We present an 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 $3.1(pm 3.9)times 10^{-20}$ 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 $4times 10^{-21}$ level after 16 days of integration and demonstrate that frequency comparison with instability as low as $8times 10^{-18}$ would be achievable with uni-directional fibers in urban area.
It is well known that temperature variations and acoustic noise affect ultrastable frequency dissemination along optical fiber. Active stabilization techniques are in general adopted to compensate for the fiber-induced phase noise. However, despite this compensation, the ultimate link performances remain limited by the so called delay-unsuppressed fiber noise that is related to the propagation delay of the light in the fiber. In this paper, we demonstrate a data post-processing approach which enables us to overcome this limit. We implement a subtraction algorithm between the optical signal delivered at the remote link end and the round-trip signal. In this way, a 6 dB improvement beyond the fundamental limit imposed by delay-unsuppressed noise is obtained. This result enhances the resolution of possible comparisons between remote optical clocks by a factor of 2. We confirm the theoretical prediction with experimental data obtained on a 47 km metropolitan fiber link, and propose how to extend this method for frequency dissemination purposes as well.
We measure the detection efficiency of single-photon detectors at wavelengths near 851 nm and 1533.6 nm. We investigate the spatial uniformity of one free-space-coupled single-photon avalanche diode and present a comparison between fusion-spliced and connectorized fiber-coupled single-photon detectors. We find that our expanded relative uncertainty for a single measurement of the detection efficiency is as low as 0.70 % for fiber-coupled measurements at 1533.6 nm and as high as 1.78 % for our free-space characterization at 851.7 nm. The detection-efficiency determination includes corrections for afterpulsing, dark count, and count-rate effects of the single-photon detector with the detection efficiency interpolated to operation at a specified detected count rate.
We present the first experimental demonstration over a 43-km-long urban fiber network of a local two-way optical frequency comparison, which does not require any synchronization of the measurements. It was combined with a regular active-noise compensation on another parallel fiber leading to a very reliable and robust frequency transfer. This hybrid scheme enables us to investigate the major limiting factors of the local two-way comparison. We analyze the contribution to the phase noise of the recovered signal by the interferometers at local and remote places. By using the ability of this set up to be injected by a single laser or two independent lasers, we measure the contribution to the long-term instability by the demodulated laser instabilities. We show that a fractional frequency instability level of $1times10^{-20}$ at 10 000 s can be obtained with this simple setup after 43-km-long propagation in an urban area.
We demonstrate a remote microwave/radio-frequency (RF) transfer technique based on the stabilization of a fiber link using a fiber-loop optical-microwave phase detector (FLOM-PD). This method compensates for the excess phase fluctuations introduced in fiber transfer by direct phase comparison between the optical pulse train reflected from the remote site and the local microwave/RF signal using the FLOM-PD. This enables sub-fs resolution and long-term stable link stabilization while having wide timing detection range and less demand in fiber dispersion compensation. The demonstrated relative frequency instability between 2.856-GHz RF oscillators separated by a 2.3-km fiber link is $7.6 times 10^{-18}$ and $6.5 times 10^{-19}$ at 1000 s and 82500 s averaging time, respectively.
We present the results of an operational use of experimentally measured optical tomograms to determine state characteristics (purity) avoiding any reconstruction of quasiprobabilities. We also develop a natural way how to estimate the errors (including both statistical and systematic ones) by an analysis of the experimental data themselves. Precision of the experiment can be increased by postselecting the data with minimal (systematic) errors. We demonstrate those techniques by considering coherent and photon-added coherent states measured via the time-domain improved homodyne detection. The operational use and precision of the data allowed us to check for the first time purity-dependent uncertainty relations and uncertainty relations for Shannon and R{e}nyi entropies.