Hz Linewidth Research Articles

A strontium lattice clock with both stability and uncertainty below 5×10−18

We report the realization of the closed-loop operation of an optical lattice clock based on 87Sr atoms. A cavity-stabilized 698 nm laser is used to probe the 1S0→3P0 clock transition of strontium atoms trapped in optical lattices. Therein, we obtain a Fourier-limited Rabi spectrum with 0.6 Hz linewidth. The two transitions from mF=±9/2 ground states are alternatively interrogated to realize the closed-loop operation of the clock, and the clock laser light is frequency-stabilized to the center of the two transitions. Based on the interleaved measurement, the frequency instability of a single optical clock is optimized for the Dick effect, which is demonstrated to be 4.5×10−16/τ , with τ being the averaging time for measurement. Further, we build another similar setup of the strontium lattice clock, which is used for the asynchronous comparison between the two clocks, where the stability is measured as 2.1×10−18 at 47 000 s. Moreover, we carefully calibrate the systematic effects of the Sr1 optical clock, and the total uncertainty is evaluated as 4.4×10−18 .

High-power quantum-limited 35 MHz photodiode and classical laser noise suppression

To benefit high-power interferometry and the creation of low-noise light sources, we develop a simple lead-compensated photodetector enabling quantum-limited readout from 0.3 to 10 mW and 10 kΩ gain from 85 Hz to 35 MHz, with a noise equivalent power of 9 pW/Hz. Feeding the detector output back to an intensity modulator, we suppress the classical amplitude noise of a commercial 1550 nm fiber laser to the shot noise limit over a bandwidth of 700 Hz–200 kHz, observing no degradation to its (nominally ∼100 Hz) linewidth.

Multi-wavelength sub-100 Hz linewidth Brillouin fiber laser with cascaded SBS polarization parity-time symmetry

A multi-wavelength sub-100 Hz linewidth Brillouin fiber laser (BFL) with cascaded stimulated Brillouin scattering (SBS) polarization parity-time (PT) symmetry is proposed and experimentally investigated. Multi-order Stokes wave generation using a structure consisting of a main fiber ring (MFR) and a sub fiber loop (SFL). The MFR is used to excite the Stokes laser and to guarantee single longitudinal mode (SLM) operation of the generated stokes laser of each order and the SFL cascades each Stokes lasing emission to act as a Brillouin pump for the next order of Stokes generation. A Sagnac loop in the MFR consisting of optical coupler (OC), polarization beam splitter (PBS) and two polarization controllers (PCs), is used to achieve cascaded SBS polarization PT symmetry. By tuning the PC to control the polarization state of each order linearly polarized light injected into PBS at each order, thus controlling the gain and loss of the loop corresponding to the two backpropagating light waves. When the gain and loss of the coupling loops are the same in magnitude and greater than the coupling coefficient, the cascaded SBS polarization PT symmetry is broken, resulting in SLM operation for each order of Stokes waves. Experimental results reveal that thirteen Stokes waves were obtained from two different output ports at an erbium-doped fiber amplifier (EDFA) output power of 28 dBm. The measured linewidths at — 20 dB power were 0.34, 0.39, 0.33, 0.4, 0.39 and 0.43 kHz for the 1st-6th order Stokes emission, corresponding to linewidths of 17.1, 19.6, 16.6, 20.1 19.6 and 21.6 Hz, respectively, while the maximum side mode suppression ratios (SMSRs) were measured to be 47, 45, 49, 44, 41 and 41 dB for the 1st-6th order Stokes emission. Within 60 min of the stability experiment, the wavelength and power stability were ±2 pm and ±0.6 dB, respectively. Compared with previous studies, the present design guarantees the operation of SLM for each order of Stokes waves with sub-100 Hz laser linewidth.

Frequency stable and low phase noise THz synthesis for precision spectroscopy

We present a robust approach to generate a continuously tunable, low phase noise, Hz linewidth and mHz/s stability THz emission in the 0.1 THz to 1.4 THz range. This is achieved by photomixing two commercial telecom, distributed feedback lasers locked by optical-feedback onto a single highly stable V-shaped optical cavity. The phase noise is evaluated up to 1.2 THz, demonstrating Hz-level linewidth. To illustrate the spectral performances and agility of the source, low pressure absorption lines of methanol and water vapors have been recorded up to 1.4 THz. In addition, the hyperfine structure of a water line at 556.9 GHz, obtained by saturation spectroscopy, is also reported, resolving spectral features displaying a full-width at half-maximum of 10 kHz. The present results unambiguously establish the performances of this source for ultra-high resolution molecular physics.

