Frequency ratio measurements at 18-digit accuracy using an optical clock network

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 5.4 Hz 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.

Coherent fibre link for synchronization of delocalized atomic clocks

Challenging experiments for tests in fundamental physics require highly coherent optical frequency references with suppressed phase noise from hundreds of kHz down to μHz of Fourier frequencies. It can be achieved by remote synchronization of many frequency references interconnected by stabilized optical fibre links. Here we describe the path to realize a delocalized optical frequency reference for spectroscopy of the isomeric state of the nucleus of Thorium-229 atom. This is a prerequisite for the realization of the next generation of an optical clock - the nuclear clock. We present the established 235 km long phase-coherent stabilized cross-border fibre link connecting two delocalized metrology laboratories in Brno and Vienna operating highly-coherent lasers disciplined by active Hydrogen masers through optical frequency combs. A significant part (up to tens of km) of the optical fibre is passing urban combined collectors with a non-negligible level of acoustic interference and temperature changes, which results in a power spectral density of phase noise over 10⁵ rad²· Hz^-1. Therefore, we deploy a digital signal processing technique to suppress the fibre phase noise over a wide dynamic range of phase fluctuations. To demonstrate the functionality of the link, we measured the phase noise power spectral density of a remote beat note between two independent lasers, locked to high-finesse stable resonators. Using optical frequency combs at both ends of the link, a long-term fractional frequency stability in the order of 10^-15 between local active Hydrogen masers was measured as well. Thanks to this technique, we have achieved reliable operation of the phase-coherent fibre link with fractional stability of 7 × 10^-18 in 10³ s.

Digital Doppler-Cancellation Servo for Ultrastable Optical Frequency Dissemination Over Fiber

Progress made in optical references, including ultrastable Fabry-Perot cavities, optical frequency combs, and optical atomic clocks, has driven the need for ultrastable optical fiber networks. Telecom-wavelength ultrapure optical signal transport has been demonstrated on distances ranging from the laboratory scale to the continental scale. In this article, we present a Doppler-cancellation setup based on a digital phase-locked loop (PLL) for ultrastable optical signal dissemination over fiber. The optical phase stabilization setup is based on a usual heterodyne Michelson-interferometer setup, while the software-defined radio (SDR) implementation of the PLL is based on a compact commercial board embedding a field-programmable gate array and analog-to-digital and digital-to-analog converters. Using three different configurations, including an undersampling method, we demonstrate a 20-m-long fiber link with residual fractional frequency instability as low as 10^-18 at 1000 s and optical phase noise of -70 dBc/Hz at 1 Hz with a telecom frequency carrier.

Radium Ion Optical Clock

We report the first operation of a Ra^{+} optical clock, a promising high-performance clock candidate. The clock uses a single trapped ^{226}Ra^{+} ion and operates on the 7s ^{2}S_{1/2}→6d ^{2}D_{5/2} electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1×10^{-13}/sqrt[τ], where τ is the averaging time in seconds. The total systematic uncertainty is evaluated to be Δν/ν=9×10^{-16}. Using the clock, we realize the first measurement of the ratio of the D_{5/2} state to the S_{1/2} state Landé g-factors: g_{D}/g_{S}=0.598 805 3(11). A Ra^{+} optical clock could improve limits on the time variation of the fine structure constant, α[over ˙]/α, in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.

Spectral compression by phase doubling in second harmonic generation

In second harmonic generation, the phase of the optical field is doubled, which has important implications. Here, the phase-doubling effect is utilized to solve a long-standing challenge in the power scaling of single-frequency laser. (-π/2, π/2) binary phase modulation is applied to a single-frequency seed laser to broaden the spectrum and suppress the stimulated Brillouin scattering in a high-power fiber amplifier. The second harmonic of the phase-modulated laser returns to single frequency because the (-π/2, π/2) modulation is doubled to (-π, π) for the second harmonic. A compression-to-single-frequency rate as high as 95% is demonstrated in experiments limited by the electronic bandwidth of the setup. Such phase manipulation in wave-mixing processes may open up a new field of development in nonlinear optics and laser technology.

