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Quantum Electronics

Effect of dipole blockade on the laser excitation spectra of mesoscopic ensembles of cold Rydberg atoms

I. I. Ryabtsev, Ilya I. Beterov, Denis B. Tretyakov, Elena A. Yakshina, Vasily M. Entin

Published May 8, 2019• 3 citations
Publisher

Abstract

Abstract The results of theoretical calculations of the multiatom laser excitation spectra of Rydberg atoms under conditions of a dipole blockade are presented, and the effect of the laser radiation line width and the interaction energy of Rydberg atoms on the dipole blockade completeness degree is discussed. It is shown that in order to increase the fidelity of performing quantum gates based on a dipole blockade, it is necessary to use resonance dipole − dipole interaction and exciting laser radiation with a line width smaller than 10 kHz.

DOI
10.1070/qel17003

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Abstract The results of theoretical calculations of the multiatom laser excitation spectra of Rydberg atoms under conditions of a dipole blockade are presented, and the effect of the laser radiation line width and the interaction energy of Rydberg atoms on the dipole blockade completeness degree is discussed. It is shown that in order to increase the fidelity of performing quantum gates based on a dipole blockade, it is necessary to use resonance dipole − dipole interaction and exciting laser radiation with a line width smaller than 10 kHz.
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 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.
Results of numerical Monte Carlo simulations for the Stark-tuned $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster resonance and dipole blockade between two to five cold rubidium Rydberg atoms in various spatial configurations are presented. The effects of the atoms' spatial uncertainties on the resonance amplitude and spectra are investigated. The feasibility of observing coherent Rabi-like population oscillations at a $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster resonance between two cold Rydberg atoms is analyzed. Spectra and the fidelity of the Rydberg dipole blockade are calculated for various experimental conditions, including nonzero detuning from the $\mathrm{F}\stackrel{\mathrm{\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}}}{\mathrm{o}}$rster resonance and finite laser linewidth. The results are discussed in the context of quantum-information processing with Rydberg atoms.
High resolution laser Stark excitation of np (60<n<85) Rydberg states of ultracold cesium atoms shows an efficient blockade of the excitation attributed to long-range dipole-dipole interaction. The dipole blockade effect is observed as a quenching of the Rydberg excitation depending on the value of the dipole moment induced by the external electric field. Effects of ions which could match the dipole blockade effect are discussed in detail but are ruled out for our experimental conditions. Analytic and Monte Carlo simulations of the excitation of an ensemble of interacting Rydberg atoms agree with the experiments and indicate a major role of the nearest neighboring Rydberg atom.
Summary form only given. Interactions between neutral atoms are generally weak, but exciting these atoms in a Rydberg state considerably enhances their interaction through a long-range dipole-dipole potential. An interesting application of this dipole-dipole interaction is the dipole blockade in Rydberg excitation. This effect offers exciting possibilities for manipulating quantum bits stored in a single collective excitations in mesoscopic ensembles, or for realizing scalable quantum logic gate. The dipole blockade effect has been demonstrated in atomic ensembles by different groups, and recently also with two independently trapped atoms, which shows the possibility of creating entangle states and quantum logic gates. To extend and continue these results with more atoms, a promising method is to use atoms trapped in an optical lattice in the Mott insulator phase. To excite atoms into a Rydberg state, and to control the interactions and the dipole blockade, a high resolution laser scheme is needed. We use a two-photon excitation scheme 5s1/2rarr 6p3/2rarr ns or nd. The first step, at 420 nm, is realized by doubling a MOPA laser, with the second step at ~ 1000 nm. Both lasers are locked to a Fabry-Perot cavity, and the total excitation bandwidth is less than 3 MHz. After the excitation into the Rydberg state, we apply a pulsed electric field to ionize and detect the Rydberg atoms with an ion detector. To characterize and improve the efficiency of our ion detection, we have explored the direct ionization of ultracold atoms in a magneto-optical trap, or in a Bose-Einstein condensate. This calibration will allows us to characterize precisely the Rydberg excitation and to monitor its time evolution. First results on the Rydberg excitation of ultracold atoms in dipole traps and optical lattices will be presented. The prospect for creating Rydberg excitations inside a Mott insulator will also be discussed.
The spectra of three-photon laser excitation (according to the 5 S 1/2 → 5 P 3/2 → 6 S 1/2 → 37 P 3/2 scheme) of mesoscopic ensembles of cold Rb Rydberg atoms in a magneto-optical trap, using cw single-frequency lasers in each stage, have been investigated. The ensembles consisted of 1 to 5 atoms, and their presence was recorded by the selective field ionisation method with postselection according to the number of atoms. The dependence of the spectral shape on the excitation laser pulse duration has been studied. For 2-μs pulses, the minimum spectral width was found to be 1.3 MHz; it was determined by the laser linewidth and the spectral width of laser pulse. For pulses shorter than 0.5 μs, additional spectral broadening and occurrence of Rabi oscillations in the wings of three-photon resonances have been observed, a fact indicative of implementation of coherent three-photon laser excitation of Rydberg atoms. An analysis of the spectra within the four-level theoretical model based on optical Bloch equations showed good agreement between the experimental and theoretical results. The dependence of the shape of three-photon excitation spectrum on the number of recorded atoms was also studied. An increase in the average number of atoms leads to the occurrence of a dip in the single-atom excitation spectra; this dip is due to the specificity of the excitation and detection statistics of Rydberg atoms. The results obtained are important for applications of Rydberg atoms in quantum informatics.