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Optics Express

Characterisation and feasibility study for superradiant lasing in 40Ca atoms

Anahit L. Gogyan, Georgy A. Kazakov, Marcin Bober, M. Zawada

Published Feb 8, 2020• 17 citations
Publisher

Abstract

Superradiant active clocks operating on narrow linewidth clock transitions are predicted to achieve precision orders of magnitude higher than any currently existing optical atomic clocks. We introduce a theory of superradiant lasing and implement it for the example of 40Ca atoms. The presented model, however, is valid for any two- or three-level system in an optical lattice. We perform a feasibility analysis and suggest a set of parameters for the experimental fulfillment of superradiant lasing in Ca. Moreover, we present an overview of different magic wavelengths for the 4s2 1S0 ↔ 4s4p 3P1 (m J = 0) transition in Ca for different polarizations and a robustness analysis of these magic conditions. We also report the magic-zero wavelengths for the 4s4p 3P1, m J = 0 state.

DOI
10.1364/oe.381991

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Superradiant active clocks operating on narrow linewidth clock transitions are predicted to achieve precision orders of magnitude higher than any currently existing optical atomic clocks. We introduce a theory of superradiant lasing and implement it for the example of 40Ca atoms. The presented model, however, is valid for any two- or three-level system in an optical lattice. We perform a feasibility analysis and suggest a set of parameters for the experimental fulfillment of superradiant lasing in Ca. Moreover, we present an overview of different magic wavelengths for the 4s2 1S0 ↔ 4s4p 3P1 (m J = 0) transition in Ca for different polarizations and a robustness analysis of these magic conditions. We also report the magic-zero wavelengths for the 4s4p 3P1, m J = 0 state.
Active optical atomic clocks operating on narrow linewidth clock transitions based on a superradiant lasing are predicted to achieve precision orders of magnitude higher than any currently existing optical atomic clocks. We introduce a general theory of superradiant lasing and implement it for the examples of Ca and Sr atoms. Our simulations coincide well with the experimental results and explain some features of it. The presented model is valid for any two- and three-level system in an optical lattice.
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.
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.
We demonstrate the state-of-the-art technique of an active clock to provide a continuous superradiant lasing signal using an ensemble of trapped Cs atoms in an optical lattice. A magic wavelength of the proposed $|7{S}_{1/2};F=4,{M}_{F}=0\ensuremath{\rangle}\ensuremath{\rightarrow}|6{P}_{3/2};F=3,{M}_{F}=0\ensuremath{\rangle}$ clock transition in Cs atoms is identified at 1181 nm for constructing the optical lattice. Pertinent optical lines are also found for pumping and repumping atoms from their ground states. A fractional uncertainty about ${10}^{\ensuremath{-}15}$ in the clock frequency has been predicted by carrying out rigorous calculations of several atomic properties. The bad-cavity operational mode of the active clock is anticipated to improve remarkably its short-term stability by suppressing intrinsic thermal fluctuations. Thus, a composite clock system with better short-term and long-term stabilities can be built by combining the proposed active clock with another high-accuracy passive optical clock.
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.