Chapter Two - Interactions in Ultracold Rydberg Gases

ABSTRACTFew-body interactions offer the opportunity to study the isolated atom to few-body coupled molecules, and to condensed matter transitions. Atoms in molecules and in condensed matters are coupled by different orders of multipole–multipole interactions, which all stem from different orders of approximations from coulomb interactions between multiple charges. The lowest order multipole–multipole interaction is the dipole–dipole interaction, which is proportional to the size of the dipole. In this article, we use Rydberg atoms, which have more than 1000 times greater electric dipoles than the ground state atoms, to study the van der Waals interaction between few bodies. In addition to the large dipoles, the kinetic energy of the atoms is significantly reduced by reducing the temperature, which makes these interactions stable and observable. Here, we report on the 2D and 3D few-body interaction potentials and possible ways of creating semistable molecules in such an ultracold Rydberg gas with a temperature of ≈100 nK. Although we use Rydberg atoms in this article, this calculation can be applied to other states too. The results reported here are useful for studying repulsive van der Waals interactions and creating ultracold molecules.

Atoms and molecules in highly excited electronic states ('Rydberg atoms') have been the object of broad scientific research for almost a century. Despite this long history, the field of research has never lost its buoyancy, and recent years in particular have seen a tremendous revival of interest in the physics of Rydberg atoms and molecules from many different perspectives. Rydberg systems touch a wide range of research areas including, among others, ultralong-range molecules, artificial ('designer') atoms, quantum chaos, quantum information, ultracold Rydberg gases and plasmas, and anti-hydrogen formation. Due to the many fields involved, the physical insight and technical know-how are scattered over different communities. The goal of this special issue is to provide an integral overview of the latest developments in this highly innovative research field and to make the physical knowledge available to a wide audience. Groups from various fields of atomic, molecular and optical physics as well as condensed matter and plasma physics have contributed to this issue, which therefore spans a wide range of areas connected through the common theme: 'Rydberg physics'.This name was given to a four-week International Workshop and Seminar which was held from 19 April to 14 May 2004 at the Max-Planck-Institut für Physik Komplexer Systeme in Dresden, Germany, and organized by the three of us. The workshop and seminar programme was a very successful mixture of topics bringing together colleagues working in different but related areas of research centred about the physics of highly excited Rydberg atoms and molecules. We would like to take this opportunity to express our gratitude to the organization team of the MPI-PKS Dresden, especially the Director, Jan-Michael Rost, and the Visitors' Programme coordinator, Mandy Lochar. The generous support of the Max Planck Society, which made this successful workshop and seminar possible, is also gratefully acknowledged. Inspired by the great response to the 'Rydberg physics' conference we thought that it would be timely and appropriate to recognize the importance of Rydberg physics with a special issue of a scientific journal. The 'unbureaucratic' and highly efficient editorial and publishing team of Journal of Physics B: Atomic, Molecular and Optical Physics (J. Phys. B) allowed this to become a reality; it was a real pleasure for us to serve as guest editors. Unlike a conventional conference proceedings, this special issue has not been restricted to participants of the 'Rydberg physics' conference, and all the original papers contained in it have been peer-reviewed to the usual high standards of J. Phys. B.The variety and integrated discussion on the physics of Rydberg systems during the 'Rydberg physics' conference is reflected in the papers presented here. We have tried to group the papers according to the subject areas which are addressed. The first part of this special issue is devoted to high-resolution spectroscopy revealing deeper insights into the structure of Rydberg atoms and molecules as well as electronic interaction processes. The second part contains experimental and theoretical investigations on the influence of external static and oscillatory fields on Rydberg atoms. The third part takes account of the newly established field of ultracold Rydberg gases and plasmas with special emphasis on the appearance of ultralong-range interactions in these systems. Finally, the issue is concluded by articles on new developments including 'exotic' Rydberg systems.We would like to thank all of the participants of the 'Rydberg physics' workshop and seminar, and, in particular, thecontributors to this special collection of papers, for their involvement. We are deeply indebted to the J. Phys. B editorial and publishing team both for making its realization possible in an extremely efficient way, and for the journal's commitment to the physics of Rydberg systems. We are impressed by the continuing progress in this fascinating and rapidly growing field of research and we look forward to many more thrilling and surprising achievements.