Sub-Hz Closed-Loop Electro-Optomechanical Oscillator with Gallium Phosphide Photonic Crystal Integrated on SoI Circuitry.

We report on a new approach of a low phase noise electro-optomechanical oscillator directly working in the GHz frequency range. The developed nanoscale oscillator is a one-dimensional photonic crystal made of gallium phosphide (GaP), heterogeneously integrated on silicon-on-insulator circuitry. Based on the strong interaction between the optical mode at the telecommunication wavelength and the mechanical mode in GHz, ultra-pure mechanical oscillations are enabled and directly imprinted on an optical carrier. Further stabilization is achieved with a delayed optoelectronic feedback loop using integrated electro-mechanical self-injection. We achieve a short-term stability of 0.7 Hz linewidth and a long-term stability with an Allan deviation below 10-7 Hz/Hz at 10 s averaging time, which represents an important step toward fully integrated optomechanical oscillators. Integrability and the low phase noise of this oscillator address some of the most important needs of optoelectronic oscillators and pave the way toward on-chip integrated microwave oscillators for microwave applications such as RADARs.

Coherent terahertz radiation with 2.8-octave tunability through chip-scale photomixed microresonator optical parametric oscillation

High-spectral-purity frequency-agile room-temperature sources in the terahertz spectrum are foundational elements for imaging, sensing, metrology, and communications. Here we present a chip-scale optical parametric oscillator based on an integrated nonlinear microresonator that provides broadly tunable single-frequency and multi-frequency oscillators in the terahertz regime. Through optical-to-terahertz down-conversion using a plasmonic nanoantenna array, coherent terahertz radiation spanning 2.8-octaves is achieved from 330 GHz to 2.3 THz, with ≈20 GHz cavity-mode-limited frequency tuning step and ≈10 MHz intracavity-mode continuous frequency tuning range at each step. By controlling the microresonator intracavity power and pump-resonance detuning, tunable multi-frequency terahertz oscillators are also realized. Furthermore, by stabilizing the microresonator pump power and wavelength, sub-100 Hz linewidth of the terahertz radiation with 10−15 residual frequency instability is demonstrated. The room-temperature generation of both single-frequency, frequency-agile terahertz radiation and multi-frequency terahertz oscillators in the chip-scale platform offers unique capabilities in metrology, sensing, imaging and communications.

36 Hz integral linewidth laser based on a photonic integrated 4.0 m coil resonator

Laser stabilization sits at the heart of many precision scientific experiments and applications, including quantum information science, metrology, and atomic timekeeping. Many of these systems narrow the laser linewidth and stabilize the carrier by use of Pound–Drever–Hall (PDH) locking to a table-scale, ultrahigh quality factor (Q), vacuum spaced Fabry–Perot reference cavity. Integrating these cavities to bring characteristics of PDH stabilization to the chip scale is critical to reducing their size, cost, and weight, and enabling a wide range of portable and system-on-chip applications. We report a significant advance in integrated laser linewidth narrowing, stabilization, and noise reduction by use of a photonic integrated 4.0 m long coil resonator to stabilize a semiconductor laser. We achieve a 36 Hz 1 / π -integral linewidth, Allan deviation of 1.8 × 10 − 13 at 10 ms measurement time, and a 2.3 kHz/s drift—to the best of our knowledge, the lowest integral linewidth and highest stability demonstrated for an integrated waveguide reference cavity. This performance represents over an order of magnitude improvement in integral linewidth and frequency noise over previous integrated waveguide PDH stabilized reference cavities and bulk-optic and integrated injection locked approaches, and over two orders of magnitude improvement in frequency and phase noise than integrated injection locked approaches. Two different wavelength coil designs are demonstrated, stabilizing lasers at 1550 nm and 1319 nm. The resonator is bus-coupled to a 4.0 m long coil, with a 49 MHz free spectral range, mode volume of 1.0 × 10 10 µ m 3 , and 142 million intrinsic Q , fabricated in a CMOS compatible, ultralow loss silicon nitride waveguide platform. Our measurements and simulations show that the thermorefractive noise floor for this particular cavity is reached for frequencies down to 20 Hz in an ambient environment with simple passive vibration isolation and without vacuum or thermal isolation. The thermorefractive noise limited performance is estimated to yield an 8 Hz 1 / π -integral linewidth and Allan deviation of 5 × 10 − 14 at 10 ms, opening a stability regime that heretofore has been available only in fundamentally non-integrated systems. These results demonstrate the potential to bring the characteristics of laboratory-scale stabilized lasers to the integrated, wafer-scale compatible chip scale, and are of interest for a number of applications in quantum technologies and atomic, molecular, and optical physics, and with further developments below 10 Hz linewidth, can be highly relevant to ultralow noise microwave generation.

