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)
In Sweden—the land of the northern lights—Anders Jonas Ångström (1814–74) pioneered the ﬁeld of atomic spectroscopy, identifying the spectral lines of hydrogen in 1862. In 1885, Swiss physicist Johann Jacob Balmer (1825–98) wrote down a formula that described Ångström’s hydrogen spectra. Then a few years later (1890), another Swedish physicist Johannes (Janne) Robert Rydberg (1854–1919) penned a more general formula that described the spectral lines emitted by atoms that have a single outer shell (valence) electron.
According to Rydberg’s formula, the energy of the nth energy level of hydrogen is given by
where RH is known as Rydberg’s constant and n is known as the principal quantum number. Any system with a ‘delocalized’ electron plus a more localized positively charged core looks somewhat hydrogen-like, and a modiﬁed form of Rydberg’s formula is applicable where the energy levels are arranged in a speciﬁcally ordered series. We illustrate these Rydberg series with two very different examples—a hot gas and a cold semiconductor where excited electrons are bound by the negative hole left behind, forming an exciton. As many systems display these properties, any atom (molecule or semiconductor) with a highly excited electron in a state with high n is known as a Rydberg atom. We shall use the generic word ‘atom’ from now on. Ångström’s measurements and Rydberg’s formula became hugely signiﬁcant because of what followed: ﬁrst, the birth of quantum physics with Niels Bohr’s model of the atom, and then the birth of scattering theory developed by Enrico Fermi, built on the study of the broadening of Rydberg spectral lines by Edoardo Amaldi (1908–89) and Emilio Gino Segre (1905–89). These initial experimental observations of Rydberg series were made in hot gases, excited with broadband lamp light sources. Broadening of the spectral lines due to collisions, and weaker absorption of the lamp light by high-lying states, allowed clear observation only of states with low principal quantum numbers. As technology developed, physicists were able to observe Rydberg atoms with higher and higher principal quantum numbers. In 1965, astronomers at the National Radio Astronomy Observatory in West Virginia, USA, detected the microwave radiation emitted by hydrogen atoms in Orion making a transition beginning in a state with initial principal quantum number n = 110; see ﬁgure 2. Such highly-excited Rydberg atoms are enormous—of the order of a micron across—larger than a virus, and 10 000 times larger than a ground-state atom. More recently, states with n = 1000 have been observed.
The fact that the outer electron is on average so far from the core makes it very weakly bound, and hence very sensitive to external electric ﬁelds, including ﬁelds induced by nearby Rydberg atoms. This exaggerated sensitivity makes Rydberg atoms ideal for sensing electric ﬁelds. The large coupling between Rydberg atoms and microwave ﬁelds was exploited by Serge Haroche (1944–present)—winner of the Nobel Prize for Physics in 2011—and colleagues in pioneering light–matter interactions at the level of single quanta. Current theoretical and experimental efforts are broadly directed towards applications in three areas: sensing, quantum optics and quantum simulation.