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arXiv:0901.3105 · Physical Review Letters

Prospects for a Millihertz-Linewidth Laser

D. Meiser, Jun Ye, David R. Carlson, Murray Holland

Published Apr 20, 2009• 378 citations
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Abstract

We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultranarrow clock transition into the mode of a high Q resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order 10;{-12} W is possible, sufficient for phase locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by 2 orders of magnitude.

DOI
10.1103/physrevlett.102.163601

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We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultranarrow clock transition into the mode of a high Q resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order 10;{-12} W is possible, sufficient for phase locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by 2 orders of magnitude.
The superradiant laser, based on the clock transition between the electric ground state 1S0{}^{1}{S}_{0}1S0​ and the metastable state 3P0{}^{3}{P}_{0}3P0​ of fermionic alkaline-earth-metal-like atoms, has been proposed to be a new promising light source with linewidth of the order of millihertz. However, due to the small 1S0{}^{1}{S}_{0}1S0​ to 3P0{}^{3}{P}_{0}3P0​ transition strength, the steady-state power in that system is relatively low (approximately ${10}^{\ensuremath{-}12}\phantom{\rule{4pt}{0ex}}\mathrm{W}$). In this work we propose an alternative superradiant laser scheme based on a Raman-transition-induced coupling between the 3P0{}^{3}{P}_{0}3P0​ and 3P1{}^{3}{P}_{1}3P1​ states in bosonic alkaline-earth-metal-like atoms and achieve a laser with narrow linewidth (less than approximately $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}1\phantom{\rule{4pt}{0ex}}\mathrm{Hz}$) and high power (greater than approximately ${10}^{\ensuremath{-}10}\phantom{\rule{4pt}{0ex}}\mathrm{W}$, approximately 103{10}^{3}103 photons in steady state) at a small pumping cost (less than approximately $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$). The Raman beams play two significant roles in our scheme. First, the coherence between the dark and bright states induced by the Raman beams produces a new local minimum in the pumping-linewidth curve with pumping rate lower than $2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}$, which is beneficial for continuous output. Second, the Raman beams mix the long-lived 3P0{}^{3}{P}_{0}3P0​ state into the lasing state and thus make the laser linewidth tunable. Our work greatly improves the output performance of the superradiant laser system with coherence induced by Raman transitions and may offer a firm foundation for its practical use in the future.
Achieving superradiant lasing with an ultranarrow linewidth is crucial for enhancing atomic clock stability in quantum precision measurement. By employing the exceptional point (EP) property of the system, we demonstrate theoretically superradiant lasing with linewidths in the μμμHz range, sustained at the high-power level. This is achieved by incoherently pumping optical lattice clock transitions with ultracold alkaline-earth strontium-87 atoms in the EP of a PT\mathcal{PT}PT-symmetric system. Physically, the atomic coherence reaches a maximum in the EP, significantly amplifying the superradiance effect and resulting in superradiant lasing with an ultranarrow linewidth. This linewidth is even three orders of magnitude smaller than that of superradiant lasing in the systems without EP. Our work extends the realm of superradiant lasing by introducing the EP property, and offers promising applications for developing atomic clocks with exceptional stability and accuracy.
Atoms with narrow-linewidth transition trapped within the Lamb-Dick regime of optical lattice are proposed be used as laser gain medium to build a laser. The gain medium atoms can be the alkaline-earth species, Magnesium, Calcium, and Strontium, including Ytterbium. These atoms possess promising super-narrow optical clock transitions, but here, this clock transition is proposed to be used as the lasing transition of the output laser. This optical lattice laser with expected super-narrow linewidth is an active optical clock with high accuracy and stability.
An ideal superradiant laser on an optical clock transition of noninteracting cold atoms is predicted to exhibit an extreme frequency stability and accuracy far below mHz-linewidth. In any concrete setup sufficiently many atoms have to be confined and pumped within a finite cavity mode volume. Using a magic wavelength lattice minimizes light shifts and allows for almost uniform coupling to the cavity mode. Nevertheless, the atoms are subject to dipole-dipole interaction and collective spontaneous decay which compromises the ultimate frequency stability. In the high density limit the Dicke superradiant linewidth enhancement will broaden the laser line and nearest neighbor couplings will induce shifts and fluctuations of the laser frequency. We estimate the magnitude and scaling of these effects by direct numerical simulations of few atom systems for different geometries and densities. For Strontium in a regularly filled magic wavelength configuration atomic interactions induce small laser frequency shifts only and collective spontaneous emission weakly broadens the laser. These interactions generally enhance the laser sensitivity to cavity length fluctuations but for optimally chosen operating conditions can lead to an improved synchronization of the atomic dipoles.
Laser light with spectral purity and frequency stability is pursued in precision spectroscopy and precision measurements. We propose a scheme to generate millihertz-linewidth laser light with a frequency instability of 10−18 via optical four-wave mixing in alkaline-earth atoms. We show that the linewidth of the mixing laser light is ultimately limited by the natural linewidth of the atomic transition rather than by the linewidth of the input lasers. The frequency stability of the mixing laser light depends largely on the intensity stability of the input lasers. It is possible to generate a millihertz-linewidth laser light with a frequency instability of 10−18 and a power of 10−12 W when the input lasers with a relative intensity instability of 10−4 and a spectral width of 1 Hz interact with strontium (Sr) atoms with a density of 1 × 1011 cm−3.
We propose a superradiant laser based on two-photon Raman transition of caesium-133 atoms which collectively emit photons on an ultra narrow transition into the mode of a low Q resonator known as optical bad-cavity regime. The spin-spin correlation which characterizes the collective effect is demonstrated. We theoretically predict that the optical radiation has an extremely narrow linewidth in the 98 (1) *10-2 mHz range, smaller than the transition itself due to collective effects, and a power level of 7 (1)*10-10 W is possible, which can provide a possible new way to realize an optical clock with a millihertz linewidth.