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arXiv:0805.3384 · Optics Letters

Lineshape asymmetry for joint coherent population trapping and three-photon N resonances

Cindy Hancox, Michael Hohensee, Michael Crescimanno, David F. Phillips, Ronald L. Walsworth

Published Jun 26, 2008• 15 citations
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Abstract

We show that a characteristic two-photon lineshape asymmetry arises in coherent population trapping (CPT) and three-photon (N) resonances, because both resonances are simultaneously induced by modulation sidebands in the interrogating laser light. The N resonance is a three-photon resonance in which a two-photon Raman excitation is combined with a resonant optical pumping field. This joint CPT and N resonance can be the dominant source of lineshape distortion, with direct relevance for the operation of miniaturized atomic frequency standards. We present the results of both an experimental study and theoretical treatment of the asymmetry of the joint CPT and N resonance under conditions typical to the operation of an N resonance clock.

DOI
10.1364/ol.33.001536

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We show that a characteristic two-photon lineshape asymmetry arises in coherent population trapping (CPT) and three-photon (N) resonances, because both resonances are simultaneously induced by modulation sidebands in the interrogating laser light. The N resonance is a three-photon resonance in which a two-photon Raman excitation is combined with a resonant optical pumping field. This joint CPT and N resonance can be the dominant source of lineshape distortion, with direct relevance for the operation of miniaturized atomic frequency standards. We present the results of both an experimental study and theoretical treatment of the asymmetry of the joint CPT and N resonance under conditions typical to the operation of an N resonance clock.
In a typical compact atomic time standard a current modulated semiconductor laser is used to create the optical fields that interrogate the atomic hyperfine transition. A pair of optical sidebands created by modulating the diode laser become the coherent population trapping (CPT) fields. At the same time, other pairs of optical sidebands may contribute to other multiphoton resonances, such as three-photon N-resonance [Phys. Rev. A65, 043817 (2002)]. We analyze the resulting joint CPT and N-resonance (hereafter N+CPT) analytically and numerically. Analytically we solve a four-level quantum optics model for this joint resonance and perturbatively include the leading ac Stark effects from the five largest optical fields in the laser's modulation comb. Numerically we use a truncated Floquet solving routine that first symbolically develops the optical Bloch equations to a prescribed order of perturbation theory before evaluating. This numerical approach has, as input, the complete physical details of the first two excited-state manifolds of Rb87. We test these theoretical approaches with experiments by characterizing the optimal clock operating regimes.
We theoretically study the frequency shift in atomic clocks caused by the line-shape asymmetry of coherent population trapping (CPT) resonance in a bichromatic laser field. This asymmetry arises due to the inequality of the resonant spectral components and nonzero one-photon detuning. The line-shape-asymmetry-induced shift depends on the intensity of the resonant fields, which leads to a degradation in long-term stability due to fluctuations of the laser field parameters. A frequency stabilization based on the harmonic modulation of two-photon detuning is considered. It is shown that the use of a high-frequency modulation (compared to the CPT resonance width, i.e., the Pound-Drever-Hall regime) makes it possible to significantly suppress this shift (by one to two orders of magnitude).
Traditional coherent population trapping (CPT) atomic clocks use single circularly polarized coherent multichromatic light to interact with atoms for preparing CPT dark states. While this configuration is simple, it suffers from the trap states and involves only the ±1st-order sidebands in the CPT resonance, excluding the carrier and other sidebands. This results in a lower CPT signal amplitude and higher laser noise, limiting the frequency stability of CPT atomic clocks. To address this issue, we developed and experimentally validated a scheme utilizing left- and right-circularly polarized light based on multiple coherent superpositions. This scheme significantly enhances the amplitude of the CPT resonance. Furthermore, by incorporating a Michelson interferometer, the polarization direction of the ±1st-order sidebands in the coherent multichromatic light is adjusted from parallel to perpendicular, enabling the filtering of one sideband to be detected while eliminating other unwanted sidebands and effectively suppressing laser noise. The results show that, under identical conditions, the short-term frequency stability of this method is theoretically improved by a factor of seven compared to the traditional circularly polarized light scheme, providing an effective pathway for the development of high-performance CPT atomic clocks.
SummaryWe investigated the Ramsey–coherent population trapping (CPT) characteristics of a new observation method that employs different laser sideband combinations as the two interrogation pulses during Ramsey–CPT resonance observation. In an experimental setup using a gas cell containing Cs atoms, Ramsey–CPT resonance was observed using the 1st-1stsideband combination for the common preparation pulse and the 1st-1stand C-2nd sideband combinations for the detection pulse. The Ramsey–CPT spectral shapes were inverted to each other. The light shift characteristic was 2.7 times different to its light sensitivity. This difference in the light shift characteristics is expected to allow the estimation of the light frequency shift in the Ramsey–CPT atomic clock during operation.
We present a joint theoretical and experimental characterization of the coherent population trapping (CPT) resonance excited on the D1{D}_{1}D1​ line of 87Rb^{87}\mathrm{Rb}87Rb atoms by bichromatic linearly polarized laser light. We observe high-contrast transmission resonances (up to $\ensuremath{\approx}25%$), which makes this excitation scheme promising for miniature all-optical atomic clock applications. We also demonstrate cancellation of the first-order light shift by proper choice of the frequencies and relative intensities of the two laser-field components. Our theoretical predictions are in good agreement with the experimental results.
State-of-the-art miniature atomic clocks (MACs) are based on the phenomenon of coherent population trapping (CPT) in alkali-metal atomic vapors (Rb\mathrm{Rb}Rb or Cs\mathrm{Cs}Cs). Improving the stability of the clock frequency is a crucial issue; resolving it would result in significant progress in numerous applications. Here, we examine the configuration of the light field, which is composed of two bichromatic beams with opposing handedness of circular polarization. The beams are in resonance with optical transitions in the Cs\mathrm{Cs}Cs D1{D}_{1}D1​ line ($\ensuremath{\lambda}\ensuremath{\approx}895$ nm). This configuration has previously been shown to produce observed CPT resonances with higher contrast than a standard single-beam scheme; however, our scheme implements pump and probe beams that operate independently, with the transmission of the probe beam being monitored separately. This approach differs from previous studies. The experiments are carried out using a cubic $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\phantom{\rule{0.2em}{0ex}}{\mathrm{mm}}^{3}$ vapor cell filled with buffer gas. It is shown that the line shape of the resonance acquires an asymmetry that can be efficiently controlled by a microwave (Raman) phase between the beams. As a proof of concept, we study the way in which this asymmetry can help to mitigate the influence of the ac Stark (light) shift on the long-term frequency stability of CPT clocks based on vapor microcells ($V\ensuremath{\ll}1\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{3}$). Experimental verification is performed with both a distributed-Bragg-reflector laser and a vertical-cavity surface-emitting laser. The latter is of particular importance for the development of MACs. The experimental results are in qualitative agreement with the analytical theory based on a double-$\mathrm{\ensuremath{\Lambda}}$ scheme of atomic energy levels.