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arXiv:2211.06867 · Physical Review A

Coherence-assisted superradiant laser with hertz-level linewidth and 10−10 -W power

Guohui Dong, Yao Yao, Peng Zhang, Dazhi Xu

Published Jun 26, 2023• 5 citations
arXivHTMLPDF

Abstract

The superradiant laser, based on the clock transition between the electric ground state ${}^{1}{S}_{0}$ and the metastable state ${}^{3}{P}_{0}$ 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 ${}^{1}{S}_{0}$ to ${}^{3}{P}_{0}$ 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 ${}^{3}{P}_{0}$ and ${}^{3}{P}_{1}$ 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 ${10}^{3}$ 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 ${}^{3}{P}_{0}$ 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.

DOI
10.1103/physreva.107.063709

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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−12W{10}^{\ensuremath{-}12}\phantom{\rule{4pt}{0ex}}\mathrm{W}10\ensuremath−12W). 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\ensuremathπ\ifmmode×\else\texttimes\fi1Hz2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}1\phantom{\rule{4pt}{0ex}}\mathrm{Hz}2\ensuremathπ\ifmmode×\else\texttimes\fi1Hz) and high power (greater than approximately 10\ensuremath−10W{10}^{\ensuremath{-}10}\phantom{\rule{4pt}{0ex}}\mathrm{W}10\ensuremath−10W, approximately 103{10}^{3}103 photons in steady state) at a small pumping cost (less than approximately 2\ensuremathπ\ifmmode×\else\texttimes\fi10kHz2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{4pt}{0ex}}\mathrm{kHz}2\ensuremathπ\ifmmode×\else\texttimes\fi10kHz). 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\ensuremathπ\ifmmode×\else\texttimes\fi10kHz2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}2\ensuremathπ\ifmmode×\else\texttimes\fi10kHz, 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.
A new class of laser, which harnesses coherence in both light and atoms, is possible with ultracold alkaline-earth-metal atoms trapped in an optical lattice inside an optical cavity. Different lasing regimes, including superradiance, superradiant, and conventional lasing, are distinguished by the relative coherence stored in the atoms and in the cavity mode. We analyze the physics in two different experimentally achievable regions of the superradiant lasing regime. Our calculations confirm the narrow linewidth of superradiant lasing for the doubly forbidden clock transition ${}^{3}{P}_{0}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ of 87Sr^{87}\mathrm{Sr}87Sr atoms. Under strong driving of the dipole-forbidden transition ${}^{3}{P}_{1}\ensuremath{\rightarrow}{}^{1}{S}_{0}$ of 88Sr^{88}\mathrm{Sr}88Sr atoms, the superradiant linewidth narrows further due to the coherent excitation of the cavity field.
A superradiant laser, which exploits the clock transition of alkaline-earth-metal-like atoms to generate ultrastable light in the bad-cavity limit, has garnered much attention in the past few decades. Unlike their odd counterpart, the even isotopes of alkaline-earth-metal-like atoms possess simpler structures and longer-lived transitions, which would relax the field control requirements and enhance the frequency stability of the output light. However, due to the absence of hyperfine interaction in even isotopes, the transition from the state 3 P 0 to 1 S 0 is strictly forbidden, leading to a vanishing coupling strength between the cavity mode and the atoms (the state 3 P 0 as a dark state). In this work, we suggest a superradiant laser scheme by dressing this dark state with a small bright component by virtue of a static magnetic field. In contrast to other proposals utilizing natural atomic transitions, our dressed-state protocol can work from the crossover regime (coherence in both atoms and photons) to the superradiant lasing regime (coherence solely in atoms). Specifically, by operating deep into the superradiant lasing regime, our scheme witnesses a dramatic line-narrowing feature (mHz level) while maintaining its power. Furthermore, compared to the crossover regime, the laser frequency in the superradiant lasing regime is more robust against the fluctuations of the cavity length and magnetic field strength. Our proposal demonstrates the potential for extracting ultranarrow light from even isotopes of the alkaline-earth-metal-like atoms and may find its role in frequency stabilization and related precision measurement scenarios.
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the 3P1^{3}P_{1}3P1​ state into the long-living metastable state 3P0^{3}P_{0}3P0​, thus enabling the strictly forbidden $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ ``clock'' transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional ``state-mixing'' wave, including estimations of the ``magic'' wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.
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.
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.
Today's narrowest linewidth lasers are limited by mirror motion in the reference optical resonator used to stabilize the laser's frequency.Recent proposals suggest that superradiant lasers based on narrow dipoleforbidden transitions in cold alkaline earth atoms could offer a way around this limitation.Such lasers operating on transitions with linewidth of order mHz are predicted to achieve output spectra orders of magnitude narrower than any currently existing laser.As a step towards this goal, we demonstrate and study a laser based on the 7.5-kHz linewidth dipole-forbidden 3 P 1 to 1 S 0 transition in laser-cooled and tightly confined 88 Sr.We can operate this laser in the bad-cavity or superradiant regime, where coherence is primarily stored in the atoms, or continuously tune to the more conventional good-cavity regime, where coherence is primarily stored in the light field.We show that the cold-atom gain medium can be repumped to achieve quasi-steady-state lasing.We also demonstrate up to an order of magnitude suppression in the sensitivity of laser frequency to changes in cavity length, verifying a key feature of the proposed narrow linewidth lasers.