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arXiv:2205.14130 · Physical Review A

Ultimate stability of active optical frequency standards

Georgy A. Kazakov, Swadheen Dubey, Anna A. Bychek, Uwe Sterr, Marcin Bober, M. Zawada

Published Nov 23, 2022• 10 citations
arXivHTMLPDF

Abstract

Active optical frequency standards provide interesting alternatives to their passive counterparts. Particularly, such a clock alone continuously generates highly stable narrow-line laser radiation. Thus, a local oscillator is not required to keep the optical phase during a dead time between interrogations as in passive clocks, but only to boost the active clock's low output power to practically usable levels with the current state of technology. Here we investigate the spectral properties and the stability of active clocks, including homogeneous and inhomogeneous broadening effects. We find that for short averaging times the stability is limited by photon shot noise from the limited emitted laser power and at long averaging times by phase diffusion of the laser output. Operational parameters for best long-term stability were identified. Using realistic numbers for an active clock with $^{87}\mathrm{Sr}$, we find that optimized stability of ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}/\sqrt{\ensuremath{\tau}[\mathrm{s}]}$ is achievable.

DOI
10.1103/physreva.106.053114

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Active optical frequency standards provide interesting alternatives to their passive counterparts. Particularly, such a clock alone continuously generates highly stable narrow-line laser radiation. Thus, a local oscillator is not required to keep the optical phase during a dead time between interrogations as in passive clocks, but only to boost the active clock's low output power to practically usable levels with the current state of technology. Here we investigate the spectral properties and the stability of active clocks, including homogeneous and inhomogeneous broadening effects. We find that for short averaging times the stability is limited by photon shot noise from the limited emitted laser power and at long averaging times by phase diffusion of the laser output. Operational parameters for best long-term stability were identified. Using realistic numbers for an active clock with 87Sr^{87}\mathrm{Sr}87Sr, we find that optimized stability of \ensuremathσy(\ensuremathτ)\ensuremath≈4\ifmmode×\else\texttimes\fi10\ensuremath−18/\ensuremathτ[s]{\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}/\sqrt{\ensuremath{\tau}[\mathrm{s}]}\ensuremathσy​(\ensuremathτ)\ensuremath≈4\ifmmode×\else\texttimes\fi10\ensuremath−18/\ensuremathτ[s]​ is achievable.
Current state-of-the-art frequency standards are passive optical atomic clocks where the frequency of an optical resonator is stabilized to a narrow atomic transition. Passive clocks have achieved unprecedented stabilities of 6.6 x 10--19 over one hour of averaging time [1]. However, they face intrinsic limitations, particularly due to thermal and mechanical fluctuations of the local oscillator. To surpass the limitations of the passive clocks and go beyond the state-of-the-art, the idea of building active optical atomic clocks emerges. These clocks would be optical counterparts of hydrogen masers, with the emitted frequency defined by the atomic transition and therefore inherently stable against cavity instabilities. This paper discusses the latest developments and future prospects in the field of active optical atomic clocks.
Abstract Current state-of-the-art frequency standards are passive optical atomic clocks where the frequency of an optical resonator is stabilized to a narrow atomic transition. Passive clocks have achieved unprecedented stabilities of 6.6 × 10−19 over one hour of averaging time [1]. However, they face intrinsic limitations, particularly due to thermal and mechanical fluctuations of the local oscillator. To surpass the limitations of the passive clocks and go beyond the state-of-the-art, the idea of building active optical atomic clocks emerges. These clocks would be optical counterparts of hydrogen masers, with the emitted frequency defined by the atomic transition and therefore inherently stable against cavity instabilities. This paper discusses the latest developments and future prospects in the field of active optical atomic clocks.
