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Journal of Physics B Atomic Molecular and Optical Physics

Stark-switching technique for fast quantum gates in Rydberg atoms

I. I. Ryabtsev, Denis B. Tretyakov, Ilya I. Beterov

Published Jan 8, 2003• 19 citations
Publisher

Abstract

An experiment on Ramsey interferometry of the 37S 1/2 → 37P 1/2 microwave transition in sodium Rydberg atoms has been performed. Interaction of Rydberg atoms with a cw microwave radiation was effectively controlled by a pulse of weak (<1 V cm −1 ) electric field, that manipulated the transition frequency near 70 050 MHz. The pulse detuned the microwave radiation from exact resonance, and induced additional phases to the wavefunctions of Rydberg states due to the quadratic Stark shifts. As a result, the Ramsey fringes were observable both on scanning the frequency of the microwave field and on scanning the strength of the electric field pulse. The experiment confirmed that this Stark-switching technique provides a fast and effective control of the atom–light interactions, and preserves the atomic coherence. Possible applications of this technique to experiments on quantum computers are discussed.

DOI
10.1088/0953-4075/36/2/310

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•Feb 2, 2004•42 citations
An experiment on Ramsey interferometry of the 37S 1/2 → 37P 1/2 microwave transition in sodium Rydberg atoms has been performed. Interaction of Rydberg atoms with a cw microwave radiation was effectively controlled by a pulse of weak (<1 V cm −1 ) electric field, that manipulated the transition frequency near 70 050 MHz. The pulse detuned the microwave radiation from exact resonance, and induced additional phases to the wavefunctions of Rydberg states due to the quadratic Stark shifts. As a result, the Ramsey fringes were observable both on scanning the frequency of the microwave field and on scanning the strength of the electric field pulse. The experiment confirmed that this Stark-switching technique provides a fast and effective control of the atom–light interactions, and preserves the atomic coherence. Possible applications of this technique to experiments on quantum computers are discussed.
An interaction of microwave radiation with high-excited (Rydberg) atoms has been suggested to be used for radiation detection and measurement of its frequency. Our objective in the present work was to investigate experimentally and theoretically the spectrum of the microwave transition 37P-37S in sodium Rydberg atoms in a weak static electric field and to perform accurate measurements of the scalar and tensor polarizabilities of the 37P level. Knowledge of polarizabilities is required to find a magnitude of energy level shifts in atom by known static electric fields. The Na S and P states possess large quantum defects (1.347 and 0.854, respectively), so that a quadratic Stark effect in weak fields is characteristic for these levels.
A method for quantum interferometry and phase control of degenerate Rydberg states has been proposed and realized experimentally. Phase control was carried out by a pulse of a weak dc electric field which caused a Stark splitting of degenerate Rydberg sublevels for a short time. A strong interference dependence of the probability of the microwave transition ${37P}_{3/2}\ensuremath{\rightarrow}{37S}_{1/2}$ in sodium Rydberg atoms on a phase difference between the Stark sublevels of the 37P3/2{37P}_{3/2}37P3/2​ state has been detected. Changes in the probability were measured directly by a pulsed resonant microwave radiation applied after the electric-field pulse. Records of the quantum interference signals and Stark spectra of the microwave transition are presented and discussed. An influence of the laboratory magnetic field has been analyzed.
Long-range interactions between cold Rydberg atoms are being investigated for neutral-atom quantum computing, quantum simulations, phase transitions in cold Rydberg gases and other applications. Fine tuning of the interaction strength can be implemented using Förster resonances between Rydberg atoms controlled by an electric field. The observation of the Stark-tuned Förster resonances between Rydberg atoms excited by narrowband cw laser radiation requires usage of a Stark-switching technique in order to excite the atoms first in a fixed electric field and then to induce the interactions in a varied electric field, which is scanned across the Förster resonance. The application of the radio-frequency field causes additional Förster resonances between collective states, whose line shape depends on the interaction strengths and time. Spatial averaging over the atom positions in a single interaction volume yields a cusped line shape of the Förster resonance. We present a detailed experimental and theoretical analysis of the line shape and time dynamics of the Stark-tuned Förster resonances Rb( nP 3/2 ) + Rb( nP 3/2 ) → Rb( nS 1/2 ) + Rb([ n + 1] S 1/2 ) for two Rb Rydberg atoms interacting in a time-varying electric field.
Applicability of Rydberg atoms to quantum computers is examined from experimental point of view. In many theoretical proposals appeared recently, excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole-dipole interaction that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase gate have been analyzed. We also present the results of modeling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S-37P and two-photon 37S-38S transitions in an ensemble of a few sodium Rydberg atoms. The microwave spectra were investigated for various final states of the ensemble initially prepared in its ground state. The quantum NOT operation with single atoms was found to be affected by the Doppler effect and fluctuations of the microwave field. The spectrum of full excitation of several Rydberg atoms was much narrower than that of a single atom. This effect might be useful for the high-resolution spectroscopy. The results may be also applied to the studies on collective laser excitation of ground-state atoms aiming to realize quantum gates.
The results of experimental and theoretical investigations of the fine structure of the spectrum of the microwave transition 37 P -37 S in sodium Rydberg atoms in a weak electric field are reported. New data are obtained on the experimental values of the scalar and tensor polarizabilities of the 37 P level. A numerical simulation of the Stark diagram, taking into account the influence of the anticrossings of the Rydberg levels, is performed, and the results are found to be in good agreement with experiment.
Applicability of Rydberg atoms to quantum computers is examined from experimental point of view. In many theoretical proposals appeared recently, excitation of atoms into highly excited Rydberg states was considered as a way to achieve quantum entanglement in cold atomic ensembles via dipole-dipole interaction that could be strong for Rydberg atoms. Appropriate conditions to realize a conditional quantum phase have been analyzed. We also present the results of modeling experiments on microwave spectroscopy of single- and multi-atom excitations at the one-photon 37S-37P and two-photon 37S-38S transitions in an ensemble of a few sodium Rydberg atoms. The microwave spectra were investigated for various final states of the ensemble initially prepared in its ground state. The quantum NOT operation with single atoms was found to be affected by the Doppler effect and fluctuations of the microwave field. The spectrum of full excitation of several Rydberg atoms was found to be much narrower than that of a single atom. This effect might be useful for the high-resolution spectroscopy. The results may be also applied to the studies on collective laser excitation of ground-state atoms aiming to realize quantum gates.