Non-reciprocity in optical fiber links: experimental evidence.

Fundamental limits of fiber link are set by non-reciprocal effects that violate the hypothesis of equality between forward and backward path. Non-reciprocal noise arises technically from the set-up asymmetry, and fundamentally by the Sagnac effect when the fiber link encloses a non-zero area. As a pre-requisite for observation of Sagnac effect in fiber links, we present a study on phase noise and frequency stability contributions affecting coherent optical frequency transfer in bi-directional fiber links. Both technical and fundamental limitations of Two-Way optical frequency transfer are discussed. Our model predicts and our experiments substantially verify that the dominant noise mechanism at low Fourier frequencies is the polarization asymmetry induced by the temperature and relative humidity variations impacted on fiber links. The flicker noise floor due to the non-reciprocal noise arising from polarization mode dispersion is evidenced for the first time. We perform a post-processing approach which enables us to remove this polarization noise, improve the long-term stability and remove a frequency bias. We evaluate the uncertainty contributions of all the effects discussed for our 50 km spooled fiber link, dominated by its non-reciprocal noise induced by polarization mode dispersion with uncertainty of 1.9( ± 0.8)( ± 1.2) × 10-20. After correction, the linear drift of the residual phase is as low as 27 yoctosecond/s, leading to an uncertainty of the frequency transfer of 2.6 ( ± 39) × 10-22, confirming its potential for searching for more fundamental effects such as Sagnac effect or transient frequency variation due to dark matter.

Unidirectional two-way optical frequency comparison and its fundamental limitations.

High-quality frequency transfer based on existing telecommunication fiber links allows state-of-the-art microwave and optical clocks to be compared on a continental and potentially even intercontinental scale. We present a half-a-year-long data set of unidirectional optical frequency transfer over a 2×43km urban fiber link. We observe a relative frequency instability of 8.0×10-16 at 1 s and at best 6.0×10-18 at 106s integration time. Our results show that the unidirectional two-way method gives the possibility to perform comparisons of international primary standards over fiber links faster than over satellite links. Moreover, we investigate the major limiting factors of such a unidirectional setup.

Reciprocity of propagation in optical fiber links demonstrated to 10-21.

We present a study of the fundamental limit of fiber links using dedicated link architecture. We use an experimental arrangement that enables us to detect the forward and backward propagation noise independently and simultaneously in optical fiber and where the optical phase evolution is expected to be driven by the only contribution of the reference arms of the Michelson interferometer ensemble. In this article, we demonstrate indeed the high correlation between the optical phase evolution and the temperature variation of the interferometer ensemble, leading to a frequency offset of (4.4±2.3)×10-21. Using a simple temperature model and a Bayesian analysis to evaluate the model parameters, we show that the temperature effect can be compensated with post-processing, removing the frequency offset down to (0.5±2.0)×10-21. The residual slope of the optical phase evolution over 33 days is 350 yoctosecond/s. Using a global temperature parameter, we divide these 33 days dataset in four subsets and analyse their uncertainties. We show that they are self-consistent when the temperature is taken into account. This provides an alternative method to evaluate the accuracy of a fiber link, especially when the dataset includes large dead times. The result is finally interpreted as a test of the reciprocity of the propagation delay in an optical fiber. This unprecedented transfer capability could enable the comparisons of future optical clocks with expected performance at 10-20 level and open new possibilities for stringent tests of special and general relativity.

Studying the fundamental limit of optical fiber links to the 10-21 level.

We present a hybrid fiber link combining effective optical frequency transfer and evaluation of performances with a self-synchronized two-way comparison. It enables us to detect the round-trip fiber noise and each of the forward and backward one-way fiber noises simultaneously. The various signals acquired with this setup allow us to study quantitatively several properties of optical fiber links. We check the reciprocity of the accumulated noise forth and back over a bi-directional fiber to the level of 3.1(±3.9) × 10-20 based on a 160000s continuous data. We also analyze the noise correlation between two adjacent fibers and show the first experimental evidence of interferometric noise at very low Fourier frequency. We estimate redundantly and consistently the stability and accuracy of the transferred optical frequency over 43 km at 4 × 10-21 level after 16 days of integration and demonstrate that a frequency comparison with instability as low as 8 × 10-18 would be achievable with uni-directional fibers in urban area.

Cascaded optical fiber link using the internet network for remote clocks comparison.

We report a cascaded optical link of 1100 km for ultra-stable frequency distribution over an Internet fiber network. The link is composed of four spans for which the propagation noise is actively compensated. The robustness and the performance of the link are ensured by five fully automated optoelectronic stations, two of them at the link ends, and three deployed on the field and connecting the spans. This device coherently regenerates the optical signal with the heterodyne optical phase locking of a low-noise laser diode. Optical detection of the beat-note signals for the laser lock and the link noise compensation are obtained with stable and low-noise fibered optical interferometer. We show 3.5 days of continuous operation of the noise-compensated 4-span cascaded link leading to fractional frequency instability of 4x10(-16) at 1-s measurement time and 1x10(-19) at 2000 s. This cascaded link was extended to 1480-km with the same performance. This work is a significant step towards a sustainable wide area ultra-stable optical frequency distribution and comparison network at a very high level of performance.