We study resonant energy exchange among atoms in an ultracold Rydberg gas. We explore the transition between two- and many-body interactions by exciting a long thin tube of atoms that restricts the sample's dimensionality.

Coherent excitation of Rydberg atoms in an ultracold gas

An ensemble of excited atoms can synchronize emission of light collectively in a process known as superradiance when its characteristic size is smaller than the wavelength of emitted photons. The underlying superradiance depends strongly on electromagnetic (photon) fields surrounding the atomic ensemble. High mode densities of microwave photons from 300 K blackbody radiation (BBR) significantly enhance decay rates of Rydberg states to neighbouring states, enabling superradiance that is not possible with bare vacuum induced spontaneous decay. Here we report observations of the superradiance of ultracold Rydberg atoms embedded in a bath of room-temperature photons. The temporal evolution of the Rydberg |nD⟩ to |(n + 1)P⟩ superradiant decay of Cs atoms (n the principal quantum number) is measured directly in free space. Theoretical simulations confirm the BBR enhanced superradiance in large Rydberg ensembles. We demonstrate that the van der Waals interactions between Rydberg atoms change the superradiant dynamics and modify the scaling of the superradiance. In the presence of static electric fields, we find that the superradiance becomes slow, potentially due to many-body interaction induced dephasing. Our study provides insights into many-body dynamics of interacting atoms coupled to thermal BBR, and might open a route to the design of blackbody thermometry at microwave frequencies via collective, dissipative photon-atom interactions.

Chapter 5 - Ultracold Atoms and Molecules in Optical Lattices

We present measurements of inelastic collisions between ultracold Cs Rydberg atoms using time-of-flight velocity distributions. The collision mechanism is identified by comparison to Rydberg atom pair potentials calculated using matrix diagonalization.

Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with many-body correlations among Rydberg atoms beyond mean-field approximations. This coherent and ultrafast many-body dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate non-equilibrium dynamics of quantum many-body systems on the ultrafast timescale.

Quantum computers, although not yet available on the market, will revolutionise the future of information processing. Already now, quantum computers of special purpose, i.e., quantum simulators, are within reach. The physics of ultracold atoms, ions, and molecules offers unprecedented possibilities of control of quantum many systems, and novel possibilities of applications for quantum information and quantum metrology. Particularly fascinating is the possibility of using ultracold atoms in lattices to simulate condensed matter or even high energy physics. This book provides a comprehensive overview of ultracold lattice gases as quantum simulators, an interdisciplinary field involving atomic, molecular, and optical physics; quantum optics; quantum information; and condensed matter and high energy physics. It includes some introductory chapters on basic concepts and methods, and focuses on the physics of spinor, dipolar, disordered, and frustrated lattice gases, before reviewing in detail artificial lattice gauge fields with ultracold gases. The last part of the book moves onto a discussion of possible implementations universal quantum computers with ultracold atoms. After a crash course in quantum information theory, several models of quantum computation with ultracold gases are presented, as well as the current understanding of condensed matter from a quantum information perspective. The book ends with the general discussion of various detection methods that are unique for ultracold atoms.

The collisional loss rates of 63${S}_{1/2}$ Rydberg atoms in cesium magneto-optical trap are measured by using the state-selective pulse field ionization technique and used to investigate the interaction between Rydberg atoms. The collisional loss rate coefficients due to collisions with Rydberg atoms and ground-state atoms are obtained by fitting the experimental data. The results indicate that the large collisional loss mainly comes from the strong long-range interaction between ultracold Rydberg atoms, and the loss rate is significantly increased under a weak electric field.

The previous chapter can be viewed as a “first” approach to ultracold Rydberg atoms and ultralong-range Rydberg molecules motivated by the promising applications of these entities in quantum technologies and the quantum simulation of complex systems [1]. The approach has focused on static properties of Rydberg atoms and ultralong-range Rydberg molecules. However, nothing has been said about the dynamics of these systems and how they behave in different environments, which is the topic of the present chapter. In particular, the main ultracold chemical reactions involving Rydberg atoms and ground-state atoms are elucidated. Indeed, the Rydberg–ground-state atom chemical reactions are the primary decay mechanism of Rydberg atoms in high-density media [2], which is of capital interest for most of the applications of Rydberg atoms.

