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Physical Review A

Spatial correlations between Rydberg atoms in an optical dipole trap

Andrew Schwarzkopf, David Alexander Anderson, Nithiwadee Thaicharoen, Georg A. Raithel

Published Dec 23, 2013• 53 citations
Publisher

Abstract

We use direct spatial ion imaging of cold ${}^{85}$Rb Rydberg atom clouds to measure the Rydberg-Rydberg correlation function, with and without light-shift potentials generated by an optical dipole trap. We find that the blockade radius depends on laser detunings and spatially varying light shifts. At certain laser detunings the probability of exciting Rydberg atoms at particular separations is enhanced, which we interpret to be a result of direct two-photon excitation of Rydberg atom pairs. The results are in accordance with predictions [F. Robicheaux and J. V. Hern\'andez, Phys. Rev. A 72, 063403 (2005)] and a model we develop that accounts for a one-dimensional dipole-trap potential.

DOI
10.1103/physreva.88.061406

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Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.

•Jan 1, 2018•0 citations
We use direct spatial ion imaging of cold 85{}^{85}85Rb Rydberg atom clouds to measure the Rydberg-Rydberg correlation function, with and without light-shift potentials generated by an optical dipole trap. We find that the blockade radius depends on laser detunings and spatially varying light shifts. At certain laser detunings the probability of exciting Rydberg atoms at particular separations is enhanced, which we interpret to be a result of direct two-photon excitation of Rydberg atom pairs. The results are in accordance with predictions [F. Robicheaux and J. V. Hern'andez, Phys. Rev. A 72, 063403 (2005)] and a model we develop that accounts for a one-dimensional dipole-trap potential.
When cold atoms are laser-excited to Rydberg states, the strong interactions between Rydberg excitations can lead to complex many-body entanglement in the system. The excitation process results in spatial correlations between excitations in the system. In most cases, Rydberg excitation positions are anticorrelated such that no two excitations are within a "blockade radius" of each other. Such systems are well-suited for studying basic many-body physics, as well as for future technological applications such as quantum computation. This thesis describes an experimental apparatus we constructed to perform spatially-sensitive detection of Rydberg atoms. We use the apparatus to perform measurements of the Rydberg-Rydberg pair-correlation function. This results in the first direct spatial images of the Rydberg blockade effect. We measure the blockade radius for a variety of S and D Rydberg states in rubidium. We investigate the dependence of the blockade radius on laser detunings and energy level shifts induced by optical potentials due to trapping lasers. Our results have some implications for atom traps used for neutral atom quantum computation. We also present simulations results used to characterize the performance of the imaging system.
Creating ultracold Rydberg atoms in lattices imprinted with a spatial light modulator offers the possibility to simulate quantum processes. Strong dipole forces between Rydberg atoms provide the required correlations between lattice sites. With a high ground-state atomic density per lattice site, blockade phenomenon may induce single Rydberg atom occupancy per lattice site. Readout of resulting patterns requires single-atom detection with spatial resolution. The grand challenge is to create systems of interacting Rydberg atoms with scalability. So far, we have achieved spatial imaging of Rydberg atoms using ion optics and incorporated in-vacuo aberration correction for imprinted light patterns. Presently, we are studying the effect of dipole blockade on Rydberg excitation statistics. For this we have set up a tuneable Rydberg excitation laser system using an ultra stable reference. Measurements of spatial correlation functions show that achieving a blockade radius of 10 μm is possible. Combined with a dark-spot MOT, this is sufficient to achieve precisely one Rydberg atom per lattice site.