Floquet Engineering Hz-Level Rabi Spectra in Shallow Optical Lattice Clock.

Quantum metrology with ultrahigh precision usually requires atoms prepared in an ultrastable environment with well-defined quantum states. Thus, in optical lattice clock systems deep lattice potentials are used to trap ultracold atoms. However, decoherence, induced by Raman scattering and higher order light shifts, can significantly be reduced if atomic clocks are realized in shallow optical lattices. On the other hand, in such lattices, tunneling among different sites can cause additional dephasing and strongly broadening of the Rabi spectrum. Here, in our experiment, we periodically drive a shallow ^{87}Sr optical lattice clock. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4Hz linewidth. With careful comparison between the theory and experiment, we demonstrate that the Rabi frequency and the Bloch bands can be tuned, simultaneously and independently. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phases of matter by engineering exotic spin orbit couplings.

Vibration modes of a transportable optical cavity.

Many factors still need to be evaluated to fully understand the physical mechanisms determining optical cavity vibration, which are crucial for designing and constructing a transportable ultra-stable laser. Herein, a detailed dynamic analysis is used to characterize the vibration modes of a transportable optical cavity. The first five resonance modes are identified in the presence of a cavity support, and the guidelines to achieve a high first-order resonance frequency are proposed; thereby, high robustness is described using a 50 mm length optical cavity. The results demonstrate that the first-order resonance of up to 681 Hz with a gross weight of 2.51 kg can be achieved using an optimization strategy for given cavity support. The theoretical results are consistent with simulation and experiment. With the optimal group, a 1.34 Hz linewidth transportable ultra-stable laser at 1550 nm is established, and a linewidth of 1.5 Hz and frequency instability of 9.5×10-15@1s are obtained after the test including 100 km actual road transportation and 34 min continuous vibration. The test condition is equivalent to ∼ 1000 km road transportation. Our method can be readily extended to other transportable optical cavities, providing a powerful tool for improving the robustness of vibration, particularly important for transportable environments.

Optomechanically induced ultraslow and ultrafast light

Slow and fast light is an important and fascinating phenomenon in quantum optics. Here, we theoretically study how to achieve the ultraslow and ultrafast light in a passive-active optomechanical system, based on the ideal optomechanically induced transparency (OMIT). Under the conditions of the ideal OMIT, an abnormal (inverted) transparency window will emerge accompanied with a very steep dispersion, resulting that the ultraslow light can be easily achieved at the transparency window by adjusting the dissipation rates of the two cavities, even with usual mechanical linewidth (such as Hz linewidth). Particularly, as the decay rate of the passive cavity tends to the gain rate of the active cavity, the ideal stopped light can be achieved. Similarly, the ultrafast light can be achieved at transparency window by tuning the coupling strength and the decay rates in the system.

Ultranarrow Superradiant Lasing by Dark Atom-Photon Dressed States.

We show that incoherent pumping of an optical lattice clock system with ultracold strontium-88 atoms produces laser light with a ≃10 Hz linewidth when the atoms are exposed to a magnetic field. This linewidth is orders of magnitude smaller than both the cavity linewidth and the incoherent atomic decay and excitation rates. The narrow lasing is due to an interplay of multiatom superradiant effects and the coupling of bright and dark atom-light dressed states by the magnetic field.

Development of an Interference Filter-Stabilized External-Cavity Diode Laser for Space Applications

The National Time Service Center of China is developing a compact, highly stable, 698 nm external-cavity diode laser (ECDL) for dedicated use in a space strontium optical clock. This article presents the optical design, structural design, and preliminary performance of this ECDL. The ECDL uses a narrow-bandwidth interference filter for spectral selection and a cat’s-eye reflector for light feedback. To ensure long-term stable laser operation suitable for space applications, the connections among all the components are rigid and the design avoids any spring-loaded adjustment. The frequency of the first lateral rocking eigenmode is 2316 Hz. The ECDL operates near 698.45 nm, and it has a current-controlled tuning range over 40 GHz and a PZT-controlled tuning range of 3 GHz. The linewidth measured by the heterodyne beating between the ECDL and an ultra-stable laser with 1 Hz linewidth is about 180 kHz. At present, the ECDL has been applied to the principle prototype of the space ultra-stable laser system.

