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arXiv:0705.3565 · Physical Review Letters

Terahertz Frequency Standard Based on Three-Photon Coherent Population Trapping

C. Champenois, G. Hagel, M. Houssin, Martina Knoop, C. Zumsteg, F. Vedel

Published Jul 6, 2007• 24 citations
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Abstract

A scheme for a terahertz frequency standard based on three-photon coherent population trapping in stored ions is proposed. Assuming the propagation directions of the three lasers obey the phase matching condition, we show that stability of few 10(-14) at 1 s can be reached with a precision limited by power broadening to 10(-11) in the less favorable case. The referenced terahertz signal can be propagated over long distances, the useful information being carried by the relative frequency of the three optical photons.

DOI
10.1103/physrevlett.99.013001

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A scheme for a terahertz frequency standard based on three-photon coherent population trapping in stored ions is proposed. Assuming the propagation directions of the three lasers obey the phase matching condition, we show that stability of few 10(-14) at 1 s can be reached with a precision limited by power broadening to 10(-11) in the less favorable case. The referenced terahertz signal can be propagated over long distances, the useful information being carried by the relative frequency of the three optical photons.
The authors significantly extend the optical technique of coherent population trapping (CPT) using three photons, based on a dark resonance of trapped Ca+{}^{+}+ ions. CPT with three photons is an important approach for high-precision measurements, as it opens up the use of large ensembles of trapped ions, rather than individual atoms. Furthermore, an atomic terahertz frequency reference based on three visible lasers can be derived from this technique. Terahertz spectroscopy is a rapidly growing field with a host of applications, and recent studies point to a clear need for frequency standards in this range.
Stringent conditions on the phase relation of multiple photons are a prerequisite for novel protocols of high-resolution coherent spectroscopy. In a recent experiment, we have implemented an interrogation process of a Ca+-ion cloud based on three-photon coherent population trapping, with the potential to serve as a frequency reference in the THz range. This high-resolution interrogation has been made possible by phase-locking both laser sources for cooling and repumping of the trapped ions to a clock laser at 729 nm by means of an optical frequency comb. The clock laser, a titanium-sapphire laser built in our lab locked onto two high-finesse cavities reaches a linewidth of a few Hertz and a frequency stability below 10−14 at 1 s, performances which can be copied onto the two other sources. In this paper, we discuss the performances of the phase transfer between the three involved lasers via the optical frequency comb.
We present a microwave frequency standard based on coherent population trapping (CPT) in the 87Rb D1 line. The CPT spectrum is obtained using two Raman lasers with a 6.8 GHz frequency offset by injection locking of a master laser to a slave laser. We have constructed an atomic clock employing a 5 cm long Rb vapor cell confined with 6.67 kPa neon buffer gas at 70 °C. Using this system, we improve the CPT contrast through the elimination of undesired off-resonant fields created by the direct modulation method. We measured the frequency shift of the CPT signal as a function of the temperature of the Rb cell and estimated it to be approximately 1.3 ×10−9/K. The frequency of a 10 MHz crystal oscillator has been stabilized to the CPT spectrum between the two ground states in 87Rb. The relative frequency stability is approximately 2.3×10−12 for an average time of 68 s.
An all-optical microwave frequency standard based on coherent population trapping (CPT) in 85Rb is developed. The CPT resonances are detected by an ordinary edge-emitting diode laser in a simple optical setup. A buffer-gas mixture is carefully optimized to yield a narrow linewidth and a reduced temperature dependence of the resonance frequency. With the developed system we are able to measure ultranarrow optically induced hyperfine CPT resonances at <20 Hz, which is in good agreement with the linewidth calculated from experimental parameters. The frequency of an RF-signal generator has been stabilized to the CPT resonance between the two mF=0 magnetic sublevels. The relative frequency stability (square root of Allan variance) follows a slope of 3.5×10-11 τ-1/2(1 s<τ<2000 s). The best stability of 6.4×10-13 is reached at an integration time of τ=2000 s. This stability is sufficient for many high-precision applications. Frequency-shift measurements were made to evaluate the frequency dependencies on the operation parameters.