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arXiv:quant-ph/0701153 · Physical Review A

Effect of finite detection efficiency on the observation of the dipole-dipole interaction of a few Rydberg atoms

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

Published Jul 31, 2007• 23 citations
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Abstract

We have developed a simple analytical model describing multiatom signals that are measured in experiments on dipole-dipole interaction at resonant collisions of a few Rydberg atoms. It has been shown that finite efficiency of the selective field-ionization detector leads to the mixing up of the spectra of resonant collisions registered for various numbers of Rydberg atoms. The formulas which help to estimate an appropriate mean Rydberg atom number for a given detection efficiency are presented. We have found that a measurement of the relation between the amplitudes of collisional resonances observed in the one- and two-atom signals provides a straightforward determination of the absolute detection efficiency and mean Rydberg atom number. We also performed a testing experiment on resonant collisions in a small excitation volume of a sodium atomic beam. The resonances observed for 1--4 detected Rydberg atoms have been analyzed and compared with theory.

DOI
10.1103/physreva.76.012722

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We have developed a simple analytical model describing multiatom signals that are measured in experiments on dipole-dipole interaction at resonant collisions of a few Rydberg atoms. It has been shown that finite efficiency of the selective field-ionization detector leads to the mixing up of the spectra of resonant collisions registered for various numbers of Rydberg atoms. The formulas which help to estimate an appropriate mean Rydberg atom number for a given detection efficiency are presented. We have found that a measurement of the relation between the amplitudes of collisional resonances observed in the one- and two-atom signals provides a straightforward determination of the absolute detection efficiency and mean Rydberg atom number. We also performed a testing experiment on resonant collisions in a small excitation volume of a sodium atomic beam. The resonances observed for 1--4 detected Rydberg atoms have been analyzed and compared with theory.
We have developed a simple theoretical model describing multi-atom signals that could be measured in experiments on resonant energy transfers in an ensemble of a few Rydberg atoms. We have shown that an efficiency of the selective field-ionization detector, which is less than 1, leads to the mixing up of the spectra of the resonant energy transfer registered for various numbers of detected Rydberg atoms. This may impede the possible observations of dipole blockade or coherent two-atom interaction required to perform basic quantum gates. The formulae are presented, which help to estimate an actual mean Rydberg atom number in an excitation volume per one exciting laser pulse at a given detection efficiency. We have also found that a measurement of relationship of the amplitudes of resonances observed in the one- and two-atom signals provides a straightforward determination of the absolute detection efficiency and actual mean Rydberg atom number. This novel method is advantageous as it is independent of the specific experimental conditions. We also performed a testing experiment on the resonant energy transfers in a small excitation volume of the velocity selected Na atomic beam. The observed one- and two-atom resonances were analyzed and compared with the theoretical predictions. A good agreement between experiment and theory in the width and amplitudes of the resonances has confirmed the validity of simple approximations used in the developed theoretical model.
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.
This paper reports on the results of experiments with cold rubidium Rydberg atoms in a magneto-optical trap. The specific feature of the experiments is the excitation of Rydberg atoms in a small volume within a cloud of cold atoms and the sorting of measured signals and spectra according to the number of detected Rydberg atoms. The effective lifetime of the 37 P Rydberg state and its polarizability in a weak electric field are measured. The results obtained are in good agreement with theoretical calculations. It is demonstrated that the localization of the excitation volume in the vicinity of the zero-magnetic-field point makes it possible to improve the spectral resolution and to obtain narrow microwave resonances in Rydberg atoms without switching off the quadrupole magnetic field of the trap. The dependence of the amplitude of dipole-dipole interaction resonances in Rydberg atoms on the number of atoms is measured. This dependence exhibits a linear behavior and agrees with the theory for a weak dipole-dipole interaction.
A careful numerical solution of the equations of the two-state theory of resonant collisions is presented. The particular process investigated is that of collisions of two sodium atoms in Rydberg states in the presence of a weak static electric field for which measurements have been carried out recently. Dipole-dipole interaction between the atoms is assumed as the interaction responsible for the transition. Comparison between calculations and experiments yields only moderately good agreement, this being ascribed mainly to simplifications adopted within the theoretical model.
We have studied the collisional energy transfer process K (ns) +K (n-2) d {yields} K (np) +K (n-1) p which is tuned into resonance with an applied static electric field. The initial Rydberg states are excited stepwise with two dye laser pulses. The resonant energy transfer is detected by selectively field ionizing the final K(np) state as the static field is swept over many laser shots. Due to fine structure splitting of the d and p levels 45 resonances are energetically allowed at n{sub s}=25. The actual number of resonances that are observed depends on the polarization of the laser light, the dipole-dipole selection rules, and the n state excited. Above n{sub s}=29 all resonances are energically forbidden. We have measured the position of the resonances in electric field from n{sub s}=25 to n{sub s}=29 and found them to be in good agreement with calculated positions.