Optical Frequency Standards Research Articles

Continuous GPS PPP-AR frequency transfer links

Abstract In this paper, we show that the SPARK software of the Natural Resources Canada (NRCan) with their DCR (Decoupled Clock Rapid) products can be used to generate the PPP-AR continuous batch clock solutions of multiple days, which we use to build frequency transfer links between two remotely located GPS receivers. The reliability and confidence in forming the long-term frequency transfer links have been improved compared to reference~\cite{jian2023gps}. We compare the SPARK PPP-AR links to an optical fiber and TWSTFT links for hundreds of days. The ∽500-day-long comparisons with TWSTFT show no frequency bias for continental and cross-continental links. Frequency transfer links formed using the SPARK solutions have uncertainty of 1×10-15/T, where T is in days, without reaching the noise floor, a critical requirement for comparing optical frequency standards and for the redefinition of the SI second. The short latency of the NRCan DCR products enables the quick availability of the PPP-AR links presented in this paper marking it particularly relevant for time sensitive applications.

Dual-frequency optical-microwave atomic clocks based on cesium atoms

133Cs, the only stable cesium (Cs) isotope, is one of the most investigated elements in atomic spectroscopy and was used to realize the atomic clock in 1955. Among all atomic clocks, the cesium atomic clock has a special place, since the current unit of time is based on a microwave transition in the Cs atom. In addition, the long lifetime of the 6P3/2 state and simple preparation technique of Cs vapor cells have great relevance to quantum and atom optics experiments, which suggests the use of the 6S−6P D2 transition as an optical frequency standard. In this work, using one laser as the local oscillator and Cs atoms as the quantum reference, we realize two atomic clocks at the optical and microwave frequencies. Both clocks can be freely switched or simultaneously output. The optical clock, based on the vapor cell, continuously operated with a frequency stability of 3.9×10−13 at 1 s, decreasing to 2.2×10−13 at 32 s, which was frequency-stabilized by modulation transfer spectroscopy and estimated by an optical comb. Then, applying this stabilized laser to an optically pumped Cs beam atomic clock to reduce the laser frequency noise, we obtained a microwave clock with a frequency stability of 1.8×10−12/τ, reaching 6×10−15 at 105 s. This study demonstrates an attractive feature for the commercialization and deployment of optical and microwave clocks, and will guide the further development of integrated atomic clocks with better stability. Therefore, this study holds significant practical implications for future applications in satellite navigation, communication, and timing.

Composite Raman-Nath heterodyne interferometry with relevance for precise spectroscopy

Atomic state manipulation by laser radiation requires a stringent control of the light phase noise for precise spectroscopy and quantum computation. In this work we describe a novel interferometer recently employed to estimate the phase noise induced by an optical frequency shifter based on serrodyne modulation for optical frequency standards (Barbiero et al., 2023). The interferometer is generated by an acousto-optic actuator working in the Raman-Nath regime. Using the heterodyne detection between the unshifted optical mode with the first higher order optical components, we are able to detect the differential phase between the two optical path arms with a reduction of the phase noise induced by the actuator. We provide a theoretical treatment for the actuator phase suppression and we estimate the detectable phase noise limit of this interferometer. Finally, we discuss the possible applications in the field of precision measurements.

Optical Frequency References at 1542 nm: Precision Spectroscopy of the R(106)50-0, R(100)49-0, R(84)47-0, R(59)45-0, P(82)47-0, and P(71)46-0 Lines of 127I2 at 514 nm

Frequency-stabilized lasers are fundamental topics in research relating to optical frequency and wavelength standards. The absolute frequencies and hyperfine structures of the R(106)50-0, R(100)49-0, R(84)47-0, R(59)45-0, P(82)47-0, and P(71)46-0 lines of molecular iodine (127I2) at 514 nm were measured using a frequency-stabilized laser based on modulation transfer spectroscopy. The hyperfine splitting of each line was fitted to a four-term Hamiltonian with an uncertainty of several kilohertz to obtain the hyperfine constants for the line. A total of 97 hyperfine transitions of the six lines were measured with an uncertainty of 5.6 kHz (fractionally 9.6 × 10−12). They can provide new optical frequency references for telecommunication and other applications.

