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arXiv:physics/0407048 · Journal of Physics B Atomic Molecular and Optical Physics

Zeros of Rydberg–Rydberg Föster interactions

Thad G Walker, Mark Saffman

Published Jan 6, 2005• 86 citations
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Abstract

Rydberg states of atoms are of great current interest for quantum manipulation of mesoscopic samples of atoms. Long-range Rydberg–Rydberg interactions can inhibit multiple excitations of atoms under the appropriate conditions. These interactions are strongest when resonant collisional processes give rise to long-range C 3 / R 3 interactions. We show in this paper that even under resonant conditions C 3 often vanishes so that care is required to realize full dipole blockade in micron-sized atom samples.

DOI
10.1088/0953-4075/38/2/022

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In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^

•Jan 1, 2007•1 citation
Rydberg states of atoms are of great current interest for quantum manipulation of mesoscopic samples of atoms. Long-range Rydberg–Rydberg interactions can inhibit multiple excitations of atoms under the appropriate conditions. These interactions are strongest when resonant collisional processes give rise to long-range C 3 / R 3 interactions. We show in this paper that even under resonant conditions C 3 often vanishes so that care is required to realize full dipole blockade in micron-sized atom samples.
Rydberg states of atoms are of great current interest for quantum manipulation of mesoscopic samples of atoms. Long-range Rydberg–Rydberg interactions can inhibit multiple excitations of atoms under the appropriate conditions. These interactions are strongest when resonant collisional processes give rise to long-range C3/R3 interactions. We show in this paper that even under resonant conditions C3 often vanishes so that care is required to realize full dipole blockade in micron-sized atom samples. (Some figures in this article are in colour only in the electronic version) 1.
A dipole blockade, in which Rydberg-atom-Rydberg-atom interactions inhibit all but a single collective Rydberg excitation, has been proposed as a mechanism to store and manipulate quantum information in mesoscopic ensembles. We investigate the excitation dynamics of a collection of a few atoms and show that they undergo an unexpected, qualitative change when the number of atoms increases from two to three. In particular, the combined action of three atoms, each of which pairwise would produce a blockade, can break the dipole blockade.
Resonant laser excitation of multiple Rydberg atoms are prohibited, leading to Rydberg blockade, when the long-range van der Waals interactions are stronger than the laser-atom coupling. Rydberg blockade can be violated, i.e., simultaneous excitation of more than one Rydberg atom, by off-resonant laser excitation, causing an excitation antiblockade. Rydberg antiblockade gives rise to strongly correlated many-body dynamics and spin-orbit coupling and also finds quantum computation applications. Instead of commonly used van der Waals interactions, we investigate antiblockade dynamics of two Rydberg atoms interacting via dipole-dipole exchange interactions. We study typical situations in current Rydberg atom experiments, where different types of dipole-dipole interactions can be achieved by varying Rydberg state couplings. An effective Hamiltonian governing underlying antiblockade dynamics is derived. We illustrate that geometric gates can be realized with the Rydberg antiblockade which is robust against the decay of Rydberg states. Our study may stimulate new experimental and theoretical exploration of quantum optics and strongly interacting many-body dynamics with Rydberg antiblockade driven by dipole-dipole interactions.
New phenomena have been observed by exciting ultracold ground-state atoms to Rydberg states. Starting with a dense sample of Rb atoms in a magneto-optical trap, we excite them to high Rydberg states (n = 30 - 90) with a single UV excitation pulse. Long-range molecular resonances with interatomic distances exceeding 104 a0 have been discovered. We have also observed the Rydberg excitation blockade, crucial for the implementation of quantum phase gates using neutral atoms. The physics behind these observations is attributed to the strong long-range van der Waals interactions among the Rydberg atoms. In addition, we have seen dipole (E1) forbidden but quadrupole (E2) allowed 5s → nd transitions, allowing us to determine the E2 oscillator strengths to these high Rydberg states. Our narrow-band UV pulsed laser system, with ∼100 MHz bandwidth, also allows us to measure the ratios of j-dependent oscillator strengths to the p and d Rydberg states. ^
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.
In this thesis I present several theoretical methods to explore the excitation dynamics of Ultracold Rydberg systems in various regimes. For some applications the details of interactions between Rydberg atoms have to be carefully examined, while for others, the many-body aspect of Rydberg excitation may be crucial. In both cases, the basic prerequisite is to know the interactions sufficiently well. I will review the basic concepts how to evaluate molecular potentials in various Hund's cases and approximations. Long-range Rydberg-Rydberg interactions between Rydberg atoms induce ℓ-mixing which in certain situations gives rise to molecular resonances. For these resonances, we calculate long-range potentials in Hund's case (c) by diagonalization of an interaction matrix. The excitation dynamics of the resonances is always modeled as pair excitation. At high principal quantum number n, the interactions between Rydberg atoms can blockade the excitation of many surrounding atoms in the range of few μm. The atoms within this range are strongly correlated so that many-body treatments are, in general, needed. To describe this blockading effect and other manifestations of the collective behavior of Rydberg excitation, such as the many-body Rabi oscillations, spatial correlations between atoms and the fluctuations of the number of excited atoms, I have used three different approaches. In the mean-field approach the interactions between different atoms is modeled by a distribution of mean-field shifts for which a distribution of probabilities is calculated, A good agreement between the theoretical model and experimental measurements is found. To study the correlations between atoms the many-body wavefunction is numerically computed. The possibility of observing the many-body Rabi oscillations of Rydberg excitation and other aspects of many-body dynamics is analyzed. Although strong interactions cannot be treated perturbatively other expansions may be feasible. I will show that the expansion in powers of the single atom Rabi frequency can be evaluated in the interaction and Heisenberg picture. The expansion is expected to behave well for arbitrary strong interactions. ^