Experimental studies of a photoinitiated collision in an ultracold Cs Rydberg gas are presented. The process is characterized by measuring the laser intensity dependence of the absorption, the number of particles leaving each collision, and the recoil velocity of the collision fragments. The results of the experiment are compared to ab initio Rydberg pair interaction potentials.

The long-range multipole interactions between ultra-cold Rydberg atoms form adiabatic potentials, one of which shows a binding potential that can be used to bind Rydberg-Rydberg molecules. Rydberg-atom molecule, known as macrodimer due to its larger size (~μm), has the properties of the abundant vibrational energy levels and large electric dipole moment and so on. Compared with Rydberg atom, the Rydberg molecule, including Rydberg-ground molecule and Rydberg-Rydberg molecule, is susceptible to manipulate by an external field and possesses potential applications in the weak-signal detection, the quantum gas correlation measurement and the vacuum fluctuation and so on.<br/>In this paper, we investigate a (60D<sub>5/2</sub>)<sub>2</sub> Rydberg macrodimer theoretically and experimentally. In the calculation, we take into account the multipole interaction of a Rydberg-atom pair, including dipole-dipole, dipole-quadrupole, dipole-octupole and quadrupole-quadrupole interaction and so on. The adiabatic potential of 60D<sub>5/2</sub> Rydberg-atom pair is obtained by diagonalizing the interaction Hamiltonian on a grid of internuclear separations, <i>R</i>. The potential depth and binding length of the Rydberg molecular potential well are obtained. In experiment, we prepare the ultra-cold Cs (60D<sub>5/2</sub>)<sub>2</sub> Rydberg molecules by a two-color photoassociation method in a cesium ultracold atom trap. The first-color (pulse-A) resonantly excites a seed Rydberg atom A, and the second color (pulse-B) is detuned and resonantly excites the second Rydberg atom B near to the atom A. Both pulse-A and pulse-B are two-photon excitations (852 nm + 510 nm), between which their 852-nm lasers have the same frequency, whereas the 510-nm laser frequency of the pulse-A is set to be resonant with the atomic transition and the frequency of the pulse-B is detuned by using a double-passed acousto-optic modulator. When the pulse-B is detuned to the molecular binding energy, atom-A and-B are bonded, forming an ultra-cold Cs (60D<sub>5/2</sub>)<sub>2</sub> Rydberg molecule. The two-color photoassociation spectra of Rydberg-Rydberg molecules are detected by the field ionization of Rydberg atoms and molecules with a ramped electric field. Molecular spectra are compared with calculated adiabatic molecular potentials, which yields the binding energy and equilibrium internuclear distance. The two-color photoassociation method used in this work has a doubly resonant character that results in the enhanced excitation rate.

We report on the observation of interactions between ultracold Rydberg atoms and ions in a Paul trap. The rate of observed inelastic collisions, which manifest themselves as charge transfer between the Rydberg atoms and ions, exceeds that of Langevin collisions for ground state atoms by about 3 orders of magnitude. This indicates a huge increase in interaction strength. We study the effect of the vacant Paul trap's electric fields on the Rydberg excitation spectra. To quantitatively describe the exhibited shape of the ion loss spectra, we need to include the ion-induced Stark shift on the Rydberg atoms. Furthermore, we demonstrate Rydberg excitation on a dipole-forbidden transition with the aid of the electric field of a single trapped ion. Our results confirm that interactions between ultracold atoms and trapped ions can be controlled by laser coupling to Rydberg states. Adding dynamic Rydberg dressing may allow for the creation of spin-spin interactions between atoms and ions, and the elimination of collisional heating due to ionic micromotion in atom-ion mixtures.

We present the observation of an autoionization of cesium 37D5/2 Rydberg atoms in ultracold gases and analyze the autoionization mechanism. The autoionization process is investigated by varying the delay time tD and Rydberg atomic density. The dependence of ionization signals on Rydberg density shows that the Rydberg density has an effect on not only the initial ion signals but also the evolution of the Rydberg atoms. The results reveal that the initial ionization of 37D5/2 Rydberg atoms is mostly attributed to the blackbody radiation (BBR)-induced photoionization, and the BBR-induced transitions to the nearby Rydberg states that lead to further ionization. Our work plays a significant role in investigating the collision between Rydberg atoms and many-body physics.