Free-space transfer of comb-rooted optical frequencies over an 18\u2009km open-air link

Phase-coherent transfer of optical frequencies over a long distance is required for diverse photonic applications, including optical clock dissemination and physical constants measurement. Several demonstrations were made successfully over fiber networks, but not much work has been done yet through the open air where atmospheric turbulence prevails. Here, we use an 18 km outdoor link to transmit multiple optical carriers extracted directly from a frequency comb of a 4.2 THz spectral width. In stabilization to a high-finesse cavity with a 1.5 Hz linewidth, the comb-rooted optical carriers are simultaneously transferred with collective suppression of atmospheric phase noise to −80 dBc Hz−1. Microwaves are also delivered by pairing two separate optical carriers bound with inter-comb-mode coherence, for example a 10 GHz signal with phase noise of −105 dBc Hz−1 at 1 Hz offset. Lastly, an add-on demonstration is given for multi-channel coherent optical communications with the potential of multi-Tbps data transmission in free space.

High-power sub-kHz linewidth lasers fully integrated on silicon

We demonstrate a fully integrated extended distributed Bragg reflector (DBR) laser with ∼1 kHz linewidth and over 37 mW output power, as well as a ring-assisted DBR laser with less than 500 Hz linewidth. The extended DBR lasers are fabricated by heterogeneously integrating III-V material on Si as a gain section plus a 15 mm long, low-kappa Bragg grating reflector in an ultralow-loss silicon waveguide. The low waveguide loss (0.16 dB/cm) and long Bragg grating with narrow bandwidth (2.9 GHz) are essential to reducing the laser linewidth while maintaining high output power and single-mode operation. The combination of narrow linewidth and high power enable its use in coherent communications, RF photonics, and optical sensing.

Comb-rooted multi-channel synthesis of ultra-narrow optical frequencies of few Hz linewidth

We report a multi-channel optical frequency synthesizer developed to generate extremely stable continuous-wave lasers directly out of the optical comb of an Er-doped fiber oscillator. Being stabilized to a high-finesse cavity with a fractional frequency stability of 3.8 × 10−15 at 0.1 s, the comb-rooted synthesizer produces multiple optical frequencies of ultra-narrow linewidth of 1.0 Hz at 1 s concurrently with an output power of tens of mW per each channel. Diode-based stimulated emission by injection locking is a key mechanism that allows comb frequency modes to sprout up with sufficient power amplification but no loss of original comb frequency stability. Channel frequencies are individually selectable with a 0.1 GHz increment over the entire comb bandwidth spanning 4.25 THz around a 1550 nm center wavelength. A series of out-of-loop test results is discussed to demonstrate that the synthesizer is able to provide stable optical frequencies with the potential for advancing diverse ultra-precision applications such as optical clocks comparison, atomic line spectroscopy, photonic microwaves generation, and coherent optical telecommunications.

NMR study of optically hyperpolarized phosphorus donor nuclei in silicon

We use above-bandgap optical excitation, via a 1047 nm laser, to hyperpolarize the $^{31}$P spins in low-doped (N$_D =6\times10^{15}$ cm$^{-3}$) natural abundance silicon at 4.2 K and 6.7 T, and inductively detect the resulting NMR signal. The $30$ kHz spectral linewidth observed is dramatically larger than the 600 Hz linewidth observed from a $^{28}$Si-enriched silicon crystal. We show that the observed broadening is consistent with previous ENDOR results showing discrete isotope mass effect contributions to the donor hyperfine coupling. A secondary source of broadening is likely due to variations in the local strain, induced by the random distribution of different isotopes in natural silicon. The nuclear spin T$_1$ and the build-up time for the optically-induced $^{31}$P hyperpolarization in the natural abundance silicon sample were observed to be $178\pm47$ s and $69\pm6$ s respectively, significantly shorter than the values previously measured in $^{28}$Si-enriched samples under the same conditions. We also measured the T$_1$ and hyperpolarization build-up time for the $^{31}$P signal in natural abundance silicon at 9.4 T to be $54\pm31$ s and $13\pm2$ s respectively. The shorter build-up and nuclear spin T$_1$ times at high field are likely due to the shorter electron-spin T$_1$, which drives nuclear spin relaxation via non-secular hyperfine interactions. At 6.7 T, the phosphorus nuclear spin T$_{2}$ was measured to be $16.7\pm1.6$ ms at 4.2 K, a factor of 4 shorter than in $^{28}$Si-enriched crystals. This was observed to further shorten to $1.9\pm0.4$ ms in the presence of the infra-red laser.

