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arXiv:1110.0576 · Physical Review A

Doppler- and recoil-free laser excitation of Rydberg states via three-photon transitions

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

Published Nov 11, 2011• 79 citations
arXivHTMLPDF

Abstract

Three-photon laser excitation of Rydberg states by three different laser beams can be arranged in a starlike geometry that simultaneously eliminates the recoil effect and Doppler broadening. Our analytical and numerical calculations for a particular laser excitation scheme $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}6{S}_{1/2}\ensuremath{\rightarrow}nP$ in Rb atoms have shown that, compared to the one- and two-photon laser excitation, this approach provides much narrower linewidth and longer coherence time for both cold atom samples and hot vapors, if the intermediate one-photon resonances of the three-photon transition are detuned by more than respective single-photon Doppler widths. This method can be used to improve fidelity of Rydberg quantum gates and precision of spectroscopic measurements in Rydberg atoms.

DOI
10.1103/physreva.84.053409

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Three-photon laser excitation of Rydberg states by three different laser beams can be arranged in a starlike geometry that simultaneously eliminates the recoil effect and Doppler broadening. Our analytical and numerical calculations for a particular laser excitation scheme 5S1/2\ensuremath→5P3/2\ensuremath→6S1/2\ensuremath→nP5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}\ensuremath{\rightarrow}6{S}_{1/2}\ensuremath{\rightarrow}nP5S1/2​\ensuremath→5P3/2​\ensuremath→6S1/2​\ensuremath→nP in Rb atoms have shown that, compared to the one- and two-photon laser excitation, this approach provides much narrower linewidth and longer coherence time for both cold atom samples and hot vapors, if the intermediate one-photon resonances of the three-photon transition are detuned by more than respective single-photon Doppler widths. This method can be used to improve fidelity of Rydberg quantum gates and precision of spectroscopic measurements in Rydberg atoms.
The common approach for producing Rydberg atoms in warm vapor cells is with lasers arranged in a counterpropagating, collinear configuration. Doppler effects in these configurations reduce the efficiency of excitation to the Rydberg state while also producing broadened spectral features. In this work, we demonstrate a three-laser Doppler-free excitation using laser beams whose k vectors sum to 0, resulting in an enhancement in the Rydberg density and narrowed spectral features. A three-times enhancement to Rydberg density along with a near four-times reduction in spectroscopic linewidths are observed compared to a collinear configuration. This Doppler-free configuration could prove beneficial to Rydberg atomic technologies, such as electric field sensing with small volumes or deterministic photon sources.
The spectra of the three-photon laser excitation 5 S 1/2 → 5 P 3/2 → 6 S 1/2 nP of cold Rb Rydberg atoms in an operating magneto-optical trap based on continuous single-frequency lasers at each stage are studied. These spectra contain two partly overlapping peaks of different amplitudes, which correspond to coherent three-photon excitation and incoherent three-step excitation due to the presence of two different ways of excitation through the dressed states of intermediate levels. A four-level theoretical model based on optical Bloch equations is developed to analyze these spectra. Good agreement between the experimental and calculated data is achieved by introducing additional decay of optical coherence induced by a finite laser line width and other broadening sources (stray electromagnetic fields, residual Doppler broadening, interatomic interactions) into the model.
This thesis presents a method for calculating the absorption of diode lasers in one-photon, two-photon and (Doppler-free) three-photon excitation configurations. The specific three-photon system studied is atomic Rb, 5s1/2 -5p3/2 - 5d5/2 -np. In principle, three-photon excitation allows for perfect compensation of the Doppler effect. The approach of the method is to construct density matrix equations and solve for the steady state density matrix elements. Solutions are obtained numerically. There is no weak intensity restriction for any laser in the excitation system, and the absorption of all the lasers in the excitation system can be evaluated. \n \nThe design and testing of a low-noise transimpedance amplifier for measuring absorption is presented.
We demonstrate coherent Doppler-free three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ optical clock transition and the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ intercombination transition in free-space thermal clouds of 88Sr^{88}\mathrm{Sr}88Sr atoms. By appropriate orientation of the wave vectors of three lasers incident on the atoms, the first-order Doppler shift can be eliminated for all velocity classes. Three-photon excitation of the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transition enables high-contrast Ramsey spectroscopy with interrogation times comparable to the $21\phantom{\rule{0.16em}{0ex}}\textmu{}\mathrm{s}$ natural lifetime using a single near-resonant laser source. Three-photon spectroscopy on the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ clock transition, using only laser frequencies nearly resonant with the $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{0}$ and $^{1}S_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\leftrightarrow}\phantom{\rule{0.16em}{0ex}}^{3}P_{1}$ transitions, enables a reduction in Doppler broadening by two orders of magnitude and a corresponding $\ensuremath{\sim}470\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}$ linewidth without a confining potential.
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.
Three-photon laser excitation of single rubidium atoms in an optical dipole trap (ODT) into the37P Rydberg state by laser radiation with wavelengths of 780, 1367, and 743 nm has been experimentally demonstrated. The excitation to Rydberg states is detected by an optical method using the losses of atoms in the ODT. The laser excitation spectra of single Rydberg atoms in the ODT are recorded, and the dependence of the excitation probability on the laser pulse duration is measured. The measured spectrum width was 2MHz. Experiments on fluorescence quenching spectroscopy of a cloud of cold atoms in a magneto-optical trap during the three-photon laser excitation of atoms to Rydberg states are also carried out. The experimental results are compared with a numerical calculation. Methods for increasing the accuracy of the coherent three-photon laser excitation of Rydberg atoms in the ODT are considered.