Ultrastable Free-Space Laser Links for a Global Network of Optical Atomic Clocks

A global network of optical atomic clocks will enable unprecedented measurement precision in fields including tests of fundamental physics, dark matter searches, geodesy, and navigation. Free-space laser links through the turbulent atmosphere are needed to fully exploit this global network, by enabling comparisons to airborne and spaceborne clocks. We demonstrate frequency transfer over a 2.4 km atmospheric link with turbulence comparable to that of a ground-to-space link, achieving a fractional frequency stability of 6.1×10^{-21} in 300 s of integration time. We also show that clock comparison between ground and low Earth orbit will be limited by the stability of the clocks themselves after only a few seconds of integration. This significantly advances the technologies needed to realize a global timescale network of optical atomic clocks.

Coherent phase transfer for real-world twin-field quantum key distribution

Quantum mechanics allows distribution of intrinsically secure encryption keys by optical means. Twin-field quantum key distribution is one of the most promising techniques for its implementation on long-distance fiber networks, but requires stabilizing the optical length of the communication channels between parties. In proof-of-principle experiments based on spooled fibers, this was achieved by interleaving the quantum communication with periodical stabilization frames. In this approach, longer duty cycles for the key streaming come at the cost of a looser control of channel length, and a successful key-transfer using this technique in real world remains a significant challenge. Using interferometry techniques derived from frequency metrology, we develop a solution for the simultaneous key streaming and channel length control, and demonstrate it on a 206 km field-deployed fiber with 65 dB loss. Our technique reduces the quantum-bit-error-rate contributed by channel length variations to <1%, representing an effective solution for real-world quantum communications.

Stochastic fluctuations of bosonic dark matter

Numerous theories extending beyond the standard model of particle physics predict the existence of bosons that could constitute dark matter. In the standard halo model of galactic dark matter, the velocity distribution of the bosonic dark matter field defines a characteristic coherence time τc. Until recently, laboratory experiments searching for bosonic dark matter fields have been in the regime where the measurement time T significantly exceeds τc, so null results have been interpreted by assuming a bosonic field amplitude Φ0 fixed by the average local dark matter density. Here we show that experiments operating in the T ≪ τc regime do not sample the full distribution of bosonic dark matter field amplitudes and therefore it is incorrect to assume a fixed value of Φ0 when inferring constraints. Instead, in order to interpret laboratory measurements (even in the event of a discovery), it is necessary to account for the stochastic nature of such a virialized ultralight field. The constraints inferred from several previous null experiments searching for ultralight bosonic dark matter were overestimated by factors ranging from 3 to 10 depending on experimental details, model assumptions, and choice of inference framework.

Compact magneto-optical trap of thulium atoms for a transportable optical clock

We have developed a compact vacuum system for laser cooling and spectroscopy of neutral thulium atoms. Compactness is achieved by obviating a classical Zeeman slower section and placing an atomic oven close to a magneto-optical trap (MOT), specifically at the distance of 11 cm. In this configuration, we significantly gained in solid angle of an atomic beam, which is affected by MOT laser beams, and reached 1 million atoms loaded directly in the MOT with only 15 mW of MOT cooling beams net power. By exploiting Zeeman-like deceleration of atoms with an additional laser beam and tailoring the MOT magnetic field gradient with a small magnetic coil, we demonstrated trapping of up to 13 million atoms. These results show great perspective of the developed setup for realizing a compact high-performance optical atomic clock based on thulium atoms.