3D printed microwave cavity for atomic clock applications: proof of concept

The authors present the realisation and characterisation of an additively manufactured (AM) microwave resonator cavity for double-resonance (DR) vapour-cell atomic clocks. The design of the compact microwave cavity is based on the loop-gap resonator approach, previously demonstrated for conventionally-machined aluminium components. In the present study, the resonator is fabricated by AM using a metal-coated polymer. A resonance frequency at the desired 6.835 GHz rubidium atomic frequency is obtained. When employed in an atomic clock setup, the AM cavity enables a DR signal of <500 Hz linewidth and of nearly 20% contrast, thus fulfilling the stringent requirements for DR atomic clocks. A clock short-term stability of 1 × 10−12 τ −1/2 is demonstrated, comparable to state-of-the-art clock performances.

Study of additive manufactured microwave cavities for pulsed optically pumped atomic clock applications

Additive manufacturing (AM) of passive microwave components is of high interest for the cost-effective and rapid prototyping or manufacture of devices with complex geometries. Here, we present an experimental study on the properties of recently demonstrated microwave resonator cavities manufactured by AM, in view of their applications to high-performance compact atomic clocks. The microwave cavities employ a loop-gap geometry using six electrodes. The critical electrode structures were manufactured monolithically using two different approaches: Stereolithography (SLA) of a polymer followed by metal coating and Selective Laser Melting (SLM) of aluminum. The tested microwave cavities show the desired TE011-like resonant mode at the Rb clock frequency of ≈6.835 GHz, with a microwave magnetic field highly parallel to the quantization axis across the vapor cell. When operated in an atomic clock setup, the measured atomic Rabi oscillations are comparable to those observed for conventionally manufactured cavities and indicate a good uniformity of the field amplitude across the vapor cell. Employing a time-domain Ramsey scheme on one of the SLA cavities, high-contrast (34%) Ramsey fringes are observed for the Rb clock transition, along with a narrow (166 Hz linewidth) central fringe. The measured clock stability of 2.2 × 10−13 τ−1/2 up to the integration time of 30 s is comparable to the current state-of-the-art stabilities of compact vapor-cell clocks based on conventional microwave cavities and thus demonstrates the feasibility of the approach.

Multiple wavelength stabilization on a single optical cavity using the offset sideband locking technique.

We implemented a compact, robust, and stable device for simultaneous frequency stabilization of lasers with different wavelengths used for the cooling and trapping of Yb atoms in an optical lattice clock. The lasers at 399, 556, and 759nm are locked to a single ultra-stable cavity using the offset sideband locking technique, a modified version of the Pound-Drever-Hall method. For the most demanding stabilization here, the 556nm laser, this system exhibits a 300Hz linewidth for an integration time of 80ms. We observed a long-term drift of less than 20kHz per day at 759nm that is suitable for operating the lattice laser with a light shift uncertainty below 1×10-18. We successfully tested the system for operating the clock during a typical working day by simultaneously locking the three lasers to the cavity.

Chasing the thermodynamical noise limit in whispering-gallery-mode resonators for ultrastable laser frequency stabilization

Ultrastable high-spectral-purity lasers have served as the cornerstone behind optical atomic clocks, quantum measurements, precision optical microwave generation, high-resolution optical spectroscopy, and sensing. Hertz-level lasers stabilized to high-finesse Fabry-Pérot cavities are typically used for these studies, which are large and fragile and remain laboratory instruments. There is a clear demand for rugged miniaturized lasers with stabilities comparable to those of bulk lasers. Over the past decade, ultrahigh-Q optical whispering-gallery-mode resonators have served as a platform for low-noise microlasers but have not yet reached the stabilities defined by their fundamental noise. Here, we show the noise characteristics of whispering-gallery-mode resonators and demonstrate a resonator-stabilized laser at this limit by compensating the intrinsic thermal expansion, allowing a sub-25 Hz linewidth and a 32 Hz Allan deviation. We also reveal the environmental sensitivities of the resonator at the thermodynamical noise limit and long-term frequency drifts governed by random-walk-noise statistics.