Abstract The dipole blockade effect at laser excitation of mesoscopic ensembles of Rydberg atoms lies in the fact that the excitation of one atom to a Rydberg state blocks the excitation of other atoms due to the shift in the collective energy levels of interacting Rydberg atoms. It is used to obtain the entangled qubit states based on single neutral atoms in optical traps. In this paper, we present our experimental results on the observation of the dipole blockade for mesoscopic ensembles of 1–5 atoms when they are detected by the selective field ionization method. We have investigated the spectra of the three-photon laser excitation 5S1/2 → 5P3/2 → 6S1/2 → nP3/2 of cold Rydberg Rb atoms in a magneto-optical trap. We have found that for mesoscopic ensembles this method allows only a partial dipole blockage to be observed. This is most likely related to the presence of parasitic electric fields reducing the interaction energy of Rydberg atoms, the decrease in the probability of detecting high states, and the strong angular dependence of the interaction energy of Rydberg atoms in a single interaction volume.
We develop a theory of the transverse spatial dynamics of two interacting photons in a Rydberg nonlinear medium. Extending the well-studied one-dimensional case, we explore both longitudinal and transverse correlations of photons propagating as Rydberg polaritons. We identify distinct behaviors and scaling laws for these correlations, arising from fundamentally different mechanisms in the two directions: diffraction for transverse correlations and diffusion for longitudinal correlations. We develop a model incorporating a Gaussian optical beam and an inhomogeneous atomic density distribution, from which we derive quantitative predictions for correlation functions in both directions. We further show that the propagation equations can be reduced to a single Schrödinger-like equation, allowing approximate solutions that are supported by full numerical results. Our findings indicate that the transverse correlation length is determined primarily by the blockade radius, whereas the longitudinal correlation length is limited by bandwidth. These results establish transverse Rydberg blockade as a distinct and measurable correlation mechanism and show that spatial photon correlations provide a direct means of measuring the blockade radius.
Rydberg atoms, i.e. atoms with one or more highly excited electrons, show exaggerated properties compared to ground state atoms. For example, their energy levels are very sensitive to external electric fields (Stark effect) and they exhibit strong interatomic interactions, which can lead to a suppression of excitation known as the Rydberg blockade. The latter property makes Rydberg atoms promising candidates for quantum simulation and quantum computing. This work describes the direct observation of the excitation blockade for highly Stark-shifted Rydberg atoms induced by controllable dipole-dipole interactions. We investigate the electric field region around and above the classical ionization threshold, which is typically not considered suitable for blockade experiments. We excite Rydberg atoms in the energy region corresponding to the unperturbed 43S1/2 state at electric fields around 127V/cm out of a magneto-optically trapped cloud of 87Rb atoms with a temperature of 150 μK. We tune the dipole-dipole interaction by the applied electric field thus changing the electric dipole moment of the excited state. The position of the Rydberg atoms is detected by ionization and subsequent ion imaging; the controlled ionization of the atoms is achieved by adiabatic transfer of the Rydberg state to an ionizing state. For the spatially resolved detection of the atoms, a high resolution ion microscope for cold atoms has been developed and experimentally characterized. It features a maximum magnification of 1000 and sub-micrometer spatial resolution. A theoretical treatment of highly Stark-shifted Rydberg states is developed introducing a complex absorbing potential. It is capable of predicting the ionization rates of the Rydberg states for a wide range of electric fields and energies with only one free parameter. Together with the numerical calculations, measurements of the ionization spectra for different Rydberg states are presented. The 43S1/2 state is measured in an electric-field range from 125V/cm to 165V/cm (classical ionization limit 127V/cm), the 70S1/2 state in an electric-field range from 15V/cm to 35V/cm (classical ionization limit 16.1V/cm) and the 100S1/2 state in an electric-field range from 7V/cm to 19V/cm (classical ionization limit 3.7V/cm). Our results show an intricate energy level structure with broad, strongly ionizing states as well as sharp, nearly non-ionizing states. The numerical calculations are also used for the prediction of selective field ionization spectra and the results are used to identify Förster resonances in the Stark spectrum of the 45D5/2 state. Complementary to the spatially resolved measurements in high electric fields, the Rydberg blockade effect is also observed via the excitation number statistics at Förster resonances.