Abstract The atomic clocks, whether operating at optical or microwave region, can be divided into two categories according to their working mode, namely the passive clocks and active clocks. The passive clocks, whose standard frequency is locked to an ultra-narrow atomic spectral line, such as laser cooled Cs beam or lattice trapped Sr atoms, depend on the spontaneous emission line. On the contrary, the active clocks, in which the atoms are used as the gain medium, are based on the stimulated emission radiation, their spectrum can be directly used as the frequency standard. Up to now, the active hydrogen maser has been the most stable microwave atomic clocks. Also, the Sr superradiant active atomic clock is prospects for a millihertz-linewidth laser. Moreover, the optical clocks are expected to surpass the performance of microwave clocks both in stability and uncertainty, since their higher working frequency. The active optical clock has the potential to improve the stability of the best clocks by 2 orders of magnitude. In this work, we introduce the development of active optical clocks, and their types is classified according to the energy-level structure of atoms for stimulated radiation.
Ultra stable frequency references such as the ones used in optical atomic clocks and for quantum metrology may be obtained by stabilizing a laser to an optical cavity that is stable over time. State-of-the-art frequency references are constructed in this way, but their stabilities are currently limited by thermally induced length fluctuations in the reference cavity. Several alternative approaches using the potential for frequency discriminating of highly forbidden narrow atomic transitions have been proposed in, e.g., [1] and [2]. In this proceeding we will present some of the ongoing experimental efforts derived from these proposals, to use cavity-enhanced interaction with atomic 88 Sr samples as a frequency reference for laser stabilization. Such systems can be realized using both passive and active approaches where either the atomic phase response is used as an error signal, or the narrow atomic transition itself is used as a source for a spectrally pure laser. Both approaches shows the promise of being able to compete with the current state of the art in stable lasers and have similar limitations on their ultimately achievable linewidths [1, 2].
High precision portable and deployable frequency standards are required for modern navigation and communication technologies. Optical frequency standards are attractive for their improved stability over their microwave counterparts; however, increased complexities have anchored them in the laboratory. Sacrificing sensitivity of the most stable optical clocks has led to the recent development of deployable and portable optical frequency standards, leveraging hot atomic or molecular vapor. The short term limit for a majority of previous reports on two-photon rubidium standards is either the shot-noise or intermodulation limit hindering the one second fractional frequency stability to around 1×10−13/τ1\times10^{-13}/\sqrtτ1×10−13/τ​. The answer for the shot-noise limit is to increase optical power and collected fluorescence, while the intermodulation limit solution requires improvements in laser linewidth, stimulated Brillouin scattering (SBS) lasers are known to reduce frequency noise, suppressing noise of the pump laser at high offset frequencies. We investigate an optical frequency standard based on the two-photon transition in 87^{87}87Rb probed with a narrow linewidth photonic integrated circuit SBS laser with a quality factor over 130 million and instantaneous linewidth <<< 10 Hz. The use of a narrow linewidth clock laser coupled with operating at higher optical intensities yields clock instabilities of 2×10−142\times10^{-14}2×10−14 at one second, currently the best reported short-term stability for a two-photon rubidium optical frequency standard.
High-precision, portable, and deployable frequency standards are required for modern navigation and communication technologies. Optical frequency standards are attractive for their improved stability over their microwave counterparts; however, increased complexities have anchored them in the laboratory. Sacrificing the sensitivity of the most stable optical clocks has led to the recent development of deployable and portable optical frequency standards, leveraging hot atomic or molecular vapor. The short-term limit for a majority of previous reports on two-photon rubidium standards is either the shot-noise or intermodulation limit hindering the 1 s fractional frequency stability to around 1 × 10 − 13 . The answer for the shot-noise limit is to increase optical power and collected fluorescence, while the intermodulation limit solution requires improvements in laser linewidth, stimulated Brillouin scattering (SBS) lasers are known to reduce frequency noise, suppressing noise of the pump laser. We investigate an optical frequency standard based on the two-photon transition in Rb 87 probed with a narrow photonic integrated circuit SBS laser with a quality factor over 130 million and instantaneous linewidth < 10 Hz . The use of a narrow clock laser coupled with operating at higher optical intensities yielded clock instabilities of 2 × 10 − 14 at 1 s, currently the best reported short-term stability for a two-photon rubidium optical frequency standard.