Optical frequency dissemination via 103-km urban fiber link with remote passive phase stabilization

In this paper, we propose a technique for a fiber-based optical frequency dissemination system with remote passive phase noise cancellation. At the remote site, a 1×2 fiber pigtailed acousto-optic modulator (AOM) with two diffraction order outputs (0 and −1 order) is employed as the phase-compensated device, the undesired phase noise of fiber link introduced by environmental perturbations are passively canceled at remote sites. Different from other existing schemes, the proposed technique harnesses the benefits of remote radio frequency (RF) independence and low-temperature sensitivity in this noise-suppression configuration. Consequently, the system noise floor of the proposed optical frequency dissemination system achieves 9.44 × 10−21 without requiring a precise remote RF reference, and the phase-temperature coefficient is reduced to about 2 fs/K. A real-world experiment is conducted over a noisy round-trip 103 km urban fiber link. After being passively compensated, we demonstrate a fractional frequency instability of 1.57 × 10−14 at the integration time of 1 s and scales down to 3.96 × 10−20 at 10,000 s in terms of modified Allan deviation. The frequency uncertainty of the retrieved light after transferring through this noise-compensated fiber link relative to that of the input light achieves 1.80 × 10−18. This work demonstrates the system’s capability to disseminate the ultra-stable optical frequency standards and is a significant step towards realizing multi-node dissemination of the state-of-the-art optical clock signal with remote noise compensation via a tree-like topology fiber network.

Switchable Faraday laser with frequencies of 85Rb and 87Rb 780 nm transitions using a single isotope 87Rb Faraday atomic filter

In the development of atomic physics, laser sources with Frequencies corresponding to atomic transition and high stability are essential. The Faraday laser is a special diode laser using the Faraday anomalous dispersion optical filter (FADOF) to realize frequency selection, so the output laser frequency is automatically limited to the atomic Doppler broadening. However, the frequency of a Faraday laser corresponds to the range around only one atomic hyperfine transition. Here, we realize a switchable Faraday laser with two isotopes laser frequencies corresponding to 85Rb 52S1/2 (F=3)→52P3/2 and 87Rb 52S1/2 (F=2)→52P3/2 transitions based on a single isotope 87Rb-FADOF. The laser has good robustness against the fluctuation of diode current and temperature, with wavelength fluctuating within 0.8 pm from 16 to 30 °C of diode temperature, and has a free-running linewidth of 18 kHz. We also lock the laser frequency to the two cycling transitions of 85Rb 52S1/2 (F=3)→52P3/2 (F′=4) and 87Rb 52S1/2 (F=2)→52P3/2 (F′=3) by the modulation transfer spectroscopy technique. The Allan deviation of the residual error signal is 3×10−14/τ, and the frequency stability of the beat detection reaches 2.8×10−12 at 1 s integration time. This 780 nm switchable Faraday laser expands the application scenarios of Faraday lasers, which can be used in laser cooling atoms, optical frequency standards, and other quantum precision measurement fields.

Macroscopic effects in generation of attosecond XUV pulses via high-order frequency mixing in gases and plasma

We theoretically study the generation of attosecond XUV pulses via high-order frequency mixing (HFM) of two intense generating fields, and compare this process with the more common high-order harmonic generation (HHG) process. We calculate the macroscopic XUV signal by numerically integrating the 1D propagation equation coupled with the 3D time-dependent Schrödinger equation. We analytically find the length scales which limit the quadratic growth of the HFM macroscopic signal with propagation length. Compared to HHG these length scales are much longer for a group of HFM components, with orders defined by the frequencies of the generating fields. This results in a higher HFM macroscopic signal despite the microscopic response being lower than for HHG. In our numerical simulations in a gas target, the intensity of the HFM signal is several times higher than that for HHG, while for a plasma target the HFM generation efficiency is up to three orders of magnitude higher than for HHG. The HFM with relatively long generating pulses provides very narrow XUV lines ( δω/ω=4.6×10−4 ) with well-defined frequencies, thus allowing for a simple extension of optical frequency standards to the XUV range. Finally, we show that the group of HFM components effectively generated due to macroscopic effects provides a train of attosecond pulses such that the carrier-envelope phase of an individual attosecond pulse can be easily controlled by tuning the phase of one of the generating fields.

Dual-interrogation method for suppressing light shift in Rb 778 nm two-photon transition optical frequency standard.

In this study, a dual-interrogation (DI) method was used to suppress the light shift in the Rb 778 nm 5S1/2→5D5/2 two-photon transition optical frequency standard (2hν-OFS). The approach used an auxiliary system to calibrate the light shift of the primary system in real time to mitigate the absolute light shift and suppress the sensitivity of the system to the light power. Results show that after using the DI method, the absolute light shift and light-power sensitivity of the system were reduced by a factor of 10. The proposed method will improve the accuracy of the Rb 778 nm 2hν-OFS and increase the mid- and long-term stability. The method can also be applied to other vapor-cell atomic frequency standards that experience light shifts.

