The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability 1,2,3 and uncertainty, 4,5,6,7 are already being used to test physical theories 8,9 and herald a revision of the International System of units (SI). 10,11 However, to unlock their potential for cross-disciplinary applications such as relativistic geodesy, 12 a major challenge remains. This is their transformation from highly specialized instruments restricted to national metrology laboratories into flexible devices deployable in different locations. 13,14,15 Here we report the first field measurement campaign performed with a ubiquitously applicable 87 Sr optical lattice clock. 13 We use it to determine the gravity potential difference between the middle of a mountain and a location 90 km apart, exploiting both local and remote clock comparisons to eliminate potential clock errors. A local comparison with a 171 Yb lattice clock 16 also serves as an important check on the international consistency of independently developed optical clocks. This campaign demonstrates the exciting prospects for transportable optical clocks.The application of clocks in geodesy fulfils long-standing proposals to interpret a measurement of the fractional relativistic redshift Δνrel/ν0 to determine the gravity potential difference ΔU = c 2 Δνrel/ν0 between clocks at two sites (c being the speed of light). 12 National geodetic height systems based on classical terrestrial and satellite-based measurements exhibit discrepancies at the decimetre level. 17 Optical clocks, combined with high performance frequency dissemination techniques 18,19 offer an attractive way to resolve these discrepancies, as they combine the advantage of high spectral resolution with small error accumulation over long distances. 18,20 However, to achieve competitive capability requires high clock performance: a fractional frequency accuracy of 1×10 17 corresponds to a resolution of about 10 cm in height. Furthermore, it is important to realize that the sideby-side frequency ratio has to be known to determine the remote frequency shift Δνrel. Taking the uncertainty budgets of optical clocks for granted, harbours the possibility of errors, because very few have been verified experimentally to the low 10 17 region or beyond. 5,7,18,21 A transportable optical clock not only increases the flexibility in measurement sites but mitigates the risk of undetected errors by enabling local calibrations to be performed.The test site chosen for our demonstration of chronometric levelling 12 with optical clocks was the Laboratoire Souterrain de Modane (LSM) in France, with the Italian metrology institute INRIM in Torino serving as the reference site. The height difference between the two sites is approximately 1000 m, corresponding to a fractional redshift of about 10 -13 . From a geodetic point of view, LSM is a challenging and interesting location in which to perform such measurements: firstly, it is located in the middl...

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α| 1.1 × 10 −8 quantifying a violation of time dilation, thus improving by a factor of around two the best known constraint obtained with Ives-Stilwell type experiments, and by two orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this paper will improve by orders of magnitude in the near future.

Ultralow-noise yet tunable lasers are a revolutionary tool in precision spectroscopy, displacement measurements at the standard quantum limit, and the development of advanced optical atomic clocks. Further applications include lidar, coherent communications, frequency synthesis, and precision sensors of strain, motion, and temperature. While all applications benefit from lower frequency noise, many also require a laser that is robust and compact. Here, we introduce a dual-microcavity laser that leverages one chipintegrable silica microresonator to generate tunable 1550 nm laser light via stimulated Brillouin scattering (SBS) and a second microresonator for frequency stabilization of the SBS light. This configuration reduces the fractional frequency noise to 7.8 × 10 −14 1∕ p Hz at 10 Hz offset, which is a new regime of noise performance for a microresonator-based laser. Our system also features terahertz tunability and the potential for chip-level integration. We demonstrate the utility of our dual-microcavity laser by performing spectral linewidth measurements with hertz-level resolution.

We demonstrate thermometry with a resolution of 80 nK= ffiffiffiffiffiffi Hz p using an isotropic crystalline whispering-gallery mode resonator based on a dichroic dual-mode technique. We simultaneously excite two modes that have a mode frequency ratio that is very close to two (AE0.3 ppm). The wavelength and temperature dependence of the refractive index means that the frequency difference between these modes is an ultrasensitive proxy of the resonator temperature. This approach to temperature sensing automatically suppresses sensitivity to thermal expansion and vibrationally induced changes of the resonator. We also demonstrate active suppression of temperature fluctuations in the resonator by controlling the intensity of the driving laser. The residual temperature fluctuations are shown to be below the limits set by fundamental thermodynamic fluctuations of the resonator material. DOI: 10.1103/PhysRevLett.112.160801 PACS numbers: 07.20.Dt, 42.60.Da, 42.62.Fi The high-resolution measurement of energy has long fascinated humans with its culmination seen in ultra-highsensitivity calorimeters [1,2] and bolometers [3]. These and related ideas have found a broad range of applications, including bolometric superconducting photon counters for quantum communication [4] and ultrasensitive radio astronomy [5,6]. The record for absolute thermometric sensitivity has been realized at cryogenic temperatures, achieving better than 100 pK= ffiffiffiffiffiffi Hz p [7]. In this Letter, we develop a new method to measure temperature based on excitation of two well-separated modes in a millimeter-scale whispering-gallery (WG) optical resonator. WG mode resonators have exceptionally high Q factors and can provide the potential of providing high-stability microwave and optical signals [8][9][10][11][12]. Recently, they have been applied to high-sensitivity label-free sensors for molecules and viruses [13,14] and for optical comb generation [15]. Nonetheless, an issue that afflicts all of these applications is the high temperature sensitivity of WG resonators [12,16], particularly when compared to conventional vacuum-spaced Fabry-Perot resonators [17][18][19][20][21]. In this Letter, we turn this problem to our advantage by using the WG resonator as an ultrasensitive thermometer.To suppress unwanted temperature fluctuations in WG resonators, several groups have demonstrated in situ thermometry by measuring the frequency difference between two orthogonally polarized modes. The best of these techniques have demonstrated a resolution of ∼100 nK= ffiffiffiffiffiffi Hz p [22], and subsequent temperature stabilization based on this sensing has resulted in improvement to the long-term frequency stability [23,24]. In contrast, we present a two-color approach to measure the resonator temperature with high resolution. In comparison to the birefringent dual-mode technique, our approach can be used in both anisotropic and isotropic resonators, which expands the range of material candidates. Isotropic materials have shown the highest Q facto...

The most frequency--stable sources of electromagnetic radiation are produced optically, and optical frequency combs provide the means for high fidelity frequency transfer across hundreds of terahertz and into the microwave domain. A critical step in this photonic--based synthesis of microwave signals is the optical--to--electrical conversion process. Here we show that attosecond (as) timing stability can be preserved across the opto-electronic interface of a photodiode, despite an intrinsic temporal response that is more than six orders of magnitude slower. The excess timing noise in the photodetection of a periodic train of ultrashort optical pulses behaves as flicker noise (1/f) with amplitude of 4 as/√Hz at 1 Hz offset. The corresponding fractional frequency fluctuations are 1.4×10 --17 at 1 second and 5.5×10 --20 at 1000 seconds. These results demonstrate that direct photodetection, as part of frequency--comb-based microwave synthesis, can support the timing performance of the best optical frequency standards, and thereby opens the possibility for generating microwave signals with significantly better stability than any existing source.