Ultra-stable long distance optical frequency distribution using the Internet fiber network.

We report an optical link of 540 km for ultrastable frequency distribution over the Internet fiber network. The stable frequency optical signal is processed enabling uninterrupted propagation on both directions. The robustness and the performance of the link are enhanced by a cost effective fully automated optoelectronic station. This device is able to coherently regenerate the return optical signal with a heterodyne optical phase locking of a low noise laser diode. Moreover the incoming signal polarization variation are tracked and processed in order to maintain beat note amplitudes within the operation range. Stable fibered optical interferometer enables optical detection of the link round trip phase signal. The phase-noise compensated link shows a fractional frequency instability in 10 Hz bandwidth of 5 × 10(-15) at one second measurement time and 2 × 10(-19) at 30,000 s. This work is a significant step towards a sustainable wide area ultrastable optical frequency distribution and comparison network.

High resolution spectroscopy of methyltrioxorhenium: towards the observation of parity violation in chiral molecules.

Originating from the weak interaction, parity violation in chiral molecules has been considered as a possible origin of biohomochirality. We have proposed the observation of molecular parity violation using the two-photon Ramsey fringes technique on a supersonic beam. As a first step in this direction, a detailed spectroscopic study of methyltrioxorhenium (MTO) has been undertaken. It is an ideal test molecule as the achiral parent molecule of chiral candidates for a parity violation experiment. For the (187)Re MTO isotopologue, a combined analysis of Fourier transform microwave and infrared spectra as well as ultra-high resolution CO(2) laser absorption spectra enabled the assignment of 28 rotational lines and 71 rovibrational lines, some of them with a resolved hyperfine structure. A set of spectroscopic parameters in the ground and first excited state, including hyperfine structure constants, was obtained for the ν(as) antisymmetric Re=O stretching mode of this molecule. This result validates the experimental approach to be followed once a chiral derivative of MTO is synthesized, and shows the benefit of the combination of several spectroscopic techniques in different spectral regions, with different set-ups and resolutions. The first high resolution spectra of jet-cooled MTO, obtained on a set-up being developed for the observation of molecular parity violation, are shown, which constitutes a major step towards the targeted objective.

Progress toward the first observation of parity violation in chiral molecules by high-resolution laser spectroscopy.

Parity violation (PV) effects in chiral molecules have so far never been experimentally observed. To take up this challenge, a consortium of physicists, chemists, theoreticians, and spectroscopists has been established and aims at measuring PV energy differences between two enantiomers by using high-resolution laser spectroscopy. In this article, we present our common strategy to reach this goal, the progress accomplished in the diverse areas, and point out directions for future PV observations. The work of André Collet on bromochlorofluoromethane (1) enantiomers, their synthesis, and their chiral recognition by cryptophanes made feasible the first generation of experiments presented in this article.

Cascaded multiplexed optical link on a telecommunication network for frequency dissemination.

We demonstrate a cascaded optical link for ultrastable frequency dissemination comprised of two compensated links of 150 km and a repeater station. Each link includes 114 km of Internet fiber simultaneously carrying data traffic through a dense wavelength division multiplexing technology, and passes through two routing centers of the telecommunication network. The optical reference signal is inserted in and extracted from the communication network using bidirectional optical add-drop multiplexers. The repeater station operates autonomously ensuring noise compensation on the two links and the ultra-stable signal optical regeneration. The compensated link shows a fractional frequency instability of 3 x 10(-15) at one second measurement time and 5 x 10(-20) at 20 hours. This work paves the way to a wide dissemination of ultra-stable optical clock signals between distant laboratories via the Internet network.

High-resolution optical frequency dissemination on a telecommunications network with data traffic.

We transferred the frequency of an ultrastable laser over a 108-km-long urban fiber link comprising 22 km of an optical communications network fiber simultaneously carrying Internet data traffic. The metrological signal and the digital data signal were transferred over two different frequency channels in a dense wavelength-division multiplexing scheme. The metrological signal was inserted in and extracted from the communication network using bidirectional off-the-shelf optical add-drop multiplexers. The link-induced phase noise was measured and canceled with a round-trip technique using an all-fiber-based interferometer. The compensated link showed an Allan deviation of a few 10(-16) at 1 s and below 10(-19) at 10,000 s. This work paves the way to a wide dissemination of ultrastable optical clock signals between distant laboratories via the Internet.

Absolute frequency measurement of a SF6 two-photon line by use of a femtosecond optical comb and sum-frequency generation.

We demonstrate a new, simple technique for measuring IR frequencies near 30 THz by using a femtosecond (fs) laser optical comb and sum-frequency generation. The optical frequency is directly compared with the distance between two modes of the fs laser, and the resultant beat note is used to control this distance, which depends only on the repetition rate of the fs laser. The absolute frequency of a CO2 laser stabilized onto a SF6 two-photon line has been measured for the first time to the authors' knowledge. This line is an attractive alternative to the usual saturated absorption OsO4 resonances used for the stabilization of CO2 lasers. First results demonstrate a fractional Allan deviation of 3 x 10(-14) at 1 s.