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arXiv:0907.5405 · Physical Review A

Simulations of the dipole-dipole interaction between two spatially separated groups of Rydberg atoms

Thomas J. Carroll, Christopher Daniel, Leah Hoover, Timothy Sidie, Michael W. Noel

Published Nov 25, 2009• 13 citations
arXivHTMLPDF

Abstract

The dipole-dipole interaction among ultracold Rydberg atoms is simulated. We examine a general interaction scheme in which two atoms excited to the $x$ and ${x}^{\ensuremath{'}}$ states are converted to $y$ and ${y}^{\ensuremath{'}}$ states via a F\"orster resonance. The atoms are arranged in two spatially separated groups, each consisting of only one species of atom. We monitor the state mixing by recording the fraction of atoms excited to the ${y}^{\ensuremath{'}}$ state as the distance between the two groups is varied. With zero detuning a many-body effect that relies on always resonant interactions causes the state mixing to have a finite range. When the detuning is greater than zero, another many-body effect causes a peak in the state mixing when the two groups of atoms are some distance away from each other. To obtain these results it is necessary to include multiple atoms and solve the full many-body wave function. These simulation results are supported by recent experimental evidence. These many-body effects, combined with appropriate spatial arrangement of the atoms, could be useful in controlling the energy exchange among the atoms.

DOI
10.1103/physreva.80.052712

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The dipole-dipole interaction among ultracold Rydberg atoms is simulated. We examine a general interaction scheme in which two atoms excited to the xxx and x\ensuremath′{x}^{\ensuremath{'}}x\ensuremath′ states are converted to yyy and y\ensuremath′{y}^{\ensuremath{'}}y\ensuremath′ states via a F"orster resonance. The atoms are arranged in two spatially separated groups, each consisting of only one species of atom. We monitor the state mixing by recording the fraction of atoms excited to the y\ensuremath′{y}^{\ensuremath{'}}y\ensuremath′ state as the distance between the two groups is varied. With zero detuning a many-body effect that relies on always resonant interactions causes the state mixing to have a finite range. When the detuning is greater than zero, another many-body effect causes a peak in the state mixing when the two groups of atoms are some distance away from each other. To obtain these results it is necessary to include multiple atoms and solve the full many-body wave function. These simulation results are supported by recent experimental evidence. These many-body effects, combined with appropriate spatial arrangement of the atoms, could be useful in controlling the energy exchange among the atoms.
The long-range, anisotropic nature of the interaction among atoms in an ultracold dipolar gas leads to a rich array of possibilities for studying many-body physics. In this work, an ultracold gas of highly excited atoms is used to study energy transport due to the long-range dipole-dipole interaction. A technique is developed to measure both the internal energy states of the interacting Rydberg atoms and their positions in space. This technique is demonstrated by observing energy exchange between two spatially separated groups of Rydberg atoms excited to two different internal states. Simulations confirm the general features of the energy transport in this system and highlight subtleties associated with the homogeneity of the electric field used in this experiment.
We examine state mixing in a dense, cold Rydberg gas. Cold Rb atom clouds in an optical dipole trap are excited into nD5/2n{D}_{5/2}nD5/2​ Rydberg levels using narrow-bandwidth laser pulses. For n=43n=43n=43, two atoms excited to 43D5/243{D}_{5/2}43D5/2​ states can be converted to 41F7/241{F}_{7/2}41F7/2​ and 45P3/245{P}_{3/2}45P3/2​ product states via a F\"orster resonance. We find, unexpectedly, that up to 50% of the Rydberg atoms are detected in such product states after only 100 ns of interaction time. The experiment is modeled using many-body quantum simulations. To reproduce the mixing fractions measured near F\"orster resonances, we use an exact, nonperturbative many-atom Hamiltonian in which product states are treated on an equal basis with the laser-excited nD5/2n{D}_{5/2}nD5/2​ Rydberg level. Simplified many-body interaction models based on sums over pairwise atomic potentials cannot reproduce the measured mixing fractions.
Ultracold Rydberg atoms in a static electric field can exchange energy via the dipole-dipole interaction. The Stark effect shifts the energy levels of the atoms which tunes the energy exchange into resonance at specific values of the electric field (F\"orster resonances). We excite rubidium atoms to Rydberg states by focusing either a 480 nm beam from a tunable dye laser or a pair of diode lasers into a magneto-optical trap. The trap lies at the center of a configuration of electrodes. We scan the electric field by controlling the voltage on the electrodes while measuring the fraction of atoms that interact. Dipole-dipole interaction spectra are presented for initially excited rubidium ndndnd states for n=31n=31n=31 to 46 and for four different pairs of initially excited rubidium nsnsns states. We also present the dipole-dipole interaction spectra for individual rubidium 32ddd (j,mj)(j,\phantom{\rule{0.16em}{0ex}}{m}_{j})(j,mj​) fine structure levels that have been selectively excited. The data are compared to calculated spectra.
We report the application of the resonant dipole – dipole interaction of Rydberg atoms for the realisation of quantum computations with ultracold neutral atoms. Coherent population oscillations between the collective states of systems consisting of two interacting atoms make it possible to implement two-qubit phase gates, which are necessary for universal quantum computations. The schemes studied are alternatives to two-qubit gates based on the Rydberg dipole blockade effect. In contrast, the schemes we propose do not require large dipole – dipole interaction energies and can be realised for atoms that are at a considerable distance from each other. The bibliography includes 27 references.
Interactions between single atoms are fundamental to physics and to control them is an ultimate goal. The exaggerated properties of Rydberg atoms offer to met the technical challenges to isolate and control single interaction channels in ultracold gases. Here, I present experiments on two subjects related to interactions of Rydberg atoms in dense ultracold clouds. One subject concerns coherence in strongly interacting ensembles of atoms, where the interaction between Rydberg atoms is induced via Stark-tuned Förster resonances. Pulsed experiments, following the idea of Ramsey experiments, are used for high resolution spectroscopy of the Förster defect and phase sensitive detection. Coherent oscillations between pair states and an interaction-induced phase shift of Rydberg atoms are measured. These experiments are accompanied by calculations of the interaction strength and by simulations using the concept of a pair state interferometer. The simulations nicely reproduce the experimental findings and support the observation that the ensemble of atoms in the presence of interactions can be described and controlled coherently. The second subject of this thesis is the measurement of a permanent dipole moment in a homonuclear diatomic molecule that arises by the interaction between a Rydberg atom and a ground state atom. Usually parity symmetry prohibits a permanent dipole moment in diatomic molecules, but here the strong asymmetry between the constituents of the ultralong-range Rydberg molecule allows breaking parity symmetry. These molecules consist of one ground state atom bound inside the Rydberg electron wavefunction of a highly excited atom. Calculations predict dipole moments on the order of 1 Debye. Experimental proof is reported on the measurement of a linear Stark effect of these molecules, in excellent agreement with the calculations.
We have observed resonant energy transfer between cold Rydberg atoms in spatially separated cylinders. Resonant dipole-dipole coupling excites the 49s atoms in one cylinder to the 49p state while the 41d atoms in the second cylinder are transferred down to the 42p state. We have measured the production of the 49p state as a function of separation of the cylinders (0-80 microm) and the interaction time (0-25 micros). In addition, we measured the width of the electric field resonances. A full many-body quantum calculation reproduces the main features of the experiments.