoms having the quantum number of several tens. In the Universe, in H II regions, the principal quantum number of Rydberg atoms can reach n ~ 1000. In the latter case, the Rydberg atoms cannot be considered anymore as microscopic objects: the diameter of their electron orbit is ~ 0.1 mm, i.e., twice the diameter of human hair. Studies of Rydberg atoms and molecules have numerous applications. Examples are highly-responsive sensing, quantum optics (where the light is manipulated at the level of a single photon), quantum computing, quantum chaos, ultracold Rydberg gases and plasmas, anti-hydrogen formation, and plasma diagnostics.