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Correlations and spatial structures in ultracold Rydberg gases

S. J. J. M. F. Kokkelmans

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Crystalline structures of highly excited Rydberg atoms can be a model for dilute metallic solids with tunable parameters, and provide access to the regime of strongly coupled systems. In practice, crystal creation is made difficult by the 'Rydberg blockade', where one atom in the Rydberg state shifts the energy levels of its neighbours out of resonance with the excitation laser. In our experiment, we can spatially detect Rydberg atoms by a combination of field-ionization, and subsequent acceleration of the remaining ions onto a multi-channel plate. In this way, we were able to determine the blockade radius from measuring second-order correlations. We have also made small ordered Rydberg structures by optically imprinting local excitations in a disordered atomic gas using a spatial light modulator. With this diffractive optical element it is possible to control the intensity of light in the far ¿eld and create almost any desired intensity pattern. We found that a Rydberg system with a dissipative mechanism can be mapped onto a set of rate equations that describe a wireless computer network. In these networks neighbouring transmitters have a similar blockade effect on each other. For the Rydberg system, we used mathematical tools developed for wireless networks, and applied this to optically imprinted square lattices.

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Crystalline structures of highly excited Rydberg atoms can be a model for dilute metallic solids with tunable parameters, and provide access to the regime of strongly coupled systems. In practice, crystal creation is made difficult by the 'Rydberg blockade', where one atom in the Rydberg state shifts the energy levels of its neighbours out of resonance with the excitation laser. In our experiment, we can spatially detect Rydberg atoms by a combination of field-ionization, and subsequent acceleration of the remaining ions onto a multi-channel plate. In this way, we were able to determine the blockade radius from measuring second-order correlations. We have also made small ordered Rydberg structures by optically imprinting local excitations in a disordered atomic gas using a spatial light modulator. With this diffractive optical element it is possible to control the intensity of light in the far ¿eld and create almost any desired intensity pattern. We found that a Rydberg system with a dissipative mechanism can be mapped onto a set of rate equations that describe a wireless computer network. In these networks neighbouring transmitters have a similar blockade effect on each other. For the Rydberg system, we used mathematical tools developed for wireless networks, and applied this to optically imprinted square lattices.
Creating ultracold Rydberg atoms in lattices imprinted with a spatial light modulator offers the possibility to simulate quantum processes. Strong dipole forces between Rydberg atoms provide the required correlations between lattice sites. With a high ground-state atomic density per lattice site, blockade phenomenon may induce single Rydberg atom occupancy per lattice site. Readout of resulting patterns requires single-atom detection with spatial resolution. The grand challenge is to create systems of interacting Rydberg atoms with scalability. So far, we have achieved spatial imaging of Rydberg atoms using ion optics and incorporated in-vacuo aberration correction for imprinted light patterns. Presently, we are studying the effect of dipole blockade on Rydberg excitation statistics. For this we have set up a tuneable Rydberg excitation laser system using an ultra stable reference. Measurements of spatial correlation functions show that achieving a blockade radius of 10 μm is possible. Combined with a dark-spot MOT, this is sufficient to achieve precisely one Rydberg atom per lattice site.
Ultracold atomic gases have been used extensively in recent years to realize textbook examples of condensed matter phenomena. Recently, phase transitions to ordered structures have been predicted for gases of highly excited, 'frozen' Rydberg atoms. Such Rydberg crystals are a model for dilute metallic solids with tunable lattice parameters, and provide access to a wide variety of fundamental phenomena. We investigate theoretically how such structures can be created in four distinct cold atomic systems, by using tailored laser-excitation in the presence of strong Rydberg-Rydberg interactions. We study in detail the experimental requirements and limitations for these systems, and characterize the basic properties of small crystalline Rydberg structures in one, two and three dimensions.
