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Physical Review A

Mesoscopic Rydberg ensembles: Beyond the pairwise-interaction approximation

Kelly Cooper Younge, Aaron Reinhard, Thomas Pohl, P. R. Berman, Georg A. Raithel

Published Apr 27, 2009• 65 citations
Publisher

Abstract

We examine state mixing in a dense, cold Rydberg gas. Cold Rb atom clouds in an optical dipole trap are excited into $n{D}_{5/2}$ Rydberg levels using narrow-bandwidth laser pulses. For $n=43$, two atoms excited to $43{D}_{5/2}$ states can be converted to $41{F}_{7/2}$ and $45{P}_{3/2}$ 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 $n{D}_{5/2}$ Rydberg level. Simplified many-body interaction models based on sums over pairwise atomic potentials cannot reproduce the measured mixing fractions.

DOI
10.1103/physreva.79.043420

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Physical Review A•Jun 16, 2014•7 citations
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.
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 ${x}^{\ensuremath{'}}$ states are converted to yyy 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.
We have studied the decay of Rydberg excitations in a cold Rb gas. A 10 ns, pulsed-dye-amplified diode laser excites Rb atoms at $70\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in a magneto-optical trap to nsnsns or npnpnp Rydberg states with principal quantum numbers $26\ensuremath{\le}n\ensuremath{\le}40$. Time-delayed state-selective field ionization is used to directly monitor the population in the initial and neighboring Rydberg levels. The measured time dependence of the Rydberg population is well described by numerical simulations which consider only spontaneous emission and population transfer by blackbody radiation. No evidence for collective decay is found at atom densities up to $3\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. This result is in contrast to a previous study [Wang et al., Phys. Rev. A 75, 033802 (2007)], in which superradiant decay was theoretically predicted and experimentally inferred for atom density and laser focal volume conditions very similar to those considered here. Suppression of collective emission is likely due to variations in transition energies within the atom sample, dominated by inhomogeneities in dipole-dipole exchange interactions for initial sss states, or by a combination of dipole-dipole and electric field inhomogeneities for the initial ppp states.
In this dissertation, I explore several aspects of Rydberg physics with laser spectroscopy. The experiments center around the use of a very deep, cavity-generated, one-dimensional optical lattice in a cold atom sample. The optical lattice produces elongated clouds of dense, cold atoms via dipole trapping and is able to generate extreme light shifts in the atoms due to its high intensity. I describe experiments which may be divided into two main classes. In the first, I use the dipole trap to prepare a dense sample of atoms for photoassociation of Rb atom pairs into diatomic Rydberg molecules. The Rydberg molecules are formed by low-energy scattering of the Rydberg electron of one atom from the other atom, which is a ground-state atom. This novel binding mechanism also has relevance for chemical physics. I present binding energy measurements for eight different cases of Rydberg molecules. The binding energies reveal information about electron-atom collisions, such as their scattering lengths, and about the spin couplings present within the molecular system. In the second class of experiments, I introduce two proposed measurements in which the optical lattice is ramped to very high intensity during the laser excitation, creating AC Stark shifts in the transition frequencies. In one measurement, low-lying atomic states are probed. Measurements of the light shifts are expected to yield data on the dynamic polarizability and the photoionization cross section of the 5D3/2D_{3/2}D3/2​-state in rubidium in a 1064-nm light field. I show corresponding preliminary experimental data. The polarizability and photo-ionization cross-section measurements will provide tests of atomic structure theory, which is important both at a fundamental level and for applications such as atomic clocks. In another proposed measurement, Rydberg atoms in the lattice experience ponderomotive shifts and strong mixing of their angular-momentum states, allowing direct optical excitation of the lattice-mixed high-angular-momentum states. I describe the theoretical basis and experimental preparation for spectroscopically characterizing the lattice-mixed states. The ability to optically excite selected high-angular-momentum states without the use of static or RF fields may be useful for quantum information processing and simulation.
The energy level spectrum of a many-body system containing two shared, collective Rydberg excitations is measured using cold atoms in an optical dipole trap. Two pairs of independently tunable laser pulses are employed to spectroscopically probe the spectrum in a double-resonance excitation scheme. Depending on the magnitude of an applied electric field, the Rydberg-atom interactions can vary from resonant dipole-dipole to attractive or repulsive van der Waals, leading to characteristic signatures in the measured spectra. Our results agree with theoretical estimates of the magnitude and sign of the interactions.
Long-range interactions between cold Rydberg atoms, which are used in many important applications, can be enhanced using F\"orster resonances between collective many-body states controlled by an external electric field. Here we report on the first experimental observation of highly resolved radio-frequency-assisted F\"orster resonances in a few cold Rb Rydberg atoms. We also observed radio-frequency-induced F\"orster resonances which cannot be tuned by a dc electric field. They imply an efficient transition from van der Waals to resonant dipole-dipole interaction due to Floquet sidebands of Rydberg levels appearing in the rf field. This method can be applied to enhance the interactions of almost arbitrary Rydberg atoms with large principal quantum numbers.
We have studied the evolution of Rydberg wave packets in the presence of interatomic dipole-dipole interactions in a frozen Rb gas. Rb atoms in a magneto-optical trap (MOT) are first laser excited to nsnsns Rydberg eigenstates. A picosecond THz pulse further excites them into coherent superposition states involving the initial-level and neighboring npnpnp states. A second, identical, time-delayed THz pulse probes the wave-packet dynamics. As the wave packets evolve they are influenced by dipole-dipole interactions, predominantly pairwise excitation-exchange processes of the form $|s\ensuremath{\rangle}|p\ensuremath{\rangle}\ensuremath{\leftrightarrow}|p\ensuremath{\rangle}|s\ensuremath{\rangle}$. The coherent electronic evolution of the ensemble dephases due to the variation in dipole-dipole coupling strength between atom pairs in the MOT. The experimental results are in good agreement with numerical calculations that simulate the interactions between nearest neighbors in a frozen gas.