Simultaneous bicolor interrogation in thulium optical clock providing very low systematic frequency shifts

Optical atomic clocks have already overcome the eighteenth decimal digit of instability and uncertainty, demonstrating incredible control over external perturbations of the clock transition frequency. At the same time, there is an increasing demand for atomic (ionic) transitions and new interrogation and readout protocols providing minimal sensitivity to external fields and possessing practical operational wavelengths. One of the goals is to simplify the clock operation while maintaining the relative uncertainty at a low 10⁻¹⁸ level achieved at the shortest averaging time. This is especially important for transportable and envisioned space-based optical clocks. Here, we demonstrate implementation of a synthetic frequency approach for a thulium optical clock with simultaneous optical interrogation of two clock transitions. Our experiment shows suppression of the quadratic Zeeman shift by at least three orders of magnitude. The effect of the tensor lattice Stark shift in thulium can also be reduced to below 10⁻¹⁸ in fractional frequency units. This makes the thulium optical clock almost free from hard-to-control systematic shifts. The “simultaneous” protocol demonstrates very low sensitivity to the cross-talks between individual clock transitions during interrogation and readout.

There are continuous efforts in improving the stability and systematic shifts of optical clocks. Here the authors demonstrate thulium optical clock utilizing bicolor scheme involving interrogation of both hyperfine levels and they are able to cancel the quadratic Zeeman shift.

SI-traceable frequency dissemination at 1572.06 nm in a stabilized fiber network with ring topology

Frequency dissemination in phase-stabilized optical fiber networks for metrological frequency comparisons and precision measurements are promising candidates to overcome the limitations imposed by satellite techniques. However, in an architecture shared with telecommunication data traffic, network constraints restrict the availability of dedicated channels in the commonly-used C-band. Here, we demonstrate the dissemination of an SI-traceable ultrastable optical frequency in the L-band over a 456 km fiber network with ring topology, in which data traffic occupies the full C-band. We characterize the optical phase noise and evaluate a link instability of 4.7 × 10^-16 at 1 s and 3.8 × 10^-19 at 2000 s integration time, and a link accuracy of 2 × 10^-18. We demonstrate the application of the disseminated frequency by establishing the SI-traceability of a laser in a remote laboratory. Finally, we show that our metrological frequency does not interfere with data traffic in the telecommunication channels. Our approach combines an unconventional spectral choice in the telecommunication L-band with established frequency-stabilization techniques, providing a novel, cost-effective solution for ultrastable frequency-comparison and dissemination, and may contribute to a foundation of a world-wide metrological network.

Prospects of a Pb^{2+} Ion Clock

We propose a high-performance atomic clock based on the 1.81 PHz transition between the ground and first-excited state of doubly ionized lead. Utilizing an even isotope of lead, both clock states have I=J=F=0, where I, J, and F are the conventional quantum numbers specifying nuclear, electronic, and total angular momentum, respectively. The clock states are nondegenerate and completely immune to nonscalar perturbations, including first order Zeeman and electric quadrupole shifts. Additionally, the proposed clock is relatively insusceptible to other frequency shifts (blackbody radiation, second order Zeeman, Doppler), accommodates "magic" rf trapping, and is robust against decoherence mechanisms that can otherwise limit clock stability. By driving the transition as a two-photon E1+M1 process, the accompanying probe Stark shift is appreciable yet manageable for practical Rabi frequencies.

Light by design: emerging frontiers in ultrafast photon sciences and light–matter interactions

Photon sciences and technologies establish the building blocks for myriad scientific and engineering frontiers in life and energy sciences. Because of their overarching functionality, the developmental roadmap and opportunities underpinned by photonics are often semiotically mediated by the delineation of subject areas of application. In this perspective article, we map current and emerging linkages between three intersecting areas of research stewarded by advanced photonics technologies, namely light by design, outlined as (a) quantum and structured photonics, (b) light–matter interactions in accelerators and accelerator-based light sources, and (c) ultrafast sciences and quantum molecular dynamics. In each section, we will concentrate on state-of-the-art achievements and present prospective applications in life sciences, biochemistry, quantum optics and information sciences, and environmental and chemical engineering, all founded on a broad range of photon sources and methodologies. We hope that this interconnected mapping of challenges and opportunities seeds new concepts, theory, and experiments in the advancement of ultrafast photon sciences and light–matter interactions. Through this mapping, we hope to inspire a critically interdisciplinary approach to the science and applications of light by design.