When cold atoms are laser-excited to Rydberg states, the strong interactions between Rydberg excitations can lead to complex many-body entanglement in the system. The excitation process results in spatial correlations between excitations in the system. In most cases, Rydberg excitation positions are anticorrelated such that no two excitations are within a "blockade radius" of each other. Such systems are well-suited for studying basic many-body physics, as well as for future technological applications such as quantum computation. This thesis describes an experimental apparatus we constructed to perform spatially-sensitive detection of Rydberg atoms. We use the apparatus to perform measurements of the Rydberg-Rydberg pair-correlation function. This results in the first direct spatial images of the Rydberg blockade effect. We measure the blockade radius for a variety of S and D Rydberg states in rubidium. We investigate the dependence of the blockade radius on laser detunings and energy level shifts induced by optical potentials due to trapping lasers. Our results have some implications for atom traps used for neutral atom quantum computation. We also present simulations results used to characterize the performance of the imaging system.
Recent developments in the study of ultracold Rydberg gases demand an advanced level of experimental sophistication, in which high atomic and optical densities must be combined with excellent control of external fields and sensitive Rydberg atom detection. We describe a tailored experimental system used to produce and study Rydberg-interacting atoms excited from dense ultracold atomic gases. The experiment has been optimized for fast duty cycles using a high flux cold atom source and a three beam optical dipole trap. The latter enables tuning of the atomic density and temperature over several orders of magnitude, all the way to the Bose-Einstein condensation transition. An electrode structure surrounding the atoms allows for precise control over electric fields and single-particle sensitive field ionization detection of Rydberg atoms. We review two experiments which highlight the influence of strong Rydberg-Rydberg interactions on different many-body systems. First, the Rydberg blockade effect is used to pre-structure an atomic gas prior to its spontaneous evolution into an ultracold plasma. Second, hybrid states of photons and atoms called dark-state polaritons are studied. By looking at the statistical distribution of Rydberg excited atoms we reveal correlations between dark-state polaritons. These experiments will ultimately provide a deeper understanding of many-body phenomena in strongly-interacting regimes, including the study of strongly-coupled plasmas and interfaces between atoms and light at the quantum level.
This thesis experimentally explores the application of strongly interacting states of Rydberg atoms as means to introduce and control correlations in many-body systems. A new apparatus has been built, which combines high atomic densities possible using optical dipole traps with the ability to detect and probe Rydberg atoms via both field ionization detection and electromagnetically induced transparency. In the first study, the interaction induced excitation of Rydberg atom pairs ('antiblockade') is demonstrated using detuned laser excitation. This provides \nthe possibility to engineer spatial correlations and to control interactions between Rydberg atoms. We then investigate the effects of Rydberg-Rydberg interactions \nand correlations on the spontaneous evolution of the system to an ultracold plasma. The initial correlations between Rydberg atoms should be preserved, suggesting a new route to overcome disorder-induced heating and to enter new strongly coupled regimes. Finally the back-action of Rydberg-Rydberg interactions on propagating light fields is explored. Dissipative interactions between dark-state polaritons give rise to a strongly nonlinear optical response and sub-Poissonian statistics of polaritons \nwhich reflect the emergence of correlations in both the atomic and light fields. Combined, these experiments help elucidate the effects of Rydberg induced correlations on diverse physical systems involving atoms, ions and photons.
Laser-driven Rydberg gases are many-body quantum systems that exhibit a pronounced collective excitation behavior due to the strong interaction between atoms in high-lying electronic states. Atoms located within a so-called blockade volume share a single Rydberg excitation, which is dynamically created and annihilated. For sufficiently long times, this driven system approaches a steady state, which lends its properties from a maximum entropy state of a Tonks gas. Using this connection, we show that spatial correlations between Rydberg atoms are controlled by the number of atoms contained within a blockade volume. For a small number, the system favors a disordered arrangement of Rydberg atoms, whereas in the opposite limit, Rydberg atoms tend to arrange in an increasingly ordered configuration. We argue that this is an entropic effect which is observable in current experiments. Our work demonstrates how ordered structures can spontaneously emerge in a strongly interacting, closed many-body system out of equilibrium.