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arXiv:1012.3810 · Journal of Physics B Atomic Molecular and Optical Physics

Spectral properties of finite laser-driven lattices of ultracold Rydberg atoms

Nikolas Tezak, Michael Mayle, Peter Schmelcher

Published Sep 14, 2011• 8 citations
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Abstract

We investigate the spectral properties of a finite laser-driven lattice of ultracold Rydberg atoms exploiting the dipole blockade effect in the frozen Rydberg gas regime. Uniform one-dimensional lattices as well as lattices with variable spacings are considered. In the case of a weak laser coupling, we find a multitude of many-body Rydberg states with well-defined excitation properties which are adiabatically accessible starting from the ground state. A comprehensive analysis of the degeneracies of the spectrum as well as of the single- and pair-excitation numbers of the eigenstates is performed. In the strong laser regime, analytical solutions for the pseudo-fermionic eigenmodes are derived. Perturbative energy corrections for this approximative approach are provided.

DOI
10.1088/0953-4075/44/18/184009

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We investigate the spectral properties of a finite laser-driven lattice of ultracold Rydberg atoms exploiting the dipole blockade effect in the frozen Rydberg gas regime. Uniform one-dimensional lattices as well as lattices with variable spacings are considered. In the case of a weak laser coupling, we find a multitude of many-body Rydberg states with well-defined excitation properties which are adiabatically accessible starting from the ground state. A comprehensive analysis of the degeneracies of the spectrum as well as of the single- and pair-excitation numbers of the eigenstates is performed. In the strong laser regime, analytical solutions for the pseudo-fermionic eigenmodes are derived. Perturbative energy corrections for this approximative approach are provided.
We investigate static properties of laser-driven ultracold Rydberg atoms confined to one- and two-dimensional uniform lattices in the limit of vanishing laser coupling. The spectral structure of square lattices is compared to those of linear chains, and similarities as well as differences are pointed out. Furthermore, we employ a method based on elements of graph theory to numerically determine the laser-detuning-dependent ground states of various lattice geometries. Ground states for chains as well as square and rectangular lattices are provided and are discussed.
The properties of a Rydberg atom immersed in an ultracold environment were investigated. Two scenarios were considered, one of which involves the neighbouring ground-state atoms arranged in a spatially structured configuration, while the other involves them distributed randomly in space. To calculate the influence of the multiple ground-state atoms on the Rydberg atom, Fermi-pseudopotential was used, which simplified greatly the numerical effort. In many cases, the few-body interaction can be written down analytically which reveals the symmetry properties of the system. In the structured case, we report the first prediction of the formation of ``Rydberg Borromean trimers''. The few-body interactions and the dynamics of the linear A-B-A trimer, where A is the ground-state atom and B is the Rydberg atom, were investigated in the framework of normal mode analysis. This exotic ultralong-range triatomic bound state exists despite that the Rydberg-ground-state interaction is repulsive. Their lifetimes were estimated using both quantum scattering calculations and semi-classical approximations which are found to be typically sub-microseconds. In the disordered case, the Rydberg-excitation spectra of a frozen-gas were simulated, where the nuclear degrees of freedom can be ignored. The systematic change of the spectral shape with respect to the density of the gas and the excitation of the Rydberg atom were found and studied. Some parts of the spectral shape can be described by simple scaling laws with exponents given by the basic properties of the atomic species such as the polarizability and the zero-energy electron-atom scattering length.
The laser excitation of Rydberg atoms in ultracold gases is often described assuming that the atomic motion is frozen during the excitation time. We show that this frozen gas approximation can break down for atoms that are held in optical lattices or microtraps. In particular, we show that the excitation dynamics is in general strongly affected by mechanical forces among the Rydberg atoms as well as the spread of the atomic wave packet in the confining potential. This causes decoherence in the excitation dynamics-resulting in a dissipative blockade effect-that renders the Rydberg excitation inefficient even in the antiblockade regime. For a strongly off-resonant laser excitation-usually considered in the context of Rydberg dressing-these motional effects compromise the applicability of the Born-Oppenheimer approximation. In particular, our results indicate that they can also lead to decoherence in the dressing regime.
We consider a dense one-dimensional laser-driven Rydberg lattice gas with perfect nearest-neighbor blockade. The ground state of this system can be found analytically in certain parameter regimes even when the applied fields are inhomogeneous in space. We will use this unique feature to investigate the effect of an impurity---introduced by the local variation of the laser parameters---on the correlations of the many-body ground state. Moreover, we explore the role of a staggered laser field which alternates from site to site thereby breaking the sublattice symmetry. We demonstrate that this technique, which can be applied experimentally, reveals insights into the role of long-range interactions on the critical properties of a Rydberg gas. Our work highlights possibilities for the exploration of many-body physics in Rydberg lattice gases based on locally tunable laser fields.
We review here the studies performed about interactions in an assembly of cold Rydberg atoms. We focus especially on the review of the dipole–dipole interactions and on the effect of the dipole blockade in the laser Rydberg excitation, which offers attractive possibilities for quantum engineering. We present first the various interactions between Rydberg atoms. The laser Rydberg excitation of such an assembly is then described with the introduction of the dipole blockade phenomenon. We report recent experiments performed in this subject by starting with the case of a pair of atoms allowing the entanglement of the wave-functions of the atoms and opening a fascinating way for the realization of quantum bits and quantum gates. We consider then several works on the blockade effect in a large assembly of atoms for three different configurations: blockade through electric-field induced dipole, through Förster resonance, and in van der Waals interaction. The properties of coherence and cooperativity are analyzed. Finally, we treat the role of dipole–dipole interactions between Rydberg atoms responsible for Penning ionization. The perturbation of the dipole blockade by ions and the evolution of the Rydberg towards an ultracold plasma are discussed.
We study a one-dimensional atomic lattice gas in which Rydberg atoms are excited by a laser and whose external dynamics is frozen. We identify a parameter regime in which the Hamiltonian is well approximated by a spin Hamiltonian with quasilocal many-body interactions which possesses an exact analytic ground state solution. This state is a superposition of all states of the system that are compatible with an interaction induced constraint weighted by a fugacity. We perform a detailed analysis of this state which exhibits a crossover between a paramagnetic phase with short-ranged correlations and a crystal. This study also leads us to a class of spin models with many-body interactions that permit an analytic ground state solution.