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arXiv:1103.2096 · Journal of Physics B Atomic Molecular and Optical Physics

Adiabatic formation of Rydberg crystals with chirped laser pulses

Rick van Bijnen, Sjoerd Smit, K. A. H. van Leeuwen, Edgar J. D. Vredenbregt, S. J. J. M. F. Kokkelmans

Published Sep 14, 2011• 65 citations
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Abstract

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.

DOI
10.1088/0953-4075/44/18/184008

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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.
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.
Abstract We examine the adiabatic preparation of crystalline phases of Rydberg excitations in a one-dimensional lattice gas by frequency sweep of the excitation laser, as proposed by Pohl et al (2010 Phys. Rev. Lett. 104 043002 ) and recently realized experimentally by Schauß et al (2015 Science 347 1455 ). We find that the preparation of crystals of a few Rydberg excitations in a unitary system of several tens of atoms requires exceedingly long times for the adiabatic following of the ground state of the system Hamiltonian. Using quantum stochastic (Monte Carlo) wavefunction simulations, we show that realistic decay and dephasing processes affecting the atoms during the preparation lead to a final state of the system that has only a small overlap with the target crystalline state. Yet, the final number and highly sub-Poissonian statistics of Rydberg excitations and their spatial order are little affected by the relaxations.
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.
Rydberg atoms have experimentally interestingproperties such as strong long-range Van der Waals interactions and the dipole blockade effect. In optical lattices the blockade effect ensures that only one Rydberg excitation per site is allowed, effectively creating a Rydberg crystal. We theoretically show that it is also possible for a one-dimensional Rydberg crystal to spontaneously form in a random ensemble of atoms, e.g. a magneto-optical trap. This is done using an existing Monte Carlo model [1] to simulate the excitation dynamics inside the intersection of two lasers for a two-step excitation scheme. With a blue-detuned laser for the upper transition, the first Rydberg excitation will occur after a relatively long time. That first Rydberg atom will then seed further Rydberg excitations, as the blockade effect shifts atoms at a certain distance into resonance. If two dimensions of the laser intersection are smaller than the blockade radius, a one-dimensional Rydberg crystal will form.
Abstract. We describe the dynamical preparation of anisotropic crystalline phases obtained by laser-exciting ultracold Alkali atoms to Rydberg p-states where they interact via anisotropic van der Waals interactions. We develop a time-dependent variational mean field ansatz to model large, but finite two-dimensional systems in experimentally accessible parameter regimes, and we present numerical simulations to illustrate the dynamical formation of anisotropic Rydberg crystals. PACS numbers: 32.80.Ee,34.20.Cf,64.70.Tg