Optical frequency divider: Capable of measuring optical frequency ratio in 22 digits

Recent advances in optical frequency standards and optical frequency combs (OFCs) have drawn wide attention since by transforming other quantities into frequency metrology, a higher measurement sensitivity or accuracy can be achieved. Among them, the search for dark matter, tests of relativity, and detection of gravitational wave anticipate even more precise frequency ratio measurement of optical signals, which challenges the state-of-the-art optical frequency standards and OFCs. Here, we report an optical frequency divider (OFD) based on a Ti:sapphire mode-locked laser, which can realize ultraprecise optical frequency ratio measurements and optical frequency division to other desired frequencies. The OFD is based on an OFC frequency-stabilized to a hydrogen maser, whose frequency noise in optical frequency division is subtracted via the transfer oscillator scheme. An optically referenced radio frequency time-base is introduced for the fine-tuning of the divisor and the reduction in division noise. Using the OFD, the frequency ratio between the fundamental and its second harmonic of a 1064 nm laser is measured with a fractional uncertainty of 3 × 10−22, nearly five times better than previous results. Meanwhile, we also report the ability to transport between laboratories, the long-term operation, and the multi-channel division of the OFD.

A Laser Based Universal Oscillator for Next Generation Optical Frequency Standards

A Laser Based Universal Oscillator for Next Generation Optical Frequency Standards

Collective Radiation of a Cascaded Quantum System: From Timed Dicke States to Inverted Ensembles.

The collective absorption and emission of light by an ensemble of atoms is at the heart of many fundamental quantum optical effects and the basis for numerous applications. However, beyond weak excitation, both experiment and theory become increasingly challenging. Here, we explore the regimes from weak excitation to inversion with ensembles of up to 1000 atoms that are trapped and optically interfaced using the evanescent field surrounding an optical nanofiber. We realize full inversion, with about 80% of the atoms being excited, and study their subsequent radiative decay into the guided modes. The data are very well-described by a simple model that assumes a cascaded interaction of the guided light with the atoms. Our results contribute to the fundamental understanding of the collective interaction of light and matter and are relevant for applications ranging from quantum memories to sources of nonclassical light to optical frequency standards.

Broadband serrodyne phase modulation for optical frequency standards and spectral purity transfer.

We perform low phase noise, efficient serrodyne modulation for optical frequency control and spectral purity transfer between two ultrastable lasers. After characterizing serrodyne modulation efficiency and its bandwidth, we estimate the phase noise induced by the modulation setup by developing a novel, to the best of our knowledge, composite self-heterodyne interferometer. Exploiting serrodyne modulation, we phase locked a 698 nm ultrastable laser to a superior ultrastable laser source at 1156 nm by means of a frequency comb as a transfer oscillator. We show that this technique is a reliable tool for ultrastable optical frequency standards.

Natural line profile asymmetry

The paper discusses the line profile asymmetry of the photon scattering process that arises naturally in quantum electrodynamics (QED). Based on precision spectroscopic experiments conducted on hydrogen atoms, we focus our attention on the two-photon 1s − 2s transition. As one of the most precisely determined transition frequencies, it is a key pillar of optical frequency standards and is used in determining fundamental physical constants, testing physical principles, and searching constraints on new fundamental interactions. The results obtained in this work show the need to take into account the natural line profile asymmetry in precision spectroscopic experiments.

Improving the Resolution of Comb-Based Frequency Measurements Using a Track-And-Hold Amplifier

The advent of optical frequency standards with ultimate uncertainties in the low $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}$ requires femtosecond frequency combs to support a similar level of resolution in the spectral transfer and the computation of optical frequency ratios. The related experimental challenges grow together with the number of optical frequencies to be measured simultaneously, as in many cases the comb's optical power does not allow reliable beatnote counting or tracking in all the spectral regions of interest. Here we describe the use of a track-and-hold amplifier to implement the gated detection, a previously proposed technique for improving the signal-to-noise ratio of the beatnote between a low-power tooth of the frequency comb and a continuous-wave laser. We demonstrate a 12-dB improvement in the signal-to-noise ratio of beatnotes involving a broadband-spanning optical comb as compared to traditional detection schemes. Our approach enables reliable and cycle-slip-free spectral purity transfer and reduces the system sensitivity to power drops in the comb spectrum. Being based on a single chip, it is robust, versatile, and easily embedded in more complex experimental schemes.

Ultimate stability of active optical frequency standards

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 $^{87}$Sr we find that an optimized stability of $\sigma_y(\tau) \approx 4\times10^{-18}/\sqrt{\tau [\mathrm{s}]}$ is achievable.

Наследие Н.Г. Басова: от первых мазеров к оптическим стандартам частоты

Наследие Н.Г. Басова: от первых мазеров к оптическим стандартам частоты

Наследие Н.Г. Басова: от первых мазеров к оптическим стандартам частоты

Наследие Н.Г. Басова: от первых мазеров к оптическим стандартам частоты

High-precision measurement of the hyperfine splitting and ac Stark shift of the 7d D3/22 state in atomic cesium

We report the measurement of hyperfine splitting in the $7d$ $^{2}D_{3/2}$ state of $^{133}\mathrm{Cs}$ using high-resolution Doppler-free two-photon spectroscopy in a Cs vapor cell. We determine the hyperfine coupling constants $A=7.3509(9)$ MHz and $B=\ensuremath{-}0.041(8)$ MHz, which represent an order of magnitude improvement in the precision. We also obtain bounds on the magnitude of the nuclear magnetic octupole coupling constant $C$. Additionally, we measure the ac Stark shift of the $6s\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{S}_{1/2}\ensuremath{\rightarrow}7d$ $^{2}D_{3/2}$ transition at 767.8 nm to be $\ensuremath{-}49\ifmmode\pm\else\textpm\fi{}5\phantom{\rule{0.16em}{0ex}}\mathrm{Hz}/(\mathrm{W}/\mathrm{c}{\mathrm{m}}^{2})$, in agreement with theoretical calculations. We further report the measurement of collisional shift (\ensuremath{-}32.6 \ifmmode\pm\else\textpm\fi{} 2.0 kHz/mTorr) and pressure broadening for the individual hyperfine levels of the $6s\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{S}_{1/2}\ensuremath{\rightarrow}7d$ $^{2}D_{3/2}$ transition. These measurements provide valuable inputs for analysis of systematic effects in optical frequency standards based on the cesium $6s\phantom{\rule{0.16em}{0ex}}^{2}\mathrm{S}_{1/2}\ensuremath{\rightarrow}7d$ $^{2}D_{3/2}$ two-photon transition.

Hyperfine coupling constants of the cesium 7D5/2 state measured up to the octupole term.

We report the measurement of hyperfine splitting (HFS) in the 7D5/2 state of 133Cs using high-resolution Doppler-free two-photon spectroscopy enabled by precise frequency scans using an acousto-optic modulator (AOM). All six hyperfine levels are resolved in our spectra. We determine the hyperfine coupling constants A = -1.70867(62) MHz and B = 0.050(14) MHz which represent an over 20-times improvement in the precision of both A and B. Moreover, our measurement is sufficiently precise to put bounds on the value of the magnetic octupole coupling constant C = 0.4(1.4) kHz for the 7D5/2 state. We additionally report the measurement of the ac Stark shift [-46 ± 4 Hz/(W/cm2)], collisional shift, and pressure broadening which are important for optical frequency standards based on the 6S1/2 → 7D5/2 two-photon transition.

Compact 459-nm Cs Cell Optical Frequency Standard with 2.1×10−13/τ Short-Term Stability

We achieve a compact optical frequency standard with an extended cavity diode laser locked to the 459-nm $6{S}_{1/2}$-$7{P}_{1/2}$ transition of thermal ${}^{133}\mathrm{Cs}$ atoms in a $\ensuremath{\phi}10\phantom{\rule{0.1em}{0ex}}\mathrm{mm}\ifmmode\times\else\texttimes\fi{}50\phantom{\rule{0.1em}{0ex}}\mathrm{mm}$ glass cell, using modulation transfer spectroscopy (MTS). The self-estimated frequency stability of this laser is $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}/\sqrt{\ensuremath{\tau}}$. With heterodyne measurement, we verify the linewidth-narrowing effect of MTS locking and measure the frequency stability of the locked laser. The linewidth of each laser is reduced from the free-running 69.6 to 10.3 kHz after MTS stabilization, by a factor of 6.75. The Allan deviation measured via beat detection is $2.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}/\sqrt{\ensuremath{\tau}}$ for each MTS-stabilized laser. In addition, we measure the hyperfine structure of the $7{P}_{1/2}$ energy level based on the heterodyne measurements, and calculate the magnetic dipole constant A of the Cs $7{P}_{1/2}$ level to be 94.38(6) MHz, which agrees well with previous measurements. This compact optical frequency standard can also be used in other applications that require high-stability lasers, such as laser interferometry, laser cooling